{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_4998/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_4998","id":"gutenberg_4998","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/4998","summary":null,"tags":["Category: Art","Category: Essays, Letters & Speeches","Category: Philosophy & Ethics","Leonardo, da Vinci, 1452-1519 -- Notebooks, sketchbooks, etc."],"text":"This eBook was produced by Charles Aldarondo and the Distributed\nProofreaders team.\n\n\n\nThe Notebooks of Leonardo Da Vinci\n\nVolume 1\n\nTranslated by Jean Paul Richter\n\n1888\n\n\n\n\n\n\nPREFACE.\n\n\n\n\n\nA singular fatality has ruled the destiny of nearly all the most\nfamous of Leonardo da Vinci's works. Two of the three most important\nwere never completed, obstacles having arisen during his life-time,\nwhich obliged him to leave them unfinished; namely the Sforza\nMonument and the Wall-painting of the Battle of Anghiari, while the\nthird--the picture of the Last Supper at Milan--has suffered\nirremediable injury from decay and the repeated restorations to\nwhich it was recklessly subjected during the XVIIth and XVIIIth\ncenturies. Nevertheless, no other picture of the Renaissance has\nbecome so wellknown and popular through copies of every description.\n\nVasari says, and rightly, in his Life of Leonardo, \"that he laboured\nmuch more by his word than in fact or by deed\", and the biographer\nevidently had in his mind the numerous works in Manuscript which\nhave been preserved to this day. To us, now, it seems almost\ninexplicable that these valuable and interesting original texts\nshould have remained so long unpublished, and indeed forgotten. It\nis certain that during the XVIth and XVIIth centuries their\nexceptional value was highly appreciated. This is proved not merely\nby the prices which they commanded, but also by the exceptional\ninterest which has been attached to the change of ownership of\nmerely a few pages of Manuscript.\n\nThat, notwithstanding this eagerness to possess the Manuscripts,\ntheir contents remained a mystery, can only be accounted for by the\nmany and great difficulties attending the task of deciphering them.\nThe handwriting is so peculiar that it requires considerable\npractice to read even a few detached phrases, much more to solve\nwith any certainty the numerous difficulties of alternative\nreadings, and to master the sense as a connected whole. Vasari\nobserves with reference to Leonardos writing: \"he wrote backwards,\nin rude characters, and with the left hand, so that any one who is\nnot practised in reading them, cannot understand them\". The aid of a\nmirror in reading reversed handwriting appears to me available only\nfor a first experimental reading. Speaking from my own experience,\nthe persistent use of it is too fatiguing and inconvenient to be\npractically advisable, considering the enormous mass of Manuscripts\nto be deciphered. And as, after all, Leonardo's handwriting runs\nbackwards just as all Oriental character runs backwards--that is\nto say from right to left--the difficulty of reading direct from the\nwriting is not insuperable. This obvious peculiarity in the writing\nis not, however, by any means the only obstacle in the way of\nmastering the text. Leonardo made use of an orthography peculiar to\nhimself; he had a fashion of amalgamating several short words into\none long one, or, again, he would quite arbitrarily divide a long\nword into two separate halves; added to this there is no punctuation\nwhatever to regulate the division and construction of the sentences,\nnor are there any accents--and the reader may imagine that such\ndifficulties were almost sufficient to make the task seem a\ndesperate one to a beginner. It is therefore not surprising that the\ngood intentions of some of Leonardo s most reverent admirers should\nhave failed.\n\nLeonardos literary labours in various departments both of Art and of\nScience were those essentially of an enquirer, hence the analytical\nmethod is that which he employs in arguing out his investigations\nand dissertations. The vast structure of his scientific theories is\nconsequently built up of numerous separate researches, and it is\nmuch to be lamented that he should never have collated and arranged\nthem. His love for detailed research--as it seems to me--was the\nreason that in almost all the Manuscripts, the different paragraphs\nappear to us to be in utter confusion; on one and the same page,\nobservations on the most dissimilar subjects follow each other\nwithout any connection. A page, for instance, will begin with some\nprinciples of astronomy, or the motion of the earth; then come the\nlaws of sound, and finally some precepts as to colour. Another page\nwill begin with his investigations on the structure of the\nintestines, and end with philosophical remarks as to the relations\nof poetry to painting; and so forth.\n\nLeonardo himself lamented this confusion, and for that reason I do\nnot think that the publication of the texts in the order in which\nthey occur in the originals would at all fulfil his intentions. No\nreader could find his way through such a labyrinth; Leonardo himself\ncould not have done it.\n\nAdded to this, more than half of the five thousand manuscript pages\nwhich now remain to us, are written on loose leaves, and at present\narranged in a manner which has no justification beyond the fancy of\nthe collector who first brought them together to make volumes of\nmore or less extent. Nay, even in the volumes, the pages of which\nwere numbered by Leonardo himself, their order, so far as the\nconnection of the texts was concerned, was obviously a matter of\nindifference to him. The only point he seems to have kept in view,\nwhen first writing down his notes, was that each observation should\nbe complete to the end on the page on which it was begun. The\nexceptions to this rule are extremely few, and it is certainly\nnoteworthy that we find in such cases, in bound volumes with his\nnumbered pages, the written observations: \"turn over\", \"This is the\ncontinuation of the previous page\", and the like. Is not this\nsufficient to prove that it was only in quite exceptional cases that\nthe writer intended the consecutive pages to remain connected, when\nhe should, at last, carry out the often planned arrangement of his\nwritings?\n\nWhat this final arrangement was to be, Leonardo has in most cases\nindicated with considerable completeness. In other cases this\nauthoritative clue is wanting, but the difficulties arising from\nthis are not insuperable; for, as the subject of the separate\nparagraphs is always distinct and well defined in itself, it is\nquite possible to construct a well-planned whole, out of the\nscattered materials of his scientific system, and I may venture to\nstate that I have devoted especial care and thought to the due\nexecution of this responsible task.\n\nThe beginning of Leonardo's literary labours dates from about his\nthirty-seventh year, and he seems to have carried them on without\nany serious interruption till his death. Thus the Manuscripts that\nremain represent a period of about thirty years. Within this space\nof time his handwriting altered so little that it is impossible to\njudge from it of the date of any particular text. The exact dates,\nindeed, can only be assigned to certain note-books in which the year\nis incidentally indicated, and in which the order of the leaves has\nnot been altered since Leonardo used them. The assistance these\nafford for a chronological arrangement of the Manuscripts is\ngenerally self evident. By this clue I have assigned to the original\nManuscripts now scattered through England, Italy and France, the\norder of their production, as in many matters of detail it is highly\nimportant to be able to verify the time and place at which certain\nobservations were made and registered. For this purpose the\nBibliography of the Manuscripts given at the end of Vol. II, may be\nregarded as an Index, not far short of complete, of all Leonardo s\nliterary works now extant. The consecutive numbers (from 1 to 1566)\nat the head of each passage in this work, indicate their logical\nsequence with reference to the subjects; while the letters and\nfigures to the left of each paragraph refer to the original\nManuscript and number of the page, on which that particular passage\nis to be found. Thus the reader, by referring to the List of\nManuscripts at the beginning of Volume I, and to the Bibliography at\nthe end of Volume II, can, in every instance, easily ascertain, not\nmerely the period to which the passage belongs, but also exactly\nwhere it stood in the original document. Thus, too, by following the\nsequence of the numbers in the Bibliographical index, the reader may\nreconstruct the original order of the Manuscripts and recompose the\nvarious texts to be found on the original sheets--so much of it,\nthat is to say, as by its subject-matter came within the scope of\nthis work. It may, however, be here observed that Leonardo s\nManuscripts contain, besides the passages here printed, a great\nnumber of notes and dissertations on Mechanics, Physics, and some\nother subjects, many of which could only be satisfactorily dealt\nwith by specialists. I have given as complete a review of these\nwritings as seemed necessary in the Bibliographical notes.\n\nIn 1651, Raphael Trichet Dufresne, of Paris, published a selection\nfrom Leonardo's writings on painting, and this treatise became so\npopular that it has since been reprinted about two-and-twenty times,\nand in six different languages. But none of these editions were\nderived from the original texts, which were supposed to have been\nlost, but from early copies, in which Leonardo's text had been more\nor less mutilated, and which were all fragmentary. The oldest and on\nthe whole the best copy of Leonardo's essays and precepts on\nPainting is in the Vatican Library; this has been twice printed,\nfirst by Manzi, in 1817, and secondly by Ludwig, in 1882. Still,\nthis ancient copy, and the published editions of it, contain much\nfor which it would be rash to hold Leonardo responsible, and some\nportions--such as the very important rules for the proportions of\nthe human figure--are wholly wanting; on the other hand they contain\npassages which, if they are genuine, cannot now be verified from any\noriginal Manuscript extant. These copies, at any rate neither give\nus the original order of the texts, as written by Leonardo, nor do\nthey afford any substitute, by connecting them on a rational scheme;\nindeed, in their chaotic confusion they are anything rather than\nsatisfactory reading. The fault, no doubt, rests with the compiler\nof the Vatican copy, which would seem to be the source whence all\nthe published and extensively known texts were derived; for, instead\nof arranging the passages himself, he was satisfied with recording a\nsuggestion for a final arrangement of them into eight distinct\nparts, without attempting to carry out his scheme. Under the\nmistaken idea that this plan of distribution might be that, not of\nthe compiler, but of Leonardo himself, the various editors, down to\nthe present day, have very injudiciously continued to adopt this\norder--or rather disorder.\n\nI, like other enquirers, had given up the original Manuscript of the\nTrattato della Pittura for lost, till, in the beginning of 1880, I\nwas enabled, by the liberality of Lord Ashburnham, to inspect his\nManuscripts, and was so happy as to discover among them the original\ntext of the best-known portion of the Trattato in his magnificent\nlibrary at Ashburnham Place. Though this discovery was of a fragment\nonly--but a considerable fragment--inciting me to further search,\nit gave the key to the mystery which had so long enveloped the first\norigin of all the known copies of the Trattato. The extensive\nresearches I was subsequently enabled to prosecute, and the results\nof which are combined in this work, were only rendered possible by\nthe unrestricted permission granted me to investigate all the\nManuscripts by Leonardo dispersed throughout Europe, and to\nreproduce the highly important original sketches they contain, by\nthe process of \"photogravure\". Her Majesty the Queen graciously\naccorded me special permission to copy for publication the\nManuscripts at the Royal Library at Windsor. The Commission Centrale\nAdministrative de l'Institut de France, Paris, gave me, in the most\nliberal manner, in answer to an application from Sir Frederic\nLeighton, P. R. A., Corresponding member of the Institut, free\npermission to work for several months in their private collection at\ndeciphering the Manuscripts preserved there. The same favour which\nLord Ashburnham had already granted me was extended to me by the\nEarl of Leicester, the Marchese Trivulsi, and the Curators of the\nAmbrosian Library at Milan, by the Conte Manzoni at Rome and by\nother private owners of Manuscripts of Leonardo's; as also by the\nDirectors of the Louvre at Paris; the Accademia at Venice; the\nUffizi at Florence; the Royal Library at Turin; and the British\nMuseum, and the South Kensington Museum. I am also greatly indebted\nto the Librarians of these various collections for much assistance\nin my labours; and more particularly to Monsieur Louis Lalanne, of\nthe Institut de France, the Abbate Ceriani, of the Ambrosian\nLibrary, Mr. Maude Thompson, Keeper of Manuscripts at the British\nMuseum, Mr. Holmes, the Queens Librarian at Windsor, the Revd Vere\nBayne, Librarian of Christ Church College at Oxford, and the Revd A.\nNapier, Librarian to the Earl of Leicester at Holkham Hall.\n\nIn correcting the Italian text for the press, I have had the\nadvantage of valuable advice from the Commendatore Giov. Morelli,\nSenatore del Regno, and from Signor Gustavo Frizzoni, of Milan. The\ntranslation, under many difficulties, of the Italian text into\nEnglish, is mainly due to Mrs. R. C. Bell; while the rendering of\nseveral of the most puzzling and important passages, particularly in\nthe second half of Vol. I, I owe to the indefatigable interest taken\nin this work by Mr. E. J. Poynter R. A. Finally I must express my\nthanks to Mr. Alfred Marks, of Long Ditton, who has most kindly\nassisted me throughout in the revision of the proof sheets.\n\nThe notes and dissertations on the texts on Architecture in Vol. II\nI owe to my friend Baron Henri de Geymuller, of Paris.\n\nI may further mention with regard to the illustrations, that the\nnegatives for the production of the \"photo-gravures\" by Monsieur\nDujardin of Paris were all taken direct from the originals.\n\nIt is scarcely necessary to add that most of the drawings here\nreproduced in facsimile have never been published before. As I am\nnow, on the termination of a work of several years' duration, in a\nposition to review the general tenour of Leonardos writings, I may\nperhaps be permitted to add a word as to my own estimate of the\nvalue of their contents. I have already shown that it is due to\nnothing but a fortuitous succession of unfortunate circumstances,\nthat we should not, long since, have known Leonardo, not merely as a\nPainter, but as an Author, a Philosopher, and a Naturalist. There\ncan be no doubt that in more than one department his principles and\ndiscoveries were infinitely more in accord with the teachings of\nmodern science, than with the views of his contemporaries. For this\nreason his extraordinary gifts and merits are far more likely to be\nappreciated in our own time than they could have been during the\npreceding centuries. He has been unjustly accused of having\nsquandered his powers, by beginning a variety of studies and then,\nhaving hardly begun, throwing them aside. The truth is that the\nlabours of three centuries have hardly sufficed for the elucidation\nof some of the problems which occupied his mighty mind.\n\nAlexander von Humboldt has borne witness that \"he was the first to\nstart on the road towards the point where all the impressions of our\nsenses converge in the idea of the Unity of Nature\" Nay, yet more\nmay be said. The very words which are inscribed on the monument of\nAlexander von Humboldt himself, at Berlin, are perhaps the most\nappropriate in which we can sum up our estimate of Leonardo's\ngenius:\n\n\"Majestati naturae par ingenium.\"\n\nLONDON, April 1883.\n\nF. P. R.\n\n\n\n\n\n\n\nCONTENTS OF VOLUME I.\n\n\n\n\n\nPROLEGOMENA AND GENERAL INTRODUCTION TO THE BOOK ON PAINTING\n\nClavis Sigillorum and Index of Manuscripts.--The author's intention\nto publish his MSS. (1).--The preparation of the MSS. for\npublication (2).--Admonition to readers (3).--The disorder in the\nMSS. (4).--Suggestions for the arrangement of MSS. treating of\nparticular subjects (5--8).--General introductions to the book on\npainting (9--13).--The plan of the book on painting (14--17).--The\nuse of the book on painting (18).--Necessity of theoretical\nknowledge (19, 20).--The function of the eye (21--23).--Variability\nof the eye (24).--Focus of sight (25).--Differences of perception by\none eye and by both eyes (26--29).--The comparative size of the\nimage depends on the amount of light (30--39).\n\nII.\n\nLINEAR PERSPECTIVE\n\nGeneral remarks on perspective (40--41).--The elements of\nperspective:--of the point (42--46).--Of the line (47--48).--The\nnature of the outline (49).--Definition of perspective (50).--The\nperception of the object depends on the direction of the eye\n(51).--Experimental proof of the existence of the pyramid of sight\n(52--55).--The relations of the distance point to the vanishing\npoint (55--56).--How to measure the pyramid of vision (57).--The\nproduction of the pyramid of vision (58--64).--Proof by experiment\n(65--66).--General conclusions (67).--That the contrary is\nimpossible (68).--A parallel case (69).--The function of the eye, as\nexplained by the camera obscura (70--71).--The practice of\nperspective (72--73).--Refraction of the rays falling upon the eye\n(74--75).--The inversion of the images (76).--The intersection of\nthe rays (77--82).--Demonstration of perspective by means of a\nvertical glass plane (83--85.)--The angle of sight varies with the\ndistance (86--88).--Opposite pyramids in juxtaposition (89).--On\nsimple and complex perspective (90).--The proper distance of objects\nfrom the eye (91--92).--The relative size of objects with regard to\ntheir distance from the eye (93--98).--The apparent size of objects\ndenned by calculation (99--106).--On natural perspective (107--109).\n\nIII.\n\nSIX BOOKS ON LIGHT AND SHADE\n\nGENERAL INTRODUCTION.--Prolegomena (110).--Scheme of the books on\nlight and shade (111).--Different principles and plans of treatment\n(112--116).--Different sorts of light (117--118).--Definition of\nthe nature of shadows (119--122).--Of the various kinds of shadows\n(123--125).--Of the various kinds of light (126--127).--General\nremarks (128--129).--FIRST BOOK ON LIGHT AND SHADE.--On the nature\nof light (130--131).--The difference between light and lustre\n(132--135).--The relations of luminous to illuminated bodies (136).\n--Experiments on the relation of light and shadow within a room\n(137--140).--Light and shadow with regard to the position of the\neye (141--145).--The law of the incidence of light\n(146--147).--SECOND BOOK ON LIGHT AND SHADE.--Gradations of strength\nin the shadows (148--149).--On the intensity of shadows as dependent\non the distance from the light (150--152).--On the proportion of\nlight and shadow (153--157).--THIRD BOOK ON LIGHT AND\nSHADE.--Definition of derived shadow (158--159).--Different sorts of\nderived shadows (160--162).--On the relation of derived and primary\nshadow (163--165).--On the shape of derived shadows (166--174).--On\nthe relative intensity of derived shadows (175--179).--Shadow as\nproduced by two lights of different size (180--181).--The effect of\nlight at different distances (182).--Further complications in the\nderived shadows (183--187).--FOURTH BOOK ON LIGHT AND SHADE.--On the\nshape of cast shadows (188--191).--On the outlines of cast shadows\n(192--195).--On the relative size of cast shadows (196.\n197).--Effects on cast shadows by the tone of the back ground\n(198).--A disputed proposition (199).--On the relative depth of\ncast shadows (200--202).--FIFTH BOOK ON LIGHT AND\nSHADE.--Principles of reflection (203. 204).--On reverberation\n(205).--Reflection on water (206. 207).--Experiments with the mirror\n(208--210).--Appendix:--On shadows in movement (211--212).--SIXTH\nBOOK ON LIGHT AND SHADE.--The effect of rays passing through holes\n(213. 214).--On gradation of shadows (215. 216).--On relative\nproportion of light and shadows (216--221).\n\nIV.\n\nPERSPECTIVE OF DISAPPEARANCE\n\nDefinition (222. 223).--An illustration by experiment (224).--A\nguiding rule (225).---An experiment (226).--On indistinctness at\nshort distances (227--231).--On indistinctness at great distances\n(232--234).--The importance of light and shade in the Prospettiva\nde' perdimenti (235--239).--The effect of light or dark backgrounds\non the apparent size of objects (240--250).--Propositions on\nProspettiva de' perdimenti from MS. C. (250--262).\n\nV.\n\nTHEORY OF COLOURS\n\nThe reciprocal effects of colours on objects placed opposite each\nother (263--271).--Combination of different colours in cast shadows\n(272).--The effect of colours in the camera obscura (273. 274).--On\nthe colours of derived shadows (275. 276).--On the nature of colours\n(277. 278).--On gradations in the depth of colours (279. 280).--On\nthe reflection of colours (281--283).--On the use of dark and light\ncolours in painting (284--286).--On the colours of the rainbow\n(287--288).\n\nVI.\n\nPERSPECTIVE OF COLOUR AND AERIAL PERSPECTIVE\n\nGeneral rules (289--291).--An exceptional case (292).--An experiment\n(293).--The practice of the Prospettiva de' colori (294).--The rules\nof aerial perspective (295--297).--On the relative density of the\natmosphere (298--299).--On the colour of the atmosphere (300--307).\n\nVII.\n\nON THE PROPORTIONS AND ON THE MOVEMENTS OF THE HUMAN FIGURE\n\nPreliminary observations (308. 309).--Proportions of the head and\nface (310--318).--Proportions of the head seen in front\n(319--321).--Proportions of the foot (322--323).--Relative\nproportions of the hand and foot (324).--Relative proportions of\nthe foot and of the face (325--327).--Proportions of the leg\n(328--331).--On the central point of the whole body (332).--The\nrelative proportions of the torso and of the whole figure\n(333).--The relative proportions of the head and of the torso\n(334).--The relative proportions of the torso and of the leg (335.\n336).--The relative proportions of the torso and of the foot\n(337).--The proportions of the whole figure (338--341).--The torso\nfrom the front and back (342).--Vitruvius' scheme of proportions\n(343).--The arm and head (344).--Proportions of the arm\n(345--349).--The movement of the arm (350--354).--The movement of\nthe torso (355--361).--The proportions vary at different ages\n(362--367).--The movement of the human figure (368--375).--Of\nwalking up and down (375--379).--On the human body in action\n(380--388).--On hair falling down in curls (389).--On draperies\n\n(390--392).\n\nVIII.\n\nBOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING\n\nClassification of trees (393).--The relative thickness of the\nbranches to the trunk (394--396).--The law of proportion in the\ngrowth of the branches (397--402).--The direction of growth\n(403--407).--The forms of trees (408--411).--The insertion of the\nleaves (412--419).--Light on branches and leaves (420--422).--The\nproportions of light and shade in a leaf (423--426).--Of the\ntransparency of leaves (427--429).--The gradations of shade and\ncolour in leaves (430--434).--A classification of trees according to\ntheir colours (435).--The proportions of light and shade in trees\n(436--440).--The distribution of light and shade with reference to\nthe position of the spectator (441--443).--The effects of morning\nlight (444--448).--The effects of midday light (449).--The\nappearance of trees in the distance (450--451).--The cast shadow of\ntrees (452. 453).--Light and shade on groups of trees\n(454--457).--On the treatment of light for landscapes\n(458--464).--On the treatment of light for views of towns\n(465--469).--The effect of wind on trees (470--473).--Light and\nshade on clouds (474--477).--On images reflected in water (478).--Of\nrainbows and rain (479. 480).--Of flower seeds (481).\n\nIX.\n\nTHE PRACTICE OF PAINTING\n\nI. MORAL PRECEPTS FOR THE STUDENT OF PAINTING.--How to ascertain the\ndispositions for an artistic career (482).--The course of\ninstruction for an artist (483--485).--The study of the antique\n(486. 487).--The necessity of anatomical knowledge (488. 489).--How\nto acquire practice (490).--Industry and thoroughness the first\nconditions (491--493.)--The artist's private life and choice of\ncompany (493. 494).--The distribution of time for studying (495--\n497).--On the productive power of minor artists (498--501).--A\ncaution against one-sided study (502).--How to acquire universality\n(503--506).--Useful games and exercises (507. 508).--II. THE\nARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF\nPERSPECTIVE.--ON JUDGING OF A PICTURE.--On the size of the studio\n(509).--On the construction of windows (510--512).--On the best\nlight for painting (513--520).--On various helps in preparing a\npicture (521--530).--On the management of works (531. 532).--On the\nlimitations of painting (533--535).--On the choice of a position\n(536. 537).--The apparent size of figures in a picture (538.\n539).--The right position of the artist, when painting and of the\nspectator (540--547).--III. THE PRACTICAL METHODS OF LIGHT AND SHADE\nAND AERIAL PERSPECTIVE.--Gradations of light and shade (548).--On\nthe choice of light for a picture (549--554).--The distribution of\nlight and shade (555--559).--The juxtaposition of light and shade\n(560. 561).--On the lighting of the background (562--565).--On the\nlighting of white objects (566).--The methods of aerial perspective\n(567--570).--IV. OF PORTRAIT AND FIGURE PAINTING.--Of sketching\nfigures and portraits (571. 572).--The position of the head\n(573).--Of the light on the face (574--576).--General suggestions\nfor historical pictures (577--581).--How to represent the\ndifferences of age and sex (582. 583).--Of representing the emotions\n(584).--Of representing imaginary animals (585).--The selection of\nforms (586--591).--How to pose figures (592).--Of appropriate\ngestures (593--600).--V. SUGGESTIONS FOR COMPOSITIONS.--Of painting\nbattle-pieces (601--603).--Of depicting night-scenes (604).--Of\ndepicting a tempest (605. 606).--Of representing the deluge\n(607--609).--Of depicting natural phenomena (610. 611).--VI. THE\nARTIST'S MATERIALS.--Of chalk and paper (612--617).--On the\npreparation and use of colours (618--627).--Of preparing the panel\n(628).--The preparation of oils (629--634).--On varnishes (635--\n637).--On chemical _materials (638--650).--VII. PHILOSOPHY AND\nHISTORY OF THE ART OF PAINTING.--The relation of art and nature\n(651. 652).--Painting is superior to poetry (653. 654).--Painting is\nsuperior to sculpture (655. 656).--Aphorisms (657--659).--On the\nhistory of painting (660. 661).--The painter's scope (662).\n\nX.\n\nSTUDIES AND SKETCHES FOR PICTURES AND DECORATIONS\n\nOn pictures of the Madonna (663).--Bernardo di Bandino's portrait\n(664).--Notes on the Last Supper (665--668).--On the battle of\nAnghiari (669).--Allegorical representations referring to the duke\nof Milan (670--673).--Allegorical representations\n(674--678).--Arrangement of a picture (679).--List of drawings\n(680).--Mottoes and Emblems (681--702).\n\n\n\n\n\n\nThe author's intention to publish his MSS.\n\n1.\n\nHow by a certain machine many may stay some time under water. And\nhow and wherefore I do not describe my method of remaining under\nwater and how long I can remain without eating. And I do not publish\nnor divulge these, by reason of the evil nature of men, who would\nuse them for assassinations at the bottom of the sea by destroying\nships, and sinking them, together with the men in them. Nevertheless\nI will impart others, which are not dangerous because the mouth of\nthe tube through which you breathe is above the water, supported on\nair sacks or cork.\n\n[Footnote: The leaf on which this passage is written, is headed with\nthe words _Casi_ 39, and most of these cases begin with the word\n'_Come_', like the two here given, which are the 26th and 27th. 7.\n_Sughero_. In the Codex Antlanticus 377a; 1170a there is a sketch,\ndrawn with the pen, representing a man with a tube in his mouth, and\nat the farther end of the tube a disk. By the tube the word\n'_Channa_' is written, and by the disk the word '_sughero_'.]\n\nThe preparation of the MSS. for publication.\n\n2.\n\nWhen you put together the science of the motions of water, remember\nto include under each proposition its application and use, in order\nthat this science may not be useless.--\n\n[Footnote: A comparatively small portion of Leonardo's notes on\nwater-power was published at Bologna in 1828, under the title: \"_Del\nmoto e misura dell'Acqua, di L. da Vinci_\".]\n\nAdmonition to readers.\n\n3.\n\nLet no man who is not a Mathematician read the elements of my work.\n\nThe disorder in the MSS.\n\n4.\n\nBegun at Florence, in the house of Piero di Braccio Martelli, on the\n22nd day of March 1508. And this is to be a collection without\norder, taken from many papers which I have copied here, hoping to\narrange them later each in its place, according to the subjects of\nwhich they may treat. But I believe that before I am at the end of\nthis [task] I shall have to repeat the same things several times;\nfor which, O reader! do not blame me, for the subjects are many and\nmemory cannot retain them [all] and say: 'I will not write this\nbecause I wrote it before.' And if I wished to avoid falling into\nthis fault, it would be necessary in every case when I wanted to\ncopy [a passage] that, not to repeat myself, I should read over all\nthat had gone before; and all the more since the intervals are long\nbetween one time of writing and the next.\n\n[Footnote: 1. In the history of Florence in the early part of the\nXVIth century _Piero di Braccio Martelli_ is frequently mentioned as\n_Commissario della Signoria_. He was famous for his learning and at\nhis death left four books on Mathematics ready for the press; comp.\nLITTA, _Famiglie celebri Italiane_, _Famiglia Martelli di\nFirenze_.--In the Official Catalogue of MSS. in the Brit. Mus., New\nSeries Vol. I., where this passage is printed, _Barto_ has been\nwrongly given for Braccio.\n\n2. _addi 22 di marzo 1508_. The Christian era was computed in\nFlorence at that time from the Incarnation (Lady day, March 25th).\nHence this should be 1509 by our reckoning.\n\n3. _racolto tratto di molte carte le quali io ho qui copiate_. We\nmust suppose that Leonardo means that he has copied out his own MSS.\nand not those of others. The first thirteen leaves of the MS. in the\nBrit. Mus. are a fair copy of some notes on physics.]\n\nSuggestions for the arrangement of MSS treating of particular\nsubjects.(5-8).\n\n5.\n\nOf digging a canal. Put this in the Book of useful inventions and in\nproving them bring forward the propositions already proved. And this\nis the proper order; since if you wished to show the usefulness of\nany plan you would be obliged again to devise new machines to prove\nits utility and thus would confuse the order of the forty Books and\nalso the order of the diagrams; that is to say you would have to mix\nup practice with theory, which would produce a confused and\nincoherent work.\n\n6.\n\nI am not to blame for putting forward, in the course of my work on\nscience, any general rule derived from a previous conclusion.\n\n7.\n\nThe Book of the science of Mechanics must precede the Book of useful\ninventions.--Have your books on anatomy bound! [Footnote: 4. The\nnumerous notes on anatomy written on loose leaves and now in the\nRoyal collection at Windsor can best be classified in four Books,\ncorresponding to the different character and size of the paper. When\nLeonardo speaks of '_li tua libri di notomia_', he probably means\nthe MSS. which still exist; if this hypothesis is correct the\npresent condition of these leaves might seem to prove that he only\ncarried out his purpose with one of the Books on anatomy. A borrowed\nbook on Anatomy is mentioned in F.O.]\n\n8.\n\nThe order of your book must proceed on this plan: first simple\nbeams, then (those) supported from below, then suspended in part,\nthen wholly [suspended]. Then beams as supporting other weights\n[Footnote: 4. Leonardo's notes on Mechanics are extraordinarily\nnumerous; but, for the reasons assigned in my introduction, they\nhave not been included in the present work.].\n\nGeneral introductions to the book on Painting (9-13).\n\n9.\n\nINTRODUCTION.\n\nSeeing that I can find no subject specially useful or\npleasing--since the men who have come before me have taken for their\nown every useful or necessary theme--I must do like one who, being\npoor, comes last to the fair, and can find no other way of providing\nhimself than by taking all the things already seen by other buyers,\nand not taken but refused by reason of their lesser value. I, then,\nwill load my humble pack with this despised and rejected\nmerchandise, the refuse of so many buyers; and will go about to\ndistribute it, not indeed in great cities, but in the poorer towns,\ntaking such a price as the wares I offer may be worth. [Footnote: It\nneed hardly be pointed out that there is in this 'Proemio' a covert\nirony. In the second and third prefaces, Leonardo characterises his\nrivals and opponents more closely. His protest is directed against\nNeo-latinism as professed by most of the humanists of his time; its\nfutility is now no longer questioned.]\n\n10.\n\nINTRODUCTION.\n\nI know that many will call this useless work [Footnote: 3. questa\nessere opera inutile. By opera we must here understand libro di\npittura and particularly the treatise on Perspective.]; and they\nwill be those of whom Demetrius [Footnote: 4. Demetrio. \"With regard\nto the passage attributed to Demetrius\", Dr. H. M\u00dcLLER STR\u00dcBING\nwrites, \"I know not what to make of it. It is certainly not\nDemetrius Phalereus that is meant and it can hardly be Demetrius\nPoliorcetes. Who then can it be--for the name is a very common one?\nIt may be a clerical error for Demades and the maxim is quite in the\nspirit of his writings I have not however been able to find any\ncorresponding passage either in the 'Fragments' (C. MULLER, _Orat.\nAtt._, II. 441) nor in the Supplements collected by DIETZ (_Rhein.\nMus._, vol. 29, p. 108).\"\n\nThe same passage occurs as a simple Memorandum in the MS. Tr. 57,\napparently as a note for this '_Proemio_' thus affording some data\nas to the time where these introductions were written.] declared\nthat he took no more account of the wind that came out their mouth\nin words, than of that they expelled from their lower parts: men who\ndesire nothing but material riches and are absolutely devoid of that\nof wisdom, which is the food and the only true riches of the mind.\nFor so much more worthy as the soul is than the body, so much more\nnoble are the possessions of the soul than those of the body. And\noften, when I see one of these men take this work in his hand, I\nwonder that he does not put it to his nose, like a monkey, or ask me\nif it is something good to eat.\n\n[Footnote: In the original, the Proemio d\u00ec prospettiva cio\u00e8\ndell'uffitio dell'occhio (see No. 21) stands between this and the\npreceding one, No. 9.]\n\nINTRODUCTION.\n\nI am fully concious that, not being a literary man, certain\npresumptuous persons will think that they may reasonably blame me;\nalleging that I am not a man of letters. Foolish folks! do they not\nknow that I might retort as Marius did to the Roman Patricians\n[Footnote 21: _Come Mario disse ai patriti Romani_. \"I am unable to\nfind the words here attributed by Leonardo to Marius, either in\nPlutarch's Life of Marius or in the Apophthegmata (_Moralia_,\np.202). Nor do they occur in the writings of Valerius Maximus (who\nfrequently mentions Marius) nor in Velleius Paterculus (II, 11 to\n43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E.\nMENDELSON of Dorpat, the editor of Herodian, assures me that no such\npassage is the found in that author\" (communication from Dr. MULLER\nSTRUBING). Leonardo evidently meant to allude to some well known\nincident in Roman history and the mention of Marius is the result\nprobably of some confusion. We may perhaps read, for Marius,\nMenenius Agrippa, though in that case it is true we must alter\nPatriti to Plebei. The change is a serious one. but it would render\nthe passage perfectly clear.] by saying: That they, who deck\nthemselves out in the labours of others will not allow me my own.\nThey will say that I, having no literary skill, cannot properly\nexpress that which I desire to treat of [Footnote 26: _le mie cose\n.... che d'altra parola_. This can hardly be reconciled with Mons.\nRAVAISSON'S estimate of L. da Vinci's learning. \"_Leonard de Vinci\netait un admirateur et un disciple des anciens, aussi bien dans\nl'art que dans la science et il tenait a passer pour tel meme aux\nyeux de la posterite._\" _Gaz. des Beaux arts. Oct. 1877.]; but they\ndo not know that my subjects are to be dealt with by experience\nrather than by words [Footnote 28: See Footnote 26]; and\n[experience] has been the mistress of those who wrote well. And so,\nas mistress, I will cite her in all cases.\n\n11.\n\nThough I may not, like them, be able to quote other authors, I shall\nrely on that which is much greater and more worthy:--on experience,\nthe mistress of their Masters. They go about puffed up and pompous,\ndressed and decorated with [the fruits], not of their own labours,\nbut of those of others. And they will not allow me my own. They will\nscorn me as an inventor; but how much more might they--who are not\ninventors but vaunters and declaimers of the works of others--be\nblamed.\n\nINTRODUCTION.\n\nAnd those men who are inventors and interpreters between Nature and\nMan, as compared with boasters and declaimers of the works of\nothers, must be regarded and not otherwise esteemed than as the\nobject in front of a mirror, when compared with its image seen in\nthe mirror. For the first is something in itself, and the other\nnothingness.--Folks little indebted to Nature, since it is only by\nchance that they wear the human form and without it I might class\nthem with the herds of beasts.\n\n12.\n\nMany will think they may reasonably blame me by alleging that my\nproofs are opposed to the authority of certain men held in the\nhighest reverence by their inexperienced judgments; not considering\nthat my works are the issue of pure and simple experience, who is\nthe one true mistress. These rules are sufficient to enable you to\nknow the true from the false--and this aids men to look only for\nthings that are possible and with due moderation--and not to wrap\nyourself in ignorance, a thing which can have no good result, so\nthat in despair you would give yourself up to melancholy.\n\n13.\n\nAmong all the studies of natural causes and reasons Light chiefly\ndelights the beholder; and among the great features of Mathematics\nthe certainty of its demonstrations is what preeminently (tends to)\nelevate the mind of the investigator. Perspective, therefore, must\nbe preferred to all the discourses and systems of human learning. In\nthis branch [of science] the beam of light is explained on those\nmethods of demonstration which form the glory not so much of\nMathematics as of Physics and are graced with the flowers of both\n[Footnote: 5. Such of Leonardo's notes on Optics or on Perspective\nas bear exclusively on Mathematics or Physics could not be included\nin the arrangement of the _libro di pittura_ which is here presented\nto the reader. They are however but few.]. But its axioms being laid\ndown at great length, I shall abridge them to a conclusive brevity,\narranging them on the method both of their natural order and of\nmathematical demonstration; sometimes by deduction of the effects\nfrom the causes, and sometimes arguing the causes from the effects;\nadding also to my own conclusions some which, though not included in\nthem, may nevertheless be inferred from them. Thus, if the Lord--who\nis the light of all things--vouchsafe to enlighten me, I will treat\nof Light; wherefore I will divide the present work into 3 Parts\n[Footnote: 10. In the middle ages--for instance, by ROGER BACON, by\nVITELLONE, with whose works Leonardo was certainly familiar, and by\nall the writers of the Renaissance Perspective and Optics were not\nregarded as distinct sciences. Perspective, indeed, is in its widest\napplication the science of seeing. Although to Leonardo the two\nsciences were clearly separate, it is not so as to their names; thus\nwe find axioms in Optics under the heading Perspective. According to\nthis arrangement of the materials for the theoretical portion of the\n_libro di pittura_ propositions in Perspective and in Optics stand\nside by side or occur alternately. Although this particular chapter\ndeals only with Optics, it is not improbable that the words _partir\u00f2\nla presente opera in 3 parti_ may refer to the same division into\nthree sections which is spoken of in chapters 14 to 17.].\n\nThe plan of the book on Painting (14--17).\n\n14.\n\nON THE THREE BRANCHES OF PERSPECTIVE.\n\nThere are three branches of perspective; the first deals with the\nreasons of the (apparent) diminution of objects as they recede from\nthe eye, and is known as Diminishing Perspective.--The second\ncontains the way in which colours vary as they recede from the eye.\nThe third and last is concerned with the explanation of how the\nobjects [in a picture] ought to be less finished in proportion as\nthey are remote (and the names are as follows):\n\nLinear Perspective. The Perspective of Colour. The Perspective of\nDisappearance.\n\n[Footnote: 13. From the character of the handwriting I infer that\nthis passage was written before the year 1490.].\n\n15.\n\nON PAINTING AND PERSPECTIVE.\n\nThe divisions of Perspective are 3, as used in drawing; of these,\nthe first includes the diminution in size of opaque objects; the\nsecond treats of the diminution and loss of outline in such opaque\nobjects; the third, of the diminution and loss of colour at long\ndistances.\n\n[Footnote: The division is here the same as in the previous chapter\nNo. 14, and this is worthy of note when we connect it with the fact\nthat a space of about 20 years must have intervened between the\nwriting of the two passages.]\n\n16.\n\nTHE DISCOURSE ON PAINTING.\n\nPerspective, as bearing on drawing, is divided into three principal\nsections; of which the first treats of the diminution in the size of\nbodies at different distances. The second part is that which treats\nof the diminution in colour in these objects. The third [deals with]\nthe diminished distinctness of the forms and outlines displayed by\nthe objects at various distances.\n\n17.\n\nON THE SECTIONS OF [THE BOOK ON] PAINTING.\n\nThe first thing in painting is that the objects it represents should\nappear in relief, and that the grounds surrounding them at different\ndistances shall appear within the vertical plane of the foreground\nof the picture by means of the 3 branches of Perspective, which are:\nthe diminution in the distinctness of the forms of the objects, the\ndiminution in their magnitude; and the diminution in their colour.\nAnd of these 3 classes of Perspective the first results from [the\nstructure of] the eye, while the other two are caused by the\natmosphere which intervenes between the eye and the objects seen by\nit. The second essential in painting is appropriate action and a due\nvariety in the figures, so that the men may not all look like\nbrothers, &c.\n\n[Footnote: This and the two foregoing chapters must have been\nwritten in 1513 to 1516. They undoubtedly indicate the scheme which\nLeonardo wished to carry out in arranging his researches on\nPerspective as applied to Painting. This is important because it is\nan evidence against the supposition of H. LUDWIG and others, that\nLeonardo had collected his principles of Perspective in one book so\nearly as before 1500; a Book which, according to the hypothesis,\nmust have been lost at a very early period, or destroyed possibly,\nby the French (!) in 1500 (see H. LUDWIG. L. da Vinci: _Das Buch van\nder Malerei_. Vienna 1882 III, 7 and 8).]\n\nThe use of the book on Painting.\n\n18.\n\nThese rules are of use only in correcting the figures; since every\nman makes some mistakes in his first compositions and he who knows\nthem not, cannot amend them. But you, knowing your errors, will\ncorrect your works and where you find mistakes amend them, and\nremember never to fall into them again. But if you try to apply\nthese rules in composition you will never make an end, and will\nproduce confusion in your works.\n\nThese rules will enable you to have a free and sound judgment; since\ngood judgment is born of clear understanding, and a clear\nunderstanding comes of reasons derived from sound rules, and sound\nrules are the issue of sound experience--the common mother of all\nthe sciences and arts. Hence, bearing in mind the precepts of my\nrules, you will be able, merely by your amended judgment, to\ncriticise and recognise every thing that is out of proportion in a\nwork, whether in the perspective or in the figures or any thing\nelse.\n\nNecessity of theoretical knowledge (19. 20).\n\n19.\n\nOF THE MISTAKES MADE BY THOSE WHO PRACTISE WITHOUT KNOWLEDGE.\n\nThose who are in love with practice without knowledge are like the\nsailor who gets into a ship without rudder or compass and who never\ncan be certain whether he is going. Practice must always be founded\non sound theory, and to this Perspective is the guide and the\ngateway; and without this nothing can be done well in the matter of\ndrawing.\n\n20.\n\nThe painter who draws merely by practice and by eye, without any\nreason, is like a mirror which copies every thing placed in front of\nit without being conscious of their existence.\n\nThe function of the eye (21-23).\n\n21.\n\nINTRODUCTION TO PERSPECTIVE:--THAT IS OF THE FUNCTION OF THE EYE.\n\nBehold here O reader! a thing concerning which we cannot trust our\nforefathers, the ancients, who tried to define what the Soul and\nLife are--which are beyond proof, whereas those things, which can at\nany time be clearly known and proved by experience, remained for\nmany ages unknown or falsely understood. The eye, whose function we\nso certainly know by experience, has, down to my own time, been\ndefined by an infinite number of authors as one thing; but I find,\nby experience, that it is quite another. [Footnote 13: Compare the\nnote to No. 70.]\n\n[Footnote: In section 13 we already find it indicated that the study\nof Perspective and of Optics is to be based on that of the functions\nof the eye. Leonardo also refers to the science of the eye, in his\nastronomical researches, for instance in MS. F 25b '_Ordine del\nprovare la terra essere una stella: Imprima difinisce l'occhio'_,\n&c. Compare also MS. E 15b and F 60b. The principles of astronomical\nperspective.]\n\n22.\n\nHere [in the eye] forms, here colours, here the character of every\npart of the universe are concentrated to a point; and that point is\nso marvellous a thing ... Oh! marvellous, O stupendous Necessity--by\nthy laws thou dost compel every effect to be the direct result of\nits cause, by the shortest path. These [indeed] are miracles;...\n\nIn so small a space it can be reproduced and rearranged in its whole\nexpanse. Describe in your anatomy what proportion there is between\nthe diameters of all the images in the eye and the distance from\nthem of the crystalline lens.\n\n23.\n\nOF THE 10 ATTRIBUTES OF THE EYE, ALL CONCERNED IN PAINTING.\n\nPainting is concerned with all the 10 attributes of sight; which\nare:--Darkness, Light, Solidity and Colour, Form and Position,\nDistance and Propinquity, Motion and Rest. This little work of mine\nwill be a tissue [of the studies] of these attributes, reminding the\npainter of the rules and methods by which he should use his art to\nimitate all the works of Nature which adorn the world.\n\n24.\n\nON PAINTING.\n\nVariability of the eye.\n\n1st. The pupil of the eye contracts, in proportion to the increase\nof light which is reflected in it. 2nd. The pupil of the eye expands\nin proportion to the diminution in the day light, or any other\nlight, that is reflected in it. 3rd. [Footnote: 8. The subject of\nthis third proposition we find fully discussed in MS. G. 44a.]. The\neye perceives and recognises the objects of its vision with greater\nintensity in proportion as the pupil is more widely dilated; and\nthis can be proved by the case of nocturnal animals, such as cats,\nand certain birds--as the owl and others--in which the pupil varies\nin a high degree from large to small, &c., when in the dark or in\nthe light. 4th. The eye [out of doors] in an illuminated atmosphere\nsees darkness behind the windows of houses which [nevertheless] are\nlight. 5th. All colours when placed in the shade appear of an equal\ndegree of darkness, among themselves. 6th. But all colours when\nplaced in a full light, never vary from their true and essential\nhue.\n\n25.\n\nOF THE EYE.\n\nFocus of sight.\n\nIf the eye is required to look at an object placed too near to it,\nit cannot judge of it well--as happens to a man who tries to see the\ntip of his nose. Hence, as a general rule, Nature teaches us that an\nobject can never be seen perfectly unless the space between it and\nthe eye is equal, at least, to the length of the face.\n\nDifferences of perception by one eye and by both eyes (26-29).\n\n26.\n\nOF THE EYE.\n\nWhen both eyes direct the pyramid of sight to an object, that object\nbecomes clearly seen and comprehended by the eyes.\n\n27.\n\nObjects seen by one and the same eye appear sometimes large, and\nsometimes small.\n\n28.\n\nThe motion of a spectator who sees an object at rest often makes it\nseem as though the object at rest had acquired the motion of the\nmoving body, while the moving person appears to be at rest.\n\nON PAINTING.\n\nObjects in relief, when seen from a short distance with one eye,\nlook like a perfect picture. If you look with the eye _a_, _b_ at\nthe spot _c_, this point _c_ will appear to be at _d_, _f_, and if\nyou look at it with the eye _g_, _h_ will appear to be at _m_. A\npicture can never contain in itself both aspects.\n\n29.\n\nLet the object in relief _t_ be seen by both eyes; if you will look\nat the object with the right eye _m_, keeping the left eye _n_ shut,\nthe object will appear, or fill up the space, at _a_; and if you\nshut the right eye and open the left, the object (will occupy the)\nspace _b_; and if you open both eyes, the object will no longer\nappear at _a_ or _b_, but at _e_, _r_, _f_. Why will not a picture\nseen by both eyes produce the effect of relief, as [real] relief\ndoes when seen by both eyes; and why should a picture seen with one\neye give the same effect of relief as real relief would under the\nsame conditions of light and shade?\n\n[Footnote: In the sketch, _m_ is the left eye and _n_ the right,\nwhile the text reverses this lettering. We must therefore suppose\nthat the face in which the eyes _m_ and _n_ are placed is opposite\nto the spectator.]\n\n30.\n\nThe comparative size of the image depends on the amount of light\n(30-39).\n\nThe eye will hold and retain in itself the image of a luminous body\nbetter than that of a shaded object. The reason is that the eye is\nin itself perfectly dark and since two things that are alike cannot\nbe distinguished, therefore the night, and other dark objects cannot\nbe seen or recognised by the eye. Light is totally contrary and\ngives more distinctness, and counteracts and differs from the usual\ndarkness of the eye, hence it leaves the impression of its image.\n\n31.\n\nEvery object we see will appear larger at midnight than at midday,\nand larger in the morning than at midday.\n\nThis happens because the pupil of the eye is much smaller at midday\nthan at any other time.\n\n32.\n\nThe pupil which is largest will see objects the largest. This is\nevident when we look at luminous bodies, and particularly at those\nin the sky. When the eye comes out of darkness and suddenly looks up\nat these bodies, they at first appear larger and then diminish; and\nif you were to look at those bodies through a small opening, you\nwould see them smaller still, because a smaller part of the pupil\nwould exercise its function.\n\n[Footnote: 9. _buso_ in the Lomb. dialect is the same as _buco_.]\n\n33.\n\nWhen the eye, coming out of darkness suddenly sees a luminous body,\nit will appear much larger at first sight than after long looking at\nit. The illuminated object will look larger and more brilliant, when\nseen with two eyes than with only one. A luminous object will appear\nsmaller in size, when the eye sees it through a smaller opening. A\nluminous body of an oval form will appear rounder in proportion as\nit is farther from the eye.\n\n34.\n\nWhy when the eye has just seen the light, does the half light look\ndark to it, and in the same way if it turns from the darkness the\nhalf light look very bright?\n\n35.\n\nON PAINTING.\n\nIf the eye, when [out of doors] in the luminous atmosphere, sees a\nplace in shadow, this will look very much darker than it really is.\nThis happens only because the eye when out in the air contracts the\npupil in proportion as the atmosphere reflected in it is more\nluminous. And the more the pupil contracts, the less luminous do the\nobjects appear that it sees. But as soon as the eye enters into a\nshady place the darkness of the shadow suddenly seems to diminish.\nThis occurs because the greater the darkness into which the pupil\ngoes the more its size increases, and this increase makes the\ndarkness seem less.\n\n[Footnote 14: _La luce entrer\u00e0_. _Luce_ occurs here in the sense of\npupil of the eye as in no 51: C. A. 84b; 245a; I--5; and in many\nother places.]\n\n36.\n\nON PERSPECTIVE.\n\nThe eye which turns from a white object in the light of the sun and\ngoes into a less fully lighted place will see everything as dark.\nAnd this happens either because the pupils of the eyes which have\nrested on this brilliantly lighted white object have contracted so\nmuch that, given at first a certain extent of surface, they will\nhave lost more than 3/4 of their size; and, lacking in size, they\nare also deficient in [seeing] power. Though you might say to me: A\nlittle bird (then) coming down would see comparatively little, and\nfrom the smallness of his pupils the white might seem black! To this\nI should reply that here we must have regard to the proportion of\nthe mass of that portion of the brain which is given up to the sense\nof sight and to nothing else. Or--to return--this pupil in Man\ndilates and contracts according to the brightness or darkness of\n(surrounding) objects; and since it takes some time to dilate and\ncontract, it cannot see immediately on going out of the light and\ninto the shade, nor, in the same way, out of the shade into the\nlight, and this very thing has already deceived me in painting an\neye, and from that I learnt it.\n\n37.\n\nExperiment [showing] the dilatation and contraction of the pupil,\nfrom the motion of the sun and other luminaries. In proportion as\nthe sky is darker the stars appear of larger size, and if you were\nto light up the medium these stars would look smaller; and this\ndifference arises solely from the pupil which dilates and contracts\nwith the amount of light in the medium which is interposed between\nthe eye and the luminous body. Let the experiment be made, by\nplacing a candle above your head at the same time that you look at a\nstar; then gradually lower the candle till it is on a level with the\nray that comes from the star to the eye, and then you will see the\nstar diminish so much that you will almost lose sight of it.\n\n[Footnote: No reference is made in the text to the letters on the\naccompanying diagram.]\n\n38.\n\nThe pupil of the eye, in the open air, changes in size with every\ndegree of motion from the sun; and at every degree of its changes\none and the same object seen by it will appear of a different size;\nalthough most frequently the relative scale of surrounding objects\ndoes not allow us to detect these variations in any single object we\nmay look at.\n\n39.\n\nThe eye--which sees all objects reversed--retains the images for\nsome time. This conclusion is proved by the results; because, the\neye having gazed at light retains some impression of it. After\nlooking (at it) there remain in the eye images of intense\nbrightness, that make any less brilliant spot seem dark until the\neye has lost the last trace of the impression of the stronger light.\n\n_II.\n\nLinear Perspective.\n\nWe see clearly from the concluding sentence of section 49, where the\nauthor directly addresses the painter, that he must certainly have\nintended to include the elements of mathematics in his Book on the\nart of Painting. They are therefore here placed at the beginning. In\nsection 50 the theory of the \"Pyramid of Sight\" is distinctly and\nexpressly put forward as the fundamental principle of linear\nperspective, and sections 52 to 57 treat of it fully. This theory of\nsight can scarcely be traced to any author of antiquity. Such\npassages as occur in Euclid for instance, may, it is true, have\nproved suggestive to the painters of the Renaissance, but it would\nbe rash to say any thing decisive on this point.\n\nLeon Battista Alberti treats of the \"Pyramid of Sight\" at some\nlength in his first Book of Painting; but his explanation differs\nwidely from Leonardo's in the details. Leonardo, like Alberti, may\nhave borrowed the broad lines of his theory from some views commonly\naccepted among painters at the time; but he certainly worked out its\napplication in a perfectly original manner.\n\nThe axioms as to the perception of the pyramid of rays are followed\nby explanations of its origin, and proofs of its universal\napplication (58--69). The author recurs to the subject with endless\nvariations; it is evidently of fundamental importance in his\nartistic theory and practice. It is unnecessary to discuss how far\nthis theory has any scientific value at the present day; so much as\nthis, at any rate, seems certain: that from the artist's point of\nview it may still claim to be of immense practical utility.\n\nAccording to Leonardo, on one hand, the laws of perspective are an\ninalienable condition of the existence of objects in space; on the\nother hand, by a natural law, the eye, whatever it sees and wherever\nit turns, is subjected to the perception of the pyramid of rays in\nthe form of a minute target. Thus it sees objects in perspective\nindependently of the will of the spectator, since the eye receives\nthe images by means of the pyramid of rays \"just as a magnet\nattracts iron\".\n\nIn connection with this we have the function of the eye explained by\nthe Camera obscura, and this is all the more interesting and\nimportant because no writer previous to Leonardo had treated of this\nsubject_ (70--73). _Subsequent passages, of no less special interest,\nbetray his knowledge of refraction and of the inversion of the image\nin the camera and in the eye_ (74--82).\n\n_From the principle of the transmission of the image to the eye and\nto the camera obscura he deduces the means of producing an\nartificial construction of the pyramid of rays or--which is the same\nthing--of the image. The fundamental axioms as to the angle of sight\nand the vanishing point are thus presented in a manner which is as\ncomplete as it is simple and intelligible_ (86--89).\n\n_Leonardo distinguishes between simple and complex perspective_ (90,\n91). _The last sections treat of the apparent size of objects at\nvarious distances and of the way to estimate it_ (92--109).\n\nGeneral remarks on perspective (40-41).\n\n40.\n\nON PAINTING.\n\nPerspective is the best guide to the art of Painting.\n\n[Footnote: 40. Compare 53, 2.]\n\n41.\n\nThe art of perspective is of such a nature as to make what is flat\nappear in relief and what is in relief flat.\n\nThe elements of perspective--Of the Point (42-46).\n\n42.\n\nAll the problems of perspective are made clear by the five terms of\nmathematicians, which are:--the point, the line, the angle, the\nsuperficies and the solid. The point is unique of its kind. And the\npoint has neither height, breadth, length, nor depth, whence it is\nto be regarded as indivisible and as having no dimensions in space.\nThe line is of three kinds, straight, curved and sinuous and it has\nneither breadth, height, nor depth. Hence it is indivisible,\nexcepting in its length, and its ends are two points. The angle is\nthe junction of two lines in a point.\n\n43.\n\nA point is not part of a line.\n\n44.\n\nOF THE NATURAL POINT.\n\nThe smallest natural point is larger than all mathematical points,\nand this is proved because the natural point has continuity, and any\nthing that is continuous is infinitely divisible; but the\nmathematical point is indivisible because it has no size.\n\n[Footnote: This definition was inserted by Leonardo on a MS. copy on\nparchment of the well-known _\"Trattato d'Architettura civile e\nmilitare\"_ &c. by FRANCESCO DI GIORGIO; opposite a passage where the\nauthor says: _'In prima he da sapere che punto \u00e8 quella parie della\nquale he nulla--Linia he luncheza senza \u00e0pieza; &c.]\n\n45.\n\n1, The superficies is a limitation of the body. 2, and the\nlimitation of a body is no part of that body. 4, and the limitation\nof one body is that which begins another. 3, that which is not part\nof any body is nothing. Nothing is that which fills no space.\n\nIf one single point placed in a circle may be the starting point of\nan infinite number of lines, and the termination of an infinite\nnumber of lines, there must be an infinite number of points\nseparable from this point, and these when reunited become one again;\nwhence it follows that the part may be equal to the whole.\n\n46.\n\nThe point, being indivisible, occupies no space. That which occupies\nno space is nothing. The limiting surface of one thing is the\nbeginning of another. 2. That which is no part of any body is called\nnothing. 1. That which has no limitations, has no form. The\nlimitations of two conterminous bodies are interchangeably the\nsurface of each. All the surfaces of a body are not parts of that\nbody.\n\nOf the line (47-48).\n\n47.\n\nDEFINITION OF THE NATURE OF THE LINE.\n\nThe line has in itself neither matter nor substance and may rather\nbe called an imaginary idea than a real object; and this being its\nnature it occupies no space. Therefore an infinite number of lines\nmay be conceived of as intersecting each other at a point, which has\nno dimensions and is only of the thickness (if thickness it may be\ncalled) of one single line.\n\nHOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN A POINT?\n\nAn angular surface is reduced to a point where it terminates in an\nangle. Or, if the sides of that angle are produced in a straight\nline, then--beyond that angle--another surface is generated,\nsmaller, or equal to, or larger than the first.\n\n48.\n\nOF DRAWING OUTLINE.\n\nConsider with the greatest care the form of the outlines of every\nobject, and the character of their undulations. And these\nundulations must be separately studied, as to whether the curves are\ncomposed of arched convexities or angular concavities.\n\n49.\n\nThe nature of the outline.\n\nThe boundaries of bodies are the least of all things. The\nproposition is proved to be true, because the boundary of a thing is\na surface, which is not part of the body contained within that\nsurface; nor is it part of the air surrounding that body, but is the\nmedium interposted between the air and the body, as is proved in its\nplace. But the lateral boundaries of these bodies is the line\nforming the boundary of the surface, which line is of invisible\nthickness. Wherefore O painter! do not surround your bodies with\nlines, and above all when representing objects smaller than nature;\nfor not only will their external outlines become indistinct, but\ntheir parts will be invisible from distance.\n\n50.\n\nDefinition of Perspective.\n\n[Drawing is based upon perspective, which is nothing else than a\nthorough knowledge of the function of the eye. And this function\nsimply consists in receiving in a pyramid the forms and colours of\nall the objects placed before it. I say in a pyramid, because there\nis no object so small that it will not be larger than the spot where\nthese pyramids are received into the eye. Therefore, if you extend\nthe lines from the edges of each body as they converge you will\nbring them to a single point, and necessarily the said lines must\nform a pyramid.]\n\n[Perspective is nothing more than a rational demonstration applied\nto the consideration of how objects in front of the eye transmit\ntheir image to it, by means of a pyramid of lines. The _Pyramid_ is\nthe name I apply to the lines which, starting from the surface and\nedges of each object, converge from a distance and meet in a single\npoint.]\n\n[Perspective is a rational demonstration, by which we may\npractically and clearly understand how objects transmit their own\nimage, by lines forming a Pyramid (centred) in the eye.]\n\nPerspective is a rational demonstration by which experience confirms\nthat every object sends its image to the eye by a pyramid of lines;\nand bodies of equal size will result in a pyramid of larger or\nsmaller size, according to the difference in their distance, one\nfrom the other. By a pyramid of lines I mean those which start from\nthe surface and edges of bodies, and, converging from a distance\nmeet in a single point. A point is said to be that which [having no\ndimensions] cannot be divided, and this point placed in the eye\nreceives all the points of the cone.\n\n[Footnote: 50. 1-5. Compare with this the Proem. No. 21. The\nparagraphs placed in brackets: lines 1-9, 10-14, and 17--20, are\nevidently mere sketches and, as such, were cancelled by the writer;\nbut they serve as a commentary on the final paragraph, lines 22-29.]\n\n51.\n\nIN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT OF IT.\n\nThe perception of the object depends on the direction of the eye.\n\nSupposing that the ball figured above is the ball of the eye and let\nthe small portion of the ball which is cut off by the line _s t_ be\nthe pupil and all the objects mirrored on the centre of the face of\nthe eye, by means of the pupil, pass on at once and enter the pupil,\npassing through the crystalline humour, which does not interfere in\nthe pupil with the things seen by means of the light. And the pupil\nhaving received the objects, by means of the light, immediately\nrefers them and transmits them to the intellect by the line _a b_.\nAnd you must know that the pupil transmits nothing perfectly to the\nintellect or common sense excepting when the objects presented to it\nby means of light, reach it by the line _a b;_ as, for instance, by\nthe line _b c_. For although the lines _m n_ and _f g_ may be seen\nby the pupil they are not perfectly taken in, because they do not\ncoincide with the line _a b_. And the proof is this: If the eye,\nshown above, wants to count the letters placed in front, the eye\nwill be obliged to turn from letter to letter, because it cannot\ndiscern them unless they lie in the line _a b;_ as, for instance, in\nthe line _a c_. All visible objects reach the eye by the lines of a\npyramid, and the point of the pyramid is the apex and centre of it,\nin the centre of the pupil, as figured above.\n\n[Footnote: 51. In this problem the eye is conceived of as fixed and\nimmovable; this is plain from line 11.]\n\nExperimental proof of the existence of the pyramid of sight (52-55).\n\n52.\n\nPerspective is a rational demonstration, confirmed by experience,\nthat all objects transmit their image to the eye by a pyramid of\nlines.\n\nBy a pyramid of lines I understand those lines which start from the\nedges of the surface of bodies, and converging from a distance, meet\nin a single point; and this point, in the present instance, I will\nshow to be situated in the eye which is the universal judge of all\nobjects. By a point I mean that which cannot be divided into parts;\ntherefore this point, which is situated in the eye, being\nindivisible, no body is seen by the eye, that is not larger than\nthis point. This being the case it is inevitable that the lines\nwhich come from the object to the point must form a pyramid. And if\nany man seeks to prove that the sense of sight does not reside in\nthis point, but rather in the black spot which is visible in the\nmiddle of the pupil, I might reply to him that a small object could\nnever diminish at any distance, as it might be a grain of millet or\nof oats or of some similar thing, and that object, if it were larger\nthan the said [black] spot would never be seen as a whole; as may be\nseen in the diagram below. Let _a_. be the seat of sight, _b e_ the\nlines which reach the eye. Let _e d_ be the grains of millet within\nthese lines. You plainly see that these will never diminish by\ndistance, and that the body _m n_ could not be entirely covered by\nit. Therefore you must confess that the eye contains within itself\none single indivisible point _a_, to which all the points converge\nof the pyramid of lines starting from an object, as is shown below.\nLet _a_. _b_. be the eye; in the centre of it is the point above\nmentioned. If the line _e f_ is to enter as an image into so small\nan opening in the eye, you must confess that the smaller object\ncannot enter into what is smaller than itself unless it is\ndiminished, and by diminishing it must take the form of a pyramid.\n\n53.\n\nPERSPECTIVE.\n\nPerspective comes in where judgment fails [as to the distance] in\nobjects which diminish. The eye can never be a true judge for\ndetermining with exactitude how near one object is to another which\nis equal to it [in size], if the top of that other is on the level\nof the eye which sees them on that side, excepting by means of the\nvertical plane which is the standard and guide of perspective. Let\n_n_ be the eye, _e f_ the vertical plane above mentioned. Let _a b c\nd_ be the three divisions, one below the other; if the lines _a n_\nand _c n_ are of a given length and the eye _n_ is in the centre,\nthen _a b_ will look as large as _b c. c d_ is lower and farther off\nfrom _n_, therefore it will look smaller. And the same effect will\nappear in the three divisions of a face when the eye of the painter\nwho is drawing it is on a level with the eye of the person he is\npainting.\n\n54.\n\nTO PROVE HOW OBJECTS REACH THE EYE.\n\nIf you look at the sun or some other luminous body and then shut\nyour eyes you will see it again inside your eye for a long time.\nThis is evidence that images enter into the eye.\n\nThe relations of the distance points to the vanishing point (55-56).\n\n55.\n\nELEMENTS OF PERSPECTIVE.\n\nAll objects transmit their image to the eye in pyramids, and the\nnearer to the eye these pyramids are intersected the smaller will\nthe image appear of the objects which cause them. Therefore, you may\nintersect the pyramid with a vertical plane [Footnote 4: _Pariete_.\nCompare the definitions in 85, 2-5, 6-27. These lines refer\nexclusively to the third diagram. For the better understanding of\nthis it should be observed that _c s_ must be regarded as\nrepresenting the section or profile of a square plane, placed\nhorizontally (comp. lines 11, 14, 17) for which the word _pianura_\nis subsequently employed (20, 22). Lines 6-13 contain certain\npreliminary observations to guide the reader in understanding the\ndiagram; the last three seem to have been added as a supplement.\nLeonardo's mistake in writing _t denota_ (line 6) for _f denota_ has\nbeen rectified.] which reaches the base of the pyramid as is shown\nin the plane _a n_.\n\nThe eye _f_ and the eye _t_ are one and the same thing; but the eye\n_f_ marks the distance, that is to say how far you are standing from\nthe object; and the eye _t_ shows you the direction of it; that is\nwhether you are opposite, or on one side, or at an angle to the\nobject you are looking at. And remember that the eye _f_ and the eye\n_t_ must always be kept on the same level. For example if you raise\nor lower the eye from the distance point _f_ you must do the same\nwith the direction point _t_. And if the point _f_ shows how far the\neye is distant from the square plane but does not show on which side\nit is placed--and, if in the same way, the point _t_ show _s_ the\ndirection and not the distance, in order to ascertain both you must\nuse both points and they will be one and the same thing. If the eye\n_f_ could see a perfect square of which all the sides were equal to\nthe distance between _s_ and _c_, and if at the nearest end of the\nside towards the eye a pole were placed, or some other straight\nobject, set up by a perpendicular line as shown at _r s_--then, I\nsay, that if you were to look at the side of the square that is\nnearest to you it will appear at the bottom of the vertical plane _r\ns_, and then look at the farther side and it would appear to you at\nthe height of the point _n_ on the vertical plane. Thus, by this\nexample, you can understand that if the eye is above a number of\nobjects all placed on the same level, one beyond another, the more\nremote they are the higher they will seem, up to the level of the\neye, but no higher; because objects placed upon the level on which\nyour feet stand, so long as it is flat--even if it be extended into\ninfinity--would never be seen above the eye; since the eye has in\nitself the point towards which all the cones tend and converge which\nconvey the images of the objects to the eye. And this point always\ncoincides with the point of diminution which is the extreme of all\nwe can see. And from the base line of the first pyramid as far as\nthe diminishing point\n\n[Footnote: The two diagrams above the chapter are explained by the\nfirst five lines. They have, however, more letters than are referred\nto in the text, a circumstance we frequently find occasion to\nremark.]\n\n56.\n\nthere are only bases without pyramids which constantly diminish up\nto this point. And from the first base where the vertical plane is\nplaced towards the point in the eye there will be only pyramids\nwithout bases; as shown in the example given above. Now, let _a b_\nbe the said vertical plane and _r_ the point of the pyramid\nterminating in the eye, and _n_ the point of diminution which is\nalways in a straight line opposite the eye and always moves as the\neye moves--just as when a rod is moved its shadow moves, and moves\nwith it, precisely as the shadow moves with a body. And each point\nis the apex of a pyramid, all having a common base with the\nintervening vertical plane. But although their bases are equal their\nangles are not equal, because the diminishing point is the\ntermination of a smaller angle than that of the eye. If you ask me:\n\"By what practical experience can you show me these points?\" I\nreply--so far as concerns the diminishing point which moves with you\n--when you walk by a ploughed field look at the straight furrows\nwhich come down with their ends to the path where you are walking,\nand you will see that each pair of furrows will look as though they\ntried to get nearer and meet at the [farther] end.\n\n[Footnote: For the easier understanding of the diagram and of its\nconnection with the preceding I may here remark that the square\nplane shown above in profile by the line _c s_ is here indicated by\n_e d o p_. According to lines 1, 3 _a b_ must be imagined as a plane\nof glass placed perpendicularly at _o p_.]\n\n57.\n\nHow to measure the pyramid of vision.\n\nAs regards the point in the eye; it is made more intelligible by\nthis: If you look into the eye of another person you will see your\nown image. Now imagine 2 lines starting from your ears and going to\nthe ears of that image which you see in the other man's eye; you\nwill understand that these lines converge in such a way that they\nwould meet in a point a little way beyond your own image mirrored in\nthe eye. And if you want to measure the diminution of the pyramid in\nthe air which occupies the space between the object seen and the\neye, you must do it according to the diagram figured below. Let _m\nn_ be a tower, and _e f_ a, rod, which you must move backwards and\nforwards till its ends correspond with those of the tower [Footnote\n9: _I sua stremi .. della storre_ (its ends ... of the tower) this\nis the case at _e f_.]; then bring it nearer to the eye, at _c d_\nand you will see that the image of the tower seems smaller, as at _r\no_. Then [again] bring it closer to the eye and you will see the rod\nproject far beyond the image of the tower from _a_ to _b_ and from\n_t_ to _b_, and so you will discern that, a little farther within,\nthe lines must converge in a point.\n\nThe Production of pyramid of Vision (58-60).\n\n58.\n\nPERSPECTIVE.\n\nThe instant the atmosphere is illuminated it will be filled with an\ninfinite number of images which are produced by the various bodies\nand colours assembled in it. And the eye is the target, a loadstone,\nof these images.\n\n59.\n\nThe whole surface of opaque bodies displays its whole image in all\nthe illuminated atmosphere which surrounds them on all sides.\n\n60.\n\nThat the atmosphere attracts to itself, like a loadstone, all the\nimages of the objects that exist in it, and not their forms merely\nbut their nature may be clearly seen by the sun, which is a hot and\nluminous body. All the atmosphere, which is the all-pervading\nmatter, absorbs light and heat, and reflects in itself the image of\nthe source of that heat and splendour and, in each minutest portion,\ndoes the same. The Northpole does the same as the loadstone shows;\nand the moon and the other planets, without suffering any\ndiminution, do the same. Among terrestrial things musk does the same\nand other perfumes.\n\n61.\n\nAll bodies together, and each by itself, give off to the surrounding\nair an infinite number of images which are all-pervading and each\ncomplete, each conveying the nature, colour and form of the body\nwhich produces it.\n\nIt can clearly be shown that all bodies are, by their images,\nall-pervading in the surrounding atmosphere, and each complete in\nitself as to substance form and colour; this is seen by the images\nof the various bodies which are reproduced in one single perforation\nthrough which they transmit the objects by lines which intersect and\ncause reversed pyramids, from the objects, so that they are upside\ndown on the dark plane where they are first reflected. The reason of\nthis is--\n\n[Footnote: The diagram intended to illustrate the statement (Pl. II\nNo. i) occurs in the original between lines 3 and 4. The three\ncircles must be understood to represent three luminous bodies which\ntransmit their images through perforations in a wall into a dark\nchamber, according to a law which is more fully explained in 75?81.\nSo far as concerns the present passage the diagram is only intended\nto explain that the images of the three bodies may be made to\ncoalesce at any given spot. In the circles are written,\ngiallo--yellow, bi\u00e0cho--white, rosso--red.\n\nThe text breaks off at line 8. The paragraph No.40 follows here in\nthe original MS.]\n\n62.\n\nEvery point is the termination of an infinite number of lines, which\ndiverge to form a base, and immediately, from the base the same\nlines converge to a pyramid [imaging] both the colour and form. No\nsooner is a form created or compounded than suddenly infinite lines\nand angles are produced from it; and these lines, distributing\nthemselves and intersecting each other in the air, give rise to an\ninfinite number of angles opposite to each other. Given a base, each\nopposite angle, will form a triangle having a form and proportion\nequal to the larger angle; and if the base goes twice into each of\nthe 2 lines of the pyramid the smaller triangle will do the same.\n\n63.\n\nEvery body in light and shade fills the surrounding air with\ninfinite images of itself; and these, by infinite pyramids diffused\nin the air, represent this body throughout space and on every side.\nEach pyramid that is composed of a long assemblage of rays includes\nwithin itself an infinite number of pyramids and each has the same\npower as all, and all as each. A circle of equidistant pyramids of\nvision will give to their object angles of equal size; and an eye at\neach point will see the object of the same size. The body of the\natmosphere is full of infinite pyramids composed of radiating\nstraight lines, which are produced from the surface of the bodies in\nlight and shade, existing in the air; and the farther they are from\nthe object which produces them the more acute they become and\nalthough in their distribution they intersect and cross they never\nmingle together, but pass through all the surrounding air,\nindependently converging, spreading, and diffused. And they are all\nof equal power [and value]; all equal to each, and each equal to\nall. By these the images of objects are transmitted through all\nspace and in every direction, and each pyramid, in itself, includes,\nin each minutest part, the whole form of the body causing it.\n\n64.\n\nThe body of the atmosphere is full of infinite radiating pyramids\nproduced by the objects existing in it. These intersect and cross\neach other with independent convergence without interfering with\neach other and pass through all the surrounding atmosphere; and are\nof equal force and value--all being equal to each, each to all. And\nby means of these, images of the body are transmitted everywhere and\non all sides, and each receives in itself every minutest portion of\nthe object that produces it.\n\nProof by experiment (65-66).\n\n65.\n\nPERSPECTIVE.\n\nThe air is filled with endless images of the objects distributed in\nit; and all are represented in all, and all in one, and all in each,\nwhence it happens that if two mirrors are placed in such a manner as\nto face each other exactly, the first will be reflected in the\nsecond and the second in the first. The first being reflected in the\nsecond takes to it the image of itself with all the images\nrepresented in it, among which is the image of the second mirror,\nand so, image within image, they go on to infinity in such a manner\nas that each mirror has within it a mirror, each smaller than the\nlast and one inside the other. Thus, by this example, it is clearly\nproved that every object sends its image to every spot whence the\nobject itself can be seen; and the converse: That the same object\nmay receive in itself all the images of the objects that are in\nfront of it. Hence the eye transmits through the atmosphere its own\nimage to all the objects that are in front of it and receives them\ninto itself, that is to say on its surface, whence they are taken in\nby the common sense, which considers them and if they are pleasing\ncommits them to the memory. Whence I am of opinion: That the\ninvisible images in the eyes are produced towards the object, as the\nimage of the object to the eye. That the images of the objects must\nbe disseminated through the air. An instance may be seen in several\nmirrors placed in a circle, which will reflect each other endlessly.\nWhen one has reached the other it is returned to the object that\nproduced it, and thence--being diminished--it is returned again to\nthe object and then comes back once more, and this happens\nendlessly. If you put a light between two flat mirrors with a\ndistance of 1 braccio between them you will see in each of them an\ninfinite number of lights, one smaller than another, to the last. If\nat night you put a light between the walls of a room, all the parts\nof that wall will be tinted with the image of that light. And they\nwill receive the light and the light will fall on them, mutually,\nthat is to say, when there is no obstacle to interrupt the\ntransmission of the images. This same example is seen in a greater\ndegree in the distribution of the solar rays which all together, and\neach by itself, convey to the object the image of the body which\ncauses it. That each body by itself alone fills with its images the\natmosphere around it, and that the same air is able, at the same\ntime, to receive the images of the endless other objects which are\nin it, this is clearly proved by these examples. And every object is\neverywhere visible in the whole of the atmosphere, and the whole in\nevery smallest part of it; and all the objects in the whole, and all\nin each smallest part; each in all and all in every part.\n\n66.\n\nThe images of objects are all diffused through the atmosphere which\nreceives them; and all on every side in it. To prove this, let _a c\ne_ be objects of which the images are admitted to a dark chamber by\nthe small holes _n p_ and thrown upon the plane _f i_ opposite to\nthese holes. As many images will be produced in the chamber on the\nplane as the number of the said holes.\n\n67.\n\nGeneral conclusions.\n\nAll objects project their whole image and likeness, diffused and\nmingled in the whole of the atmosphere, opposite to themselves. The\nimage of every point of the bodily surface, exists in every part of\nthe atmosphere. All the images of the objects are in every part of\nthe atmosphere. The whole, and each part of the image of the\natmosphere is [reflected] in each point of the surface of the bodies\npresented to it. Therefore both the part and the whole of the images\nof the objects exist, both in the whole and in the parts of the\nsurface of these visible bodies. Whence we may evidently say that\nthe image of each object exists, as a whole and in every part, in\neach part and in the whole interchangeably in every existing body.\nAs is seen in two mirrors placed opposite to each other.\n\n68.\n\nThat the contrary is impossible.\n\nIt is impossible that the eye should project from itself, by visual\nrays, the visual virtue, since, as soon as it opens, that front\nportion [of the eye] which would give rise to this emanation would\nhave to go forth to the object and this it could not do without\ntime. And this being so, it could not travel so high as the sun in a\nmonth's time when the eye wanted to see it. And if it could reach\nthe sun it would necessarily follow that it should perpetually\nremain in a continuous line from the eye to the sun and should\nalways diverge in such a way as to form between the sun and the eye\nthe base and the apex of a pyramid. This being the case, if the eye\nconsisted of a million worlds, it would not prevent its being\nconsumed in the projection of its virtue; and if this virtue would\nhave to travel through the air as perfumes do, the winds would bent\nit and carry it into another place. But we do [in fact] see the mass\nof the sun with the same rapidity as [an object] at the distance of\na braccio, and the power of sight is not disturbed by the blowing of\nthe winds nor by any other accident.\n\n[Footnote: The view here refuted by Leonardo was maintained among\nothers by Bramantino, Leonardo's Milanese contemporary. LOMAZZO\nwrites as follows in his Trattato dell' Arte della pittura &c.\n(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver gi\u00e0 letto in certi\nscritti alcune cose di Bramantino milanese, celebratissimo pittore,\nattenente alla prospettiva, le quali ho voluto riferire, e quasi\nintessere in questo luogo, affinch\u00e8 sappiamo qual fosse l'opinione\ndi cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive\nBramantino che la prospettiva \u00e8 una cosa che contraf\u00e0 il naturale, e\nche ci\u00f2 si fa in tre modi\n\nCirca il primo modo che si fa con ragione, per essere la cosa in\npoche parole conclusa da Bramantino in maniera che giudico non\npotersi dir meglio, contenendovi si tutta Parte del principio al\nfine, io riferir\u00f2 per appunto le proprie parole sue (cp. XXII, Prima\nprospettiva di Bramantino). La prima prospettiva fa le cose di\npunto, e l'altra non mai, e la terza pi\u00f9 appresso. Adunque la prima\nsi dimanda prospettiva, cio\u00e8 ragione, la quale fa l'effetto dell'\nocchio, facendo crescere e calare secondo gli effetti degli occhi.\nQuesto crescere e calare non procede della cosa propria, che in se\nper esser lontana, ovvero vicina, per quello effetto non pu\u00f2\ncrescere e sminuire, ma procede dagli effetti degli occhi, i quali\nsono piccioli, e perci\u00f2 volendo vedere tanto gran cosa_, bisogna che\nmandino fuora la virt\u00f9 visiva, _la quale si dilata in tanta\nlarghezza, che piglia tutto quello che vuoi vedere, ed_ arrivando a\nquella cosa la vede dove \u00e8: _e da lei agli occhi per quello circuito\nfino all' occhio, e tutto quello termine \u00e8 pieno di quella cosa_.\n\nIt is worthy of note that Leonardo had made his memorandum refuting\nthis view, at Milan in 1492]\n\n69.\n\nA parallel case.\n\nJust as a stone flung into the water becomes the centre and cause of\nmany circles, and as sound diffuses itself in circles in the air: so\nany object, placed in the luminous atmosphere, diffuses itself in\ncircles, and fills the surrounding air with infinite images of\nitself. And is repeated, the whole every-where, and the whole in\nevery smallest part. This can be proved by experiment, since if you\nshut a window that faces west and make a hole [Footnote: 6. Here the\ntext breaks off.] . .\n\n[Footnote: Compare LIBRI, _Histoire des sciences math\u00e9matiques en\nItalie_. Tome III, p. 43.]\n\nThe function of the eye as explained by the camera obscura (70. 71).\n\n70.\n\nIf the object in front of the eye sends its image to the eye, the\neye, on the other hand, sends its image to the object, and no\nportion whatever of the object is lost in the images it throws off,\nfor any reason either in the eye or the object. Therefore we may\nrather believe it to be the nature and potency of our luminous\natmosphere which absorbs the images of the objects existing in it,\nthan the nature of the objects, to send their images through the\nair. If the object opposite to the eye were to send its image to the\neye, the eye would have to do the same to the object, whence it\nmight seem that these images were an emanation. But, if so, it would\nbe necessary [to admit] that every object became rapidly smaller;\nbecause each object appears by its images in the surrounding\natmosphere. That is: the whole object in the whole atmosphere, and\nin each part; and all the objects in the whole atmosphere and all of\nthem in each part; speaking of that atmosphere which is able to\ncontain in itself the straight and radiating lines of the images\nprojected by the objects. From this it seems necessary to admit that\nit is in the nature of the atmosphere, which subsists between the\nobjects, and which attracts the images of things to itself like a\nloadstone, being placed between them.\n\nPROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE\nAND ALL IN EACH PART.\n\nI say that if the front of a building--or any open piazza or\nfield--which is illuminated by the sun has a dwelling opposite to\nit, and if, in the front which does not face the sun, you make a\nsmall round hole, all the illuminated objects will project their\nimages through that hole and be visible inside the dwelling on the\nopposite wall which may be made white; and there, in fact, they will\nbe upside down, and if you make similar openings in several places\nin the same wall you will have the same result from each. Hence the\nimages of the illuminated objects are all everywhere on this wall\nand all in each minutest part of it. The reason, as we clearly know,\nis that this hole must admit some light to the said dwelling, and\nthe light admitted by it is derived from one or many luminous\nbodies. If these bodies are of various colours and shapes the rays\nforming the images are of various colours and shapes, and so will\nthe representations be on the wall.\n\n[Footnote: 70. 15--23. This section has already been published in the\n\"_Saggio delle Opere di Leonardo da Vinci_\" Milan 1872, pp. 13, 14.\nG. Govi observes upon it, that Leonardo is not to be regarded as the\ninventor of the Camera obscura, but that he was the first to explain\nby it the structure of the eye. An account of the Camera obscura\nfirst occurs in CESARE CESARINI's Italian version of Vitruvius, pub.\n1523, four years after Leonardo's death. Cesarini expressly names\nBenedettino Don Papnutio as the inventor of the Camera obscura. In\nhis explanation of the function of the eye by a comparison with the\nCamera obscura Leonardo was the precursor of G. CARDANO, Professor\nof Medicine at Bologna (died 1576) and it appears highly probable\nthat this is, in fact, the very discovery which Leonardo ascribes to\nhimself in section 21 without giving any further details.]\n\n71.\n\nHOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE\nCRYSTALLINE HUMOUR OF THE EYE.\n\nAn experiment, showing how objects transmit their images or\npictures, intersecting within the eye in the crystalline humour, is\nseen when by some small round hole penetrate the images of\nilluminated objects into a very dark chamber. Then, receive these\nimages on a white paper placed within this dark room and rather near\nto the hole and you will see all the objects on the paper in their\nproper forms and colours, but much smaller; and they will be upside\ndown by reason of that very intersection. These images being\ntransmitted from a place illuminated by the sun will seem actually\npainted on this paper which must be extremely thin and looked at\nfrom behind. And let the little perforation be made in a very thin\nplate of iron. Let _a b e d e_ be the object illuminated by the sun\nand _o r_ the front of the dark chamber in which is the said hole at\n_n m_. Let _s t_ be the sheet of paper intercepting the rays of the\nimages of these objects upside down, because the rays being\nstraight, _a_ on the right hand becomes _k_ on the left, and _e_ on\nthe left becomes _f_ on the right; and the same takes place inside\nthe pupil.\n\n[Footnote: This chapter is already known through a translation into\nFrench by VENTURI. Compare his '_Essai sur les ouvrages\nphysico-math\u00e9matiques de L. da Vinci avec des fragments tir\u00e9s de ses\nManuscrits, apport\u00e9s de l'Italie. Lu a la premiere classe de\nl'Institut national des Sciences et Arts.' Paris, An V_ (1797).]\n\nThe practice of perspective (72. 73).\n\n72.\n\nIn the practice of perspective the same rules apply to light and to\nthe eye.\n\n73.\n\nThe object which is opposite to the pupil of the eye is seen by that\npupil and that which is opposite to the eye is seen by the pupil.\n\nRefraction of the rays falling upon the eye (74. 75)\n\n74.\n\nThe lines sent forth by the image of an object to the eye do not\nreach the point within the eye in straight lines.\n\n75.\n\nIf the judgment of the eye is situated within it, the straight lines\nof the images are refracted on its surface because they pass through\nthe rarer to the denser medium. If, when you are under water, you\nlook at objects in the air you will see them out of their true\nplace; and the same with objects under water seen from the air.\n\nThe intersection of the rays (76-82).\n\n76.\n\nThe inversion of the images.\n\nAll the images of objects which pass through a window [glass pane]\nfrom the free outer air to the air confined within walls, are seen\non the opposite side; and an object which moves in the outer air\nfrom east to west will seem in its shadow, on the wall which is\nlighted by this confined air, to have an opposite motion.\n\n77.\n\nTHE PRINCIPLE ON WHICH THE IMAGES OF BODIES PASS IN BETWEEN THE\nMARGINS OF THE OPENINGS BY WHICH THEY ENTER.\n\nWhat difference is there in the way in which images pass through\nnarrow openings and through large openings, or in those which pass\nby the sides of shaded bodies? By moving the edges of the opening\nthrough which the images are admitted, the images of immovable\nobjects are made to move. And this happens, as is shown in the 9th\nwhich demonstrates: [Footnote 11: _per la 9a che dicie_. When\nLeonardo refers thus to a number it serves to indicate marginal\ndiagrams; this can in some instances be distinctly proved. The ninth\nsketch on the page W. L. 145 b corresponds to the middle sketch of\nthe three reproduced.] the images of any object are all everywhere,\nand all in each part of the surrounding air. It follows that if one\nof the edges of the hole by which the images are admitted to a dark\nchamber is moved it cuts off those rays of the image that were in\ncontact with it and gets nearer to other rays which previously were\nremote from it &c.\n\nOF THE MOVEMENT OF THE EDGE AT THE RIGHT OR LEFT, OR THE UPPER, OR\nLOWER EDGE.\n\nIf you move the right side of the opening the image on the left will\nmove [being that] of the object which entered on the right side of\nthe opening; and the same result will happen with all the other\nsides of the opening. This can be proved by the 2nd of this which\nshows: all the rays which convey the images of objects through the\nair are straight lines. Hence, if the images of very large bodies\nhave to pass through very small holes, and beyond these holes\nrecover their large size, the lines must necessarily intersect.\n\n[Footnote: 77. 2. In the first of the three diagrams Leonardo had\ndrawn only one of the two margins, et _m_.]\n\n78.\n\nNecessity has provided that all the images of objects in front of\nthe eye shall intersect in two places. One of these intersections is\nin the pupil, the other in the crystalline lens; and if this were\nnot the case the eye could not see so great a number of objects as\nit does. This can be proved, since all the lines which intersect do\nso in a point. Because nothing is seen of objects excepting their\nsurface; and their edges are lines, in contradistinction to the\ndefinition of a surface. And each minute part of a line is equal to\na point; for _smallest_ is said of that than which nothing can be\nsmaller, and this definition is equivalent to the definition of the\npoint. Hence it is possible for the whole circumference of a circle\nto transmit its image to the point of intersection, as is shown in\nthe 4th of this which shows: all the smallest parts of the images\ncross each other without interfering with each other. These\ndemonstrations are to illustrate the eye. No image, even of the\nsmallest object, enters the eye without being turned upside down;\nbut as it penetrates into the crystalline lens it is once more\nreversed and thus the image is restored to the same position within\nthe eye as that of the object outside the eye.\n\n79.\n\nOF THE CENTRAL LINE OF THE EYE.\n\nOnly one line of the image, of all those that reach the visual\nvirtue, has no intersection; and this has no sensible dimensions\nbecause it is a mathematical line which originates from a\nmathematical point, which has no dimensions.\n\nAccording to my adversary, necessity requires that the central line\nof every image that enters by small and narrow openings into a dark\nchamber shall be turned upside down, together with the images of the\nbodies that surround it.\n\n80.\n\nAS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR\nNOT, WITHIN THE OPENING.\n\nIt is impossible that the line should intersect itself; that is,\nthat its right should cross over to its left side, and so, its left\nside become its right side. Because such an intersection demands two\nlines, one from each side; for there can be no motion from right to\nleft or from left to right in itself without such extension and\nthickness as admit of such motion. And if there is extension it is\nno longer a line but a surface, and we are investigating the\nproperties of a line, and not of a surface. And as the line, having\nno centre of thickness cannot be divided, we must conclude that the\nline can have no sides to intersect each other. This is proved by\nthe movement of the line _a f_ to _a b_ and of the line _e b_ to _e\nf_, which are the sides of the surface _a f e b_. But if you move\nthe line _a b_ and the line _e f_, with the frontends _a e_, to the\nspot _c_, you will have moved the opposite ends _f b_ towards each\nother at the point _d_. And from the two lines you will have drawn\nthe straight line _c d_ which cuts the middle of the intersection of\nthese two lines at the point _n_ without any intersection. For, you\nimagine these two lines as having breadth, it is evident that by\nthis motion the first will entirely cover the other--being equal\nwith it--without any intersection, in the position _c d_. And this\nis sufficient to prove our proposition.\n\n81.\n\nHOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A\nPOINT.\n\nJust as all lines can meet at a point without interfering with each\nother--being without breadth or thickness--in the same way all the\nimages of surfaces can meet there; and as each given point faces the\nobject opposite to it and each object faces an opposite point, the\nconverging rays of the image can pass through the point and diverge\nagain beyond it to reproduce and re-magnify the real size of that\nimage. But their impressions will appear reversed--as is shown in\nthe first, above; where it is said that every image intersects as it\nenters the narrow openings made in a very thin substance.\n\nRead the marginal text on the other side.\n\nIn proportion as the opening is smaller than the shaded body, so\nmuch less will the images transmitted through this opening intersect\neach other. The sides of images which pass through openings into a\ndark room intersect at a point which is nearer to the opening in\nproportion as the opening is narrower. To prove this let _a b_ be an\nobject in light and shade which sends not its shadow but the image\nof its darkened form through the opening _d e_ which is as wide as\nthis shaded body; and its sides _a b_, being straight lines (as has\nbeen proved) must intersect between the shaded object and the\nopening; but nearer to the opening in proportion as it is smaller\nthan the object in shade. As is shown, on your right hand and your\nleft hand, in the two diagrams _a_ _b_ _c_ _n_ _m_ _o_ where, the\nright opening _d_ _e_, being equal in width to the shaded object _a_\n_b_, the intersection of the sides of the said shaded object occurs\nhalf way between the opening and the shaded object at the point _c_.\nBut this cannot happen in the left hand figure, the opening _o_\nbeing much smaller than the shaded object _n_ _m_.\n\nIt is impossible that the images of objects should be seen between\nthe objects and the openings through which the images of these\nbodies are admitted; and this is plain, because where the atmosphere\nis illuminated these images are not formed visibly.\n\nWhen the images are made double by mutually crossing each other they\nare invariably doubly as dark in tone. To prove this let _d_ _e_ _h_\nbe such a doubling which although it is only seen within the space\nbetween the bodies in _b_ and _i_ this will not hinder its being\nseen from _f_ _g_ or from _f_ _m_; being composed of the images _a_\n_b_ _i_ _k_ which run together in _d_ _e_ _h_.\n\n[Footnote: 81. On the original diagram at the beginning of this\nchapter Leonardo has written \"_azurro_\" (blue) where in the\nfacsimile I have marked _A_, and \"_giallo_\" (yellow) where _B_\nstands.]\n\n[Footnote: 15--23. These lines stand between the diagrams I and III.]\n\n[Footnote: 24--53. These lines stand between the diagrams I and II.]\n\n[Footnote: 54--97 are written along the left side of diagram I.]\n\n82.\n\nAn experiment showing that though the pupil may not be moved from\nits position the objects seen by it may appear to move from their\nplaces.\n\nIf you look at an object at some distance from you and which is\nbelow the eye, and fix both your eyes upon it and with one hand\nfirmly hold the upper lid open while with the other you push up the\nunder lid--still keeping your eyes fixed on the object gazed at--you\nwill see that object double; one [image] remaining steady, and the\nother moving in a contrary direction to the pressure of your finger\non the lower eyelid. How false the opinion is of those who say that\nthis happens because the pupil of the eye is displaced from its\nposition.\n\nHow the above mentioned facts prove that the pupil acts upside down\nin seeing.\n\n[Footnote: 82. 14--17. The subject indicated by these two headings is\nfully discussed in the two chapters that follow them in the\noriginal; but it did not seem to me appropriate to include them\nhere.]\n\nDemostration of perspective by means of a vertical glass plane\n(83-85).\n\n83.\n\nOF THE PLANE OF GLASS.\n\nPerspective is nothing else than seeing place [or objects] behind a\nplane of glass, quite transparent, on the surface of which the\nobjects behind that glass are to be drawn. These can be traced in\npyramids to the point in the eye, and these pyramids are intersected\non the glass plane.\n\n84.\n\nPictorial perspective can never make an object at the same distance,\nlook of the same size as it appears to the eye. You see that the\napex of the pyramid _f c d_ is as far from the object _c_ _d_ as the\nsame point _f_ is from the object _a_ _b_; and yet _c_ _d_, which is\nthe base made by the painter's point, is smaller than _a_ _b_ which\nis the base of the lines from the objects converging in the eye and\nrefracted at _s_ _t_, the surface of the eye. This may be proved by\nexperiment, by the lines of vision and then by the lines of the\npainter's plumbline by cutting the real lines of vision on one and\nthe same plane and measuring on it one and the same object.\n\n85.\n\nPERSPECTIVE.\n\nThe vertical plane is a perpendicular line, imagined as in front of\nthe central point where the apex of the pyramids converge. And this\nplane bears the same relation to this point as a plane of glass\nwould, through which you might see the various objects and draw them\non it. And the objects thus drawn would be smaller than the\noriginals, in proportion as the distance between the glass and the\neye was smaller than that between the glass and the objects.\n\nPERSPECTIVE.\n\nThe different converging pyramids produced by the objects, will\nshow, on the plane, the various sizes and remoteness of the objects\ncausing them.\n\nPERSPECTIVE.\n\nAll those horizontal planes of which the extremes are met by\nperpendicular lines forming right angles, if they are of equal width\nthe more they rise to the level of eye the less this is seen, and\nthe more the eye is above them the more will their real width be\nseen.\n\nPERSPECTIVE.\n\nThe farther a spherical body is from the eye the more you will see\nof it.\n\nThe angle of sight varies with the distance (86-88)\n\n86.\n\nA simple and natural method; showing how objects appear to the eye\nwithout any other medium.\n\nThe object that is nearest to the eye always seems larger than\nanother of the same size at greater distance. The eye _m_, seeing\nthe spaces _o v x_, hardly detects the difference between them, and\nthe. reason of this is that it is close to them [Footnote 6: It is\nquite inconceivable to me why M. RAVAISSON, in a note to his French\ntranslation of this simple passage should have remarked: _Il est\nclair que c'est par erreur que Leonard a \u00e8crit_ per esser visino _au\nlieu de_ per non esser visino. (See his printed ed. of MS. A. p.\n38.)]; but if these spaces are marked on the vertical plane _n o_\nthe space _o v_ will be seen at _o r_, and in the same way the space\n_v x_ will appear at _r q_. And if you carry this out in any place\nwhere you can walk round, it will look out of proportion by reason\nof the great difference in the spaces _o r_ and _r q_. And this\nproceeds from the eye being so much below [near] the plane that the\nplane is foreshortened. Hence, if you wanted to carry it out, you\nwould have [to arrange] to see the perspective through a single hole\nwhich must be at the point _m_, or else you must go to a distance of\nat least 3 times the height of the object you see. The plane _o p_\nbeing always equally remote from the eye will reproduce the objects\nin a satisfactory way, so that they may be seen from place to place.\n\n87.\n\nHow every large mass sends forth its images, which may diminish\nthrough infinity.\n\nThe images of any large mass being infinitely divisible may be\ninfinitely diminished.\n\n88.\n\nObjects of equal size, situated in various places, will be seen by\ndifferent pyramids which will each be smaller in proportion as the\nobject is farther off.\n\n89.\n\nPerspective, in dealing with distances, makes use of two opposite\npyramids, one of which has its apex in the eye and the base as\ndistant as the horizon. The other has the base towards the eye and\nthe apex on the horizon. Now, the first includes the [visible]\nuniverse, embracing all the mass of the objects that lie in front of\nthe eye; as it might be a vast landscape seen through a very small\nopening; for the more remote the objects are from the eye, the\ngreater number can be seen through the opening, and thus the pyramid\nis constructed with the base on the horizon and the apex in the eye,\nas has been said. The second pyramid is extended to a spot which is\nsmaller in proportion as it is farther from the eye; and this second\nperspective [= pyramid] results from the first.\n\n90.\n\nSIMPLE PERSPECTIVE.\n\nSimple perspective is that which is constructed by art on a vertical\nplane which is equally distant from the eye in every part. Complex\nperspective is that which is constructed on a ground-plan in which\nnone of the parts are equally distant from the eye.\n\n91.\n\nPERSPECTIVE.\n\nNo surface can be seen exactly as it is, if the eye that sees it is\nnot equally remote from all its edges.\n\n92.\n\nWHY WHEN AN OBJECT IS PLACED CLOSE TO THE EYE ITS EDGES ARE\nINDISTINCT.\n\nWhen an object opposite the eye is brought too close to it, its\nedges must become too confused to be distinguished; as it happens\nwith objects close to a light, which cast a large and indistinct\nshadow, so is it with an eye which estimates objects opposite to it;\nin all cases of linear perspective, the eye acts in the same way as\nthe light. And the reason is that the eye has one leading line (of\nvision) which dilates with distance and embraces with true\ndiscernment large objects at a distance as well as small ones that\nare close. But since the eye sends out a multitude of lines which\nsurround this chief central one and since these which are farthest\nfrom the centre in this cone of lines are less able to discern with\naccuracy, it follows that an object brought close to the eye is not\nat a due distance, but is too near for the central line to be able\nto discern the outlines of the object. So the edges fall within the\nlines of weaker discerning power, and these are to the function of\nthe eye like dogs in the chase which can put up the game but cannot\ntake it. Thus these cannot take in the objects, but induce the\ncentral line of sight to turn upon them, when they have put them up.\nHence the objects which are seen with these lines of sight have\nconfused outlines.\n\nThe relative size of objects with regard to their distance from the\neye (93-98).\n\n93.\n\nPERSPECTIVE.\n\nSmall objects close at hand and large ones at a distance, being seen\nwithin equal angles, will appear of the same size.\n\n94.\n\nPERSPECTIVE.\n\nThere is no object so large but that at a great distance from the\neye it does not appear smaller than a smaller object near.\n\n95.\n\nAmong objects of equal size that which is most remote from the eye\nwill look the smallest. [Footnote: This axiom, sufficiently clear in\nitself, is in the original illustrated by a very large diagram,\nconstructed like that here reproduced under No. 108.\n\nThe same idea is repeated in C. A. I a; I a, stated as follows:\n_Infra le cose d'equal grandeza quella si dimostra di minor figura\nche sara pi\u00f9 distante dall' ochio_.--]\n\n96.\n\nWhy an object is less distinct when brought near to the eye, and why\nwith spectacles, or without the naked eye sees badly either close or\nfar off [as the case may be].\n\n97.\n\nPERSPECTIVE.\n\nAmong objects of equal size, that which is most remote from the eye\nwill look the smallest.\n\n98.\n\nPERSPECTIVE.\n\nNo second object can be so much lower than the first as that the eye\nwill not see it higher than the first, if the eye is above the\nsecond.\n\nPERSPECTIVE.\n\nAnd this second object will never be so much higher than the first\nas that the eye, being below them, will not see the second as lower\nthan the first.\n\nPERSPECTIVE.\n\nIf the eye sees a second square through the centre of a smaller one,\nthat is nearer, the second, larger square will appear to be\nsurrounded by the smaller one.\n\nPERSPECTIVE--PROPOSITION.\n\nObjects that are farther off can never be so large but that those in\nfront, though smaller, will conceal or surround them.\n\nDEFINITION.\n\nThis proposition can be proved by experiment. For if you look\nthrough a small hole there is nothing so large that it cannot be\nseen through it and the object so seen appears surrounded and\nenclosed by the outline of the sides of the hole. And if you stop it\nup, this small stopping will conceal the view of the largest object.\n\nThe apparent size of objects defined by calculation (99-105)\n\n99.\n\nOF LINEAR PERSPECTIVE.\n\nLinear Perspective deals with the action of the lines of sight, in\nproving by measurement how much smaller is a second object than the\nfirst, and how much the third is smaller than the second; and so on\nby degrees to the end of things visible. I find by experience that\nif a second object is as far beyond the first as the first is from\nthe eye, although they are of the same size, the second will seem\nhalf the size of the first and if the third object is of the same\nsize as the 2nd, and the 3rd is as far beyond the second as the 2nd\nfrom the first, it will appear of half the size of the second; and\nso on by degrees, at equal distances, the next farthest will be half\nthe size of the former object. So long as the space does not exceed\nthe length of 20 braccia. But, beyond 20 braccia figures of equal\nsize will lose 2/4 and at 40 braccia they will lose 9/10, and 19/20\nat 60 braccia, and so on diminishing by degrees. This is if the\npicture plane is distant from you twice your own height. If it is\nonly as far off as your own height, there will be a great difference\nbetween the first braccia and the second.\n\n[Footnote: This chapter is included in DUFRESNE'S and MANZI'S\neditions of the Treatise on Painting. H. LUDWIG, in his commentary,\ncalls this chapter \"_eines der wichtigsten im ganzen Tractat_\", but\nat the same time he asserts that its substance has been so\ncompletely disfigured in the best MS. copies that we ought not to\nregard Leonardo as responsible for it. However, in the case of this\nchapter, the old MS. copies agree with the original as it is\nreproduced above. From the chapters given later in this edition,\nwhich were written at a subsequent date, it would appear that\nLeonardo corrected himself on these points.]\n\n100.\n\nOF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES.\n\nA second object as far distant from the first as the first is from\nthe eye will appear half the size of the first, though they be of\nthe same size really.\n\nOF THE DEGREES OF DIMINUTION.\n\nIf you place the vertical plane at one braccio from the eye, the\nfirst object, being at a distance of 4 braccia from your eye will\ndiminish to 3/4 of its height at that plane; and if it is 8 braccia\nfrom the eye, to 7/8; and if it is 16 braccia off, it will diminish\nto 15/16 of its height and so on by degrees, as the space doubles\nthe diminution will double.\n\n101.\n\nBegin from the line _m f_ with the eye below; then go up and do the\nsame with the line _n f_, then with the eye above and close to the 2\ngauges on the ground look at _m n_; then as _c m_ is to _m n_ so\nwill _n m_ be to _n s_.\n\nIf _a n_ goes 3 times into _f b, m p_ will do the same into _p g_.\nThen go backwards so far as that _c d_ goes twice into _a n_ and _p\ng_ will be equal to _g h_. And _m p_ will go into _h p_ as often as\n_d c_ into _o p_.\n\n[Footnote: The first three lines are unfortunately very obscure.]\n\n102.\n\nI GIVE THE DEGREES OF THE OBJECTS SEEN BY THE EYE AS THE MUSICIAN\nDOES THE NOTES HEARD BY THE EAR.\n\nAlthough the objects seen by the eye do, in fact, touch each other\nas they recede, I will nevertheless found my rule on spaces of 20\nbraccia each; as a musician does with notes, which, though they can\nbe carried on one into the next, he divides into degrees from note\nto note calling them 1st, 2nd, 3rd, 4th, 5th; and has affixed a name\nto each degree in raising or lowering the voice.\n\n103.\n\nPERSPECTIVE.\n\nLet _f_ be the level and distance of the eye; and _a_ the vertical\nplane, as high as a man; let _e_ be a man, then I say that on the\nplane this will be the distance from the plane to the 2nd man.\n\n104.\n\nThe differences in the diminution of objects of equal size in\nconsequence of their various remoteness from the eye will bear among\nthemselves the same proportions as those of the spaces between the\neye and the different objects.\n\nFind out how much a man diminishes at a certain distance and what\nits length is; and then at twice that distance and at 3 times, and\nso make your general rule.\n\n105.\n\nThe eye cannot judge where an object high up ought to descend.\n\n106.\n\nPERSPECTIVE.\n\nIf two similar and equal objects are placed one beyond the other at\na given distance the difference in their size will appear greater in\nproportion as they are nearer to the eye that sees them. And\nconversely there will seem to be less difference in their size in\nproportion as they are remote from the eve.\n\nThis is proved by the proportions of their distances among\nthemselves; for, if the first of these two objects were as far from\nthe eye, as the 2nd from the first this would be called the second\nproportion: since, if the first is at 1 braccia from the eye and the\n2nd at two braccia, two being twice as much as one, the first object\nwill look twice as large as the second. But if you place the first\nat a hundred braccia from you and the second at a hundred and one,\nyou will find that the first is only so much larger than the second\nas 100 is less than 101; and the converse is equally true. And\nagain, the same thing is proved by the 4th of this book which shows\nthat among objects that are equal, there is the same proportion in\nthe diminution of the size as in the increase in the distance from\nthe eye of the spectator.\n\nOn natural perspective (107--109).\n\n107.\n\nOF EQUAL OBJECTS THE MOST REMOTE LOOK THE SMALLEST.\n\nThe practice of perspective may be divided into ... parts [Footnote\n4: _in_ ... _parte_. The space for the number is left blank in the\noriginal.], of which the first treats of objects seen by the eye at\nany distance; and it shows all these objects just as the eye sees\nthem diminished, without obliging a man to stand in one place rather\nthan another so long as the plane does not produce a second\nforeshortening.\n\nBut the second practice is a combination of perspective derived\npartly from art and partly from nature and the work done by its\nrules is in every portion of it, influenced by natural perspective\nand artificial perspective. By natural perspective I mean that the\nplane on which this perspective is represented is a flat surface,\nand this plane, although it is parallel both in length and height,\nis forced to diminish in its remoter parts more than in its nearer\nones. And this is proved by the first of what has been said above,\nand its diminution is natural. But artificial perspective, that is\nthat which is devised by art, does the contrary; for objects equal\nin size increase on the plane where it is foreshortened in\nproportion as the eye is more natural and nearer to the plane, and\nas the part of the plane on which it is figured is farther from the\neye.\n\nAnd let this plane be _d e_ on which are seen 3 equal circles which\nare beyond this plane _d e_, that is the circles _a b c_. Now you\nsee that the eye _h_ sees on the vertical plane the sections of the\nimages, largest of those that are farthest and smallest of the\nnearest.\n\n108.\n\nHere follows what is wanting in the margin at the foot on the other\nside of this page.\n\nNatural perspective acts in a contrary way; for, at greater\ndistances the object seen appears smaller, and at a smaller distance\nthe object appears larger. But this said invention requires the\nspectator to stand with his eye at a small hole and then, at that\nsmall hole, it will be very plain. But since many (men's) eyes\nendeavour at the same time to see one and the same picture produced\nby this artifice only one can see clearly the effect of this\nperspective and all the others will see confusion. It is well\ntherefore to avoid such complex perspective and hold to simple\nperspective which does not regard planes as foreshortened, but as\nmuch as possible in their proper form. This simple perspective, in\nwhich the plane intersects the pyramids by which the images are\nconveyed to the eye at an equal distance from the eye is our\nconstant experience, from the curved form of the pupil of the eye on\nwhich the pyramids are intersected at an equal distance from the\nvisual virtue.\n\n[Footnote 24: _la prima di sopra_ i. e. the first of the three\ndiagrams which, in the original MS., are placed in the margin at the\nbeginning of this chapter.]\n\n109.\n\nOF A MIXTURE OF NATURAL AND ARTIFICIAL PERSPECTIVE.\n\nThis diagram distinguishes natural from artificial perspective. But\nbefore proceeding any farther I will define what is natural and what\nis artificial perspective. Natural perspective says that the more\nremote of a series of objects of equal size will look the smaller,\nand conversely, the nearer will look the larger and the apparent\nsize will diminish in proportion to the distance. But in artificial\nperspective when objects of unequal size are placed at various\ndistances, the smallest is nearer to the eye than the largest and\nthe greatest distance looks as though it were the least of all; and\nthe cause of this is the plane on which the objects are represented;\nand which is at unequal distances from the eye throughout its\nlength. And this diminution of the plane is natural, but the\nperspective shown upon it is artificial since it nowhere agrees with\nthe true diminution of the said plane. Whence it follows, that when\nthe eye is somewhat removed from the [station point of the]\nperspective that it has been gazing at, all the objects represented\nlook monstrous, and this does not occur in natural perspective,\nwhich has been defined above. Let us say then, that the square _a b\nc d_ figured above is foreshortened being seen by the eye situated\nin the centre of the side which is in front. But a mixture of\nartificial and natural perspective will be seen in this tetragon\ncalled _el main_ [Footnote 20: _el main_ is quite legibly written in\nthe original; the meaning and derivation of the word are equally\ndoubtful.], that is to say _e f g h_ which must appear to the eye of\nthe spectator to be equal to _a b c d_ so long as the eye remains in\nits first position between _c_ and _d_. And this will be seen to\nhave a good effect, because the natural perspective of the plane\nwill conceal the defects which would [otherwise] seem monstrous.\n\n_III._\n\n_Six books on Light and Shade._\n\n_Linear Perspective cannot be immediately followed by either the_\n\"prospettiva de' perdimenti\" _or the_ \"prospettiva de' colori\" _or\nthe aerial perspective; since these branches of the subject\npresuppose a knowledge of the principles of Light and Shade. No\napology, therefore, is here needed for placing these immediately\nafter Linear Perspective._\n\n_We have various plans suggested by Leonardo for the arrangement of\nthe mass of materials treating of this subject. Among these I have\ngiven the preference to a scheme propounded in No._ III, _because,\nin all probability, we have here a final and definite purpose\nexpressed. Several authors have expressed it as their opinion that\nthe Paris Manuscript_ C _is a complete and finished treatise on\nLight and Shade. Certainly, the Principles of Light and Shade form\nby far the larger portion of this MS. which consists of two separate\nparts; still, the materials are far from being finally arranged. It\nis also evident that he here investigates the subject from the point\nof view of the Physicist rather than from that of the Painter._\n\n_The plan of a scheme of arrangement suggested in No._ III _and\nadopted by me has been strictly adhered to for the first four Books.\nFor the three last, however, few materials have come down to us; and\nit must be admitted that these three Books would find a far more\nappropriate place in a work on Physics than in a treatise on\nPainting. For this reason I have collected in Book V all the\nchapters on Reflections, and in Book VI I have put together and\narranged all the sections of MS._ C _that belong to the book on\nPainting, so far as they relate to Light and Shade, while the\nsections of the same MS. which treat of the_ \"Prospettiva de'\nperdimenti\" _have, of course, been excluded from the series on Light\nand Shade._\n\n[Footnote III: This text has already been published with some slight\nvariations in Dozio's pamphlet _Degli scritti e disegni di Leonardo\nda Vinci_, Milan 1871, pp. 30--31. Dozio did not transcribe it from\nthe original MS. which seems to have remained unknown to him, but\nfrom an old copy (MS. H. 227 in the Ambrosian Library).]\n\nGENERAL INTRODUCTION.\n\nProlegomena.\n\n110.\n\nYou must first explain the theory and then the practice. First you\nmust describe the shadows and lights on opaque objects, and then on\ntransparent bodies.\n\nScheme of the books on Light and shade.\n\n111.\n\nINTRODUCTION.\n\n[Having already treated of the nature of shadows and the way in\nwhich they are cast [Footnote 2: _Avendo io tractato._--We may\nsuppose that he here refers to some particular MS., possibly Paris\nC.], I will now consider the places on which they fall; and their\ncurvature, obliquity, flatness or, in short, any character I may be\nable to detect in them.]\n\nShadow is the obstruction of light. Shadows appear to me to be of\nsupreme importance in perspective, because, without them opaque and\nsolid bodies will be ill defined; that which is contained within\ntheir outlines and their boundaries themselves will be\nill-understood unless they are shown against a background of a\ndifferent tone from themselves. And therefore in my first\nproposition concerning shadow I state that every opaque body is\nsurrounded and its whole surface enveloped in shadow and light. And\non this proposition I build up the first Book. Besides this, shadows\nhave in themselves various degrees of darkness, because they are\ncaused by the absence of a variable amount of the luminous rays; and\nthese I call Primary shadows because they are the first, and\ninseparable from the object to which they belong. And on this I will\nfound my second Book. From these primary shadows there result\ncertain shaded rays which are diffused through the atmosphere and\nthese vary in character according to that of the primary shadows\nwhence they are derived. I shall therefore call these shadows\nDerived shadows because they are produced by other shadows; and the\nthird Book will treat of these. Again these derived shadows, where\nthey are intercepted by various objects, produce effects as various\nas the places where they are cast and of this I will treat in the\nfourth Book. And since all round the derived shadows, where the\nderived shadows are intercepted, there is always a space where the\nlight falls and by reflected dispersion is thrown back towards its\ncause, it meets the original shadow and mingles with it and modifies\nit somewhat in its nature; and on this I will compose my fifth Book.\nBesides this, in the sixth Book I will investigate the many and\nvarious diversities of reflections resulting from these rays which\nwill modify the original [shadow] by [imparting] some of the various\ncolours from the different objects whence these reflected rays are\nderived. Again, the seventh Book will treat of the various distances\nthat may exist between the spot where the reflected rays fall and\nthat where they originate, and the various shades of colour which\nthey will acquire in falling on opaque bodies.\n\nDifferent principles and plans of treatment (112--116).\n\n112.\n\nFirst I will treat of light falling through windows which I will\ncall Restricted [Light] and then I will treat of light in the open\ncountry, to which I will give the name of diffused Light. Then I\nwill treat of the light of luminous bodies.\n\n113.\n\nOF PAINTING.\n\nThe conditions of shadow and light [as seen] by the eye are 3. Of\nthese the first is when the eye and the light are on the same side\nof the object seen; the 2nd is when the eye is in front of the\nobject and the light is behind it. The 3rd is when the eye is in\nfront of the object and the light is on one side, in such a way as\nthat a line drawn from the object to the eye and one from the object\nto the light should form a right angle where they meet.\n\n114.\n\nOF PAINTING.\n\nThis is another section: that is, of the nature of a reflection\n(from) an object placed between the eye and the light under various\naspects.\n\n115.\n\nOF PAINTING.\n\nAs regards all visible objects 3 things must be considered. These\nare the position of the eye which sees: that of the object seen\n[with regard] to the light, and the position of the light which\nilluminates the object, _b_ is the eye, _a_ the object seen, _c_ the\nlight, _a_ is the eye, _b_ the illuminating body, _c_ is the\nilluminated object.\n\n116.\n\nLet _a_ be the light, _b_ the eye, _c_ the object seen by the eye\nand in the light. These show, first, the eye between the light and\nthe body; the 2nd, the light between the eye and the body; the 3rd\nthe body between the eye and the light, _a_ is the eye, _b_ the\nilluminated object, _c_ the light.\n\n117.\n\nOF PAINTING.\n\nOF THE THREE KINDS OF LIGHT THAT ILLUMINATE OPAQUE BODIES.\n\nThe first kind of Light which may illuminate opaque bodies is called\nDirect light--as that of the sun or any other light from a window or\nflame. The second is Diffused [universal] light, such as we see in\ncloudy weather or in mist and the like. The 3rd is Subdued light,\nthat is when the sun is entirely below the horizon, either in the\nevening or morning.\n\n118.\n\nOF LIGHT.\n\nThe lights which may illuminate opaque bodies are of 4 kinds. These\nare: diffused light as that of the atmosphere, within our horizon.\nAnd Direct, as that of the sun, or of a window or door or other\nopening. The third is Reflected light; and there is a 4th which is\nthat which passes through [semi] transparent bodies, as linen or\npaper or the like, but not transparent like glass, or crystal, or\nother diaphanous bodies, which produce the same effect as though\nnothing intervened between the shaded object and the light that\nfalls upon it; and this we will discuss fully in our discourse.\n\nDefinition of the nature of shadows (119--122).\n\n119.\n\nWHAT LIGHT AND SHADOW ARE.\n\nShadow is the absence of light, merely the obstruction of the\nluminous rays by an opaque body. Shadow is of the nature of\ndarkness. Light [on an object] is of the nature of a luminous body;\none conceals and the other reveals. They are always associated and\ninseparable from all objects. But shadow is a more powerful agent\nthan light, for it can impede and entirely deprive bodies of their\nlight, while light can never entirely expel shadow from a body, that\nis from an opaque body.\n\n120.\n\nShadow is the diminution of light by the intervention of an opaque\nbody. Shadow is the counterpart of the luminous rays which are cut\noff by an opaque body.\n\nThis is proved because the shadow cast is the same in shape and size\nas the luminous rays were which are transformed into a shadow.\n\n121.\n\nShadow is the diminution alike of light and of darkness, and stands\nbetween darkness and light.\n\nA shadow may be infinitely dark, and also of infinite degrees of\nabsence of darkness.\n\nThe beginnings and ends of shadow lie between the light and darkness\nand may be infinitely diminished and infinitely increased. Shadow is\nthe means by which bodies display their form.\n\nThe forms of bodies could not be understood in detail but for\nshadow.\n\n122.\n\nOF THE NATURE OF SHADOW.\n\nShadow partakes of the nature of universal matter. All such matters\nare more powerful in their beginning and grow weaker towards the\nend, I say at the beginning, whatever their form or condition may be\nand whether visible or invisible. And it is not from small\nbeginnings that they grow to a great size in time; as it might be a\ngreat oak which has a feeble beginning from a small acorn. Yet I may\nsay that the oak is most powerful at its beginning, that is where it\nsprings from the earth, which is where it is largest (To return:)\nDarkness, then, is the strongest degree of shadow and light is its\nleast. Therefore, O Painter, make your shadow darkest close to the\nobject that casts it, and make the end of it fading into light,\nseeming to have no end.\n\nOf the various kinds of shadows. (123-125).\n\n123.\n\nDarkness is absence of light. Shadow is diminution of light.\nPrimitive shadow is that which is inseparable from a body not in the\nlight. Derived shadow is that which is disengaged from a body in\nshadow and pervades the air. A cast transparent shadow is that which\nis surrounded by an illuminated surface. A simple shadow is one\nwhich receives no light from the luminous body which causes it. A\nsimple shadow begins within the line which starts from the edge of\nthe luminous body _a b_.\n\n124.\n\nA simple shadow is one where no light at all interferes with it.\n\nA compound shadow is one which is somewhat illuminated by one or\nmore lights.\n\n125.\n\nWHAT IS THE DIFFERENCE BETWEEN A SHADOW THAT IS INSEPARABLE FROM A\nBODY AND A CAST SHADOW?\n\nAn inseparable shadow is that which is never absent from the\nilluminated body. As, for instance a ball, which so long as it is in\nthe light always has one side in shadow which never leaves it for\nany movement or change of position in the ball. A separate shadow\nmay be and may not be produced by the body itself. Suppose the ball\nto be one braccia distant from a wall with a light on the opposite\nside of it; this light will throw upon the wall exactly as broad a\nshadow as is to be seen on the side of the ball that is turned\ntowards the wall. That portion of the cast shadow will not be\nvisible when the light is below the ball and the shadow is thrown up\ntowards the sky and finding no obstruction on its way is lost.\n\n126.\n\nHOW THERE ARE 2 KINDS OF LIGHT, ONE SEPARABLE FROM, AND THE OTHER\nINSEPARABLE FROM BODIES.\n\nOf the various kinds of light (126, 127).\n\nSeparate light is that which falls upon the body. Inseparable light\nis the side of the body that is illuminated by that light. One is\ncalled primary, the other derived. And, in the same way there are\ntwo kinds of shadow:--One primary and the other derived. The primary\nis that which is inseparable from the body, the derived is that\nwhich proceeds from the body conveying to the surface of the wall\nthe form of the body causing it.\n\n127.\n\nHow there are 2 different kinds of light; one being called diffused,\nthe other restricted. The diffused is that which freely illuminates\nobjects. The restricted is that which being admitted through an\nopening or window illuminates them on that side only.\n\n[Footnote: At the spot marked _A_ in the first diagram Leonardo\nwrote _lume costretto_ (restricted light). At the spot _B_ on the\nsecond diagram he wrote _lume libero_ (diffused light).]\n\nGeneral remarks (128. 129).\n\n128.\n\nLight is the chaser away of darkness. Shade is the obstruction of\nlight. Primary light is that which falls on objects and causes light\nand shade. And derived lights are those portions of a body which are\nilluminated by the primary light. A primary shadow is that side of a\nbody on which the light cannot fall.\n\nThe general distribution of shadow and light is that sum total of\nthe rays thrown off by a shaded or illuminated body passing through\nthe air without any interference and the spot which intercepts and\ncuts off the distribution of the dark and light rays.\n\nAnd the eye can best distinguish the forms of objects when it is\nplaced between the shaded and the illuminated parts.\n\n129.\n\nMEMORANDUM OF THINGS I REQUIRE TO HAVE GRANTED [AS AXIOMS] IN MY\nEXPLANATION OF PERSPECTIVE.\n\nI ask to have this much granted me--to assert that every ray\npassing through air of equal density throughout, travels in a\nstraight line from its cause to the object or place it falls upon.\n\nFIRST BOOK ON LIGHT AND SHADE.\n\nOn the nature of light (130. 131).\n\n130.\n\nThe reason by which we know that a light radiates from a single\ncentre is this: We plainly see that a large light is often much\nbroader than some small object which nevertheless--and although the\nrays [of the large light] are much more than twice the extent [of\nthe small body]--always has its shadow cast on the nearest surface\nvery visibly. Let _c f_ be a broad light and _n_ be the object in\nfront of it, casting a shadow on the plane, and let _a b_ be the\nplane. It is clear that it is not the broad light that will cast the\nshadow _n_ on the plane, but that the light has within it a centre\nis shown by this experiment. The shadow falls on the plane as is\nshown at _m o t r_.\n\n[Footnote 13: In the original MS. no explanatory text is placed\nafter this title-line; but a space is left for it and the text\nbeginning at line 15 comes next.] Why, to two [eyes] or in front of\ntwo eyes do 3 objects appear as two?\n\nWhy, when you estimate the direction of an object with two sights\nthe nearer appears confused. I say that the eye projects an infinite\nnumber of lines which mingle or join those reaching it which come to\nit from the object looked at. And it is only the central and\nsensible line that can discern and discriminate colours and objects;\nall the others are false and illusory. And if you place 2 objects at\nhalf an arm's length apart if the nearer of the two is close to the\neye its form will remain far more confused than that of the second;\nthe reason is that the first is overcome by a greater number of\nfalse lines than the second and so is rendered vague.\n\nLight acts in the same manner, for in the effects of its lines\n(=rays), and particularly in perspective, it much resembles the eye;\nand its central rays are what cast the true shadow. When the object\nin front of it is too quickly overcome with dim rays it will cast a\nbroad and disproportionate shadow, ill defined; but when the object\nwhich is to cast the shadow and cuts off the rays near to the place\nwhere the shadow falls, then the shadow is distinct; and the more so\nin proportion as the light is far off, because at a long distance\nthe central ray is less overcome by false rays; because the lines\nfrom the eye and the solar and other luminous rays passing through\nthe atmosphere are obliged to travel in straight lines. Unless they\nare deflected by a denser or rarer air, when they will be bent at\nsome point, but so long as the air is free from grossness or\nmoisture they will preserve their direct course, always carrying the\nimage of the object that intercepts them back to their point of\norigin. And if this is the eye, the intercepting object will be seen\nby its colour, as well as by form and size. But if the intercepting\nplane has in it some small perforation opening into a darker\nchamber--not darker in colour, but by absence of light--you will see\nthe rays enter through this hole and transmitting to the plane\nbeyond all the details of the object they proceed from both as to\ncolour and form; only every thing will be upside down. But the size\n[of the image] where the lines are reconstructed will be in\nproportion to the relative distance of the aperture from the plane\non which the lines fall [on one hand] and from their origin [on the\nother]. There they intersect and form 2 pyramids with their point\nmeeting [a common apex] and their bases opposite. Let _a b_ be the\npoint of origin of the lines, _d e_ the first plane, and _c_ the\naperture with the intersection of the lines; _f g_ is the inner\nplane. You will find that _a_ falls upon the inner plane below at\n_g_, and _b_ which is below will go up to the spot _f_; it will be\nquite evident to experimenters that every luminous body has in\nitself a core or centre, from which and to which all the lines\nradiate which are sent forth by the surface of the luminous body and\nreflected back to it; or which, having been thrown out and not\nintercepted, are dispersed in the air.\n\n131.\n\nTHE RAYS WHETHER SHADED OR LUMINOUS HAVE GREATER STRENGTH AND EFFECT\nAT THEIR POINTS THAN AT THEIR SIDES.\n\nAlthough the points of luminous pyramids may extend into shaded\nplaces and those of pyramids of shadow into illuminated places, and\nthough among the luminous pyramids one may start from a broader base\nthan another; nevertheless, if by reason of their various length\nthese luminous pyramids acquire angles of equal size their light\nwill be equal; and the case will be the same with the pyramids of\nshadow; as may be seen in the intersected pyramids _a b c_ and _d e\nf_, which though their bases differ in size are equal as to breadth\nand light.\n\n[Footnote: 51--55: This supplementary paragraph is indicated as being\na continuation of line 45, by two small crosses.]\n\nThe difference between light and lustre (132--135).\n\n132.\n\nOf the difference between light and lustre; and that lustre is not\nincluded among colours, but is saturation of whiteness, and derived\nfrom the surface of wet bodies; light partakes of the colour of the\nobject which reflects it (to the eye) as gold or silver or the like.\n\n133.\n\nOF THE HIGHEST LIGHTS WHICH TURN AND MOVE AS THE EYE MOVES WHICH\nSEES THE OBJECT.\n\nSuppose the body to be the round object figured here and let the\nlight be at the point _a_, and let the illuminated side of the\nobject be _b c_ and the eye at the point _d_: I say that, as lustre\nis every where and complete in each part, if you stand at the point\n_d_ the lustre will appear at _c_, and in proportion as the eye\nmoves from _d_ to _a_, the lustre will move from _c_ to _n_.\n\n134.\n\nOF PAINTING.\n\nHeigh light or lustre on any object is not situated [necessarily] in\nthe middle of an illuminated object, but moves as and where the eye\nmoves in looking at it.\n\n135.\n\nOF LIGHT AND LUSTRE.\n\nWhat is the difference between light and the lustre which is seen on\nthe polished surface of opaque bodies?\n\nThe lights which are produced from the polished surface of opaque\nbodies will be stationary on stationary objects even if the eye on\nwhich they strike moves. But reflected lights will, on those same\nobjects, appear in as many different places on the surface as\ndifferent positions are taken by the eye.\n\nWHAT BODIES HAVE LIGHT UPON THEM WITHOUT LUSTRE?\n\nOpaque bodies which have a hard and rough surface never display any\nlustre in any portion of the side on which the light falls.\n\nWHAT BODIES WILL DISPLAY LUSTRE BUT NOT LOOK ILLUMINATED?\n\nThose bodies which are opaque and hard with a hard surface reflect\nlight [lustre] from every spot on the illuminated side which is in a\nposition to receive light at the same angle of incidence as they\noccupy with regard to the eye; but, as the surface mirrors all the\nsurrounding objects, the illuminated [body] is not recognisable in\nthese portions of the illuminated body.\n\n136.\n\nThe relations of luminous to illuminated bodies.\n\nThe middle of the light and shade on an object in light and shade is\nopposite to the middle of the primary light. All light and shadow\nexpresses itself in pyramidal lines. The middle of the shadow on any\nobject must necessarily be opposite the middle of its light, with a\ndirect line passing through the centre of the body. The middle of\nthe light will be at _a_, that of the shadow at _b_. [Again, in\nbodies shown in light and shade the middle of each must coincide\nwith the centre of the body, and a straight line will pass through\nboth and through that centre.]\n\n[Footnote: In the original MS., at the spot marked _a_ of the first\ndiagram Leonardo wrote _primitiuo_, and at the spot marked\n_c_--_primitiva_ (primary); at the spot marked _b_ he wrote\n_dirivatiuo_ and at _d deriuatiua_ (derived).]\n\nExperiments on the relation of light and shadow within a room\n(137--140).\n\n137.\n\nSHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT.\n\nAlthough the balls _a b c_ are lighted from one window,\nnevertheless, if you follow the lines of their shadows you will see\nthey intersect at a point forming the angle _n_.\n\n[Footnote: The diagram belonging to this passage is slightly\nsketched on Pl. XXXII; a square with three balls below it. The first\nthree lines of the text belonging to it are written above the sketch\nand the six others below it.]\n\n138.\n\nEvery shadow cast by a body has a central line directed to a single\npoint produced by the intersection of luminous lines in the middle\nof the opening and thickness of the window. The proposition stated\nabove, is plainly seen by experiment. Thus if you draw a place with\na window looking northwards, and let this be _s f_, you will see a\nline starting from the horizon to the east, which, touching the 2\nangles of the window _o f_, reaches _d_; and from the horizon on the\nwest another line, touching the other 2 angles _r s_, and ending at\n_c_; and their intersection falls exactly in the middle of the\nopening and thickness of the window. Again, you can still better\nconfirm this proof by placing two sticks, as shown at _g h_; and you\nwill see the line drawn from the centre of the shadow directed to\nthe centre _m_ and prolonged to the horizon _n f_.\n\n[Footnote: _B_ here stands for _cerchio del' orizonte tramontano_ on\nthe original diagram (the circle of the horizon towards the North);\n_A_ for _levante_ (East) and _C_ for _ponete_ (West).]\n\n139.\n\nEvery shadow with all its variations, which becomes larger as its\ndistance from the object is greater, has its external lines\nintersecting in the middle, between the light and the object. This\nproposition is very evident and is confirmed by experience. For, if\n_a b_ is a window without any object interposed, the luminous\natmosphere to the right hand at _a_ is seen to the left at _d_. And\nthe atmosphere at the left illuminates on the right at _c_, and the\nlines intersect at the point _m_.\n\n[Footnote: _A_ here stands for _levante_ (East), _B_ for _ponente_\n(West).]\n\n140.\n\nEvery body in light and shade is situated between 2 pyramids one\ndark and the other luminous, one is visible the other is not. But\nthis only happens when the light enters by a window. Supposing _a b_\nto be the window and _r_ the body in light and shade, the light to\nthe right hand _z_ will pass the object to the left and go on to\n_p_; the light to the left at _k_ will pass to the right of the\nobject at _i_ and go on to _m_ and the two lines will intersect at\n_c_ and form a pyramid. Then again _a_ _b_ falls on the shaded body\nat _i_ _g_ and forms a pyramid _f_ _i_ _g_. _f_ will be dark because\nthe light _a_ _b_ can never fall there; _i_ _g_ _c_ will be\nilluminated because the light falls upon it.\n\nLight and shadow with regard to the position of the eye (141--145).\n\n141.\n\nEvery shaded body that is larger than the pupil and that interposes\nbetween the luminous body and the eye will be seen dark.\n\nWhen the eye is placed between the luminous body and the objects\nilluminated by it, these objects will be seen without any shadow.\n\n[Footnote: The diagram which in the original stands above line 1 is\ngiven on Plate II, No 2. Then, after a blank space of about eight\nlines, the diagram Plate II No 3 is placed in the original. There is\nno explanation of it beyond the one line written under it.]\n\n142.\n\nWhy the 2 lights one on each side of a body having two pyramidal\nsides of an obtuse apex leave it devoid of shadow.\n\n[Footnote: The sketch illustrating this is on Plate XLI No 1.]\n\n143.\n\nA body in shadow situated between the light and the eye can never\ndisplay its illuminated portion unless the eye can see the whole of\nthe primary light.\n\n[Footnote: _A_ stands for _corpo_ (body), _B_ for _lume_ (light).]\n\n144.\n\nThe eye which looks (at a spot) half way between the shadow and the\nlight which surrounds the body in shadow will see that the deepest\nshadows on that body will meet the eye at equal angles, that is at\nthe same angle as that of sight.\n\n[Footnote: In both these diagrams _A_ stands for _lume_ (light) _B_\nfor _ombra_ (shadow).]\n\n145.\n\nOF THE DIFFERENT LIGHT AND SHADE IN VARIOUS ASPECTS AND OF OBJECTS\nPLACED IN THEM.\n\nIf the sun is in the East and you look towards the West you will see\nevery thing in full light and totally without shadow because you see\nthem from the same side as the sun: and if you look towards the\nSouth or North you will see all objects in light and shade, because\nyou see both the side towards the sun and the side away from it; and\nif you look towards the coming of the sun all objects will show you\ntheir shaded side, because on that side the sun cannot fall upon\nthem.\n\nThe law of the incidence of light.\n\n146.\n\nThe edges of a window which are illuminated by 2 lights of equal\ndegrees of brightness will not reflect light of equal brightness\ninto the chamber within.\n\nIf _b_ is a candle and _a c_ our hemisphere both will illuminate the\nedges of the window _m_ _n_, but light _b_ will only illuminate _f\ng_ and the hemisphere _a_ will light all of _d e_.\n\n147.\n\nOF PAINTING.\n\nThat part of a body which receives the luminous rays at equal angles\nwill be in a higher light than any other part of it.\n\nAnd the part which the luminous rays strike between less equal\nangles will be less strongly illuminated.\n\nSECOND BOOK ON LIGHT AND SHADE.\n\nGradations of strength in the shadows (148. 149).\n\n148.\n\nTHAT PORTION OF A BODY IN LIGHT AND SHADE WILL BE LEAST LUMINOUS\nWHICH IS SEEN UNDER THE LEAST AMOUNT OF LIGHT.\n\nThat part of the object which is marked _m_ is in the highest light\nbecause it faces the window _a d_ by the line _a f_; _n_ is in the\nsecond grade because the light _b d_ strikes it by the line _b e_;\n_o_ is in the third grade, as the light falls on it from _c d_ by\nthe line _c h_; _p_ is the lowest light but one as _c d_ falls on it\nby the line _d v_; _q_ is the deepest shadow for no light falls on\nit from any part of the window.\n\nIn proportion as _c d_ goes into _a d_ so will _n r s_ be darker\nthan _m_, and all the rest is space without shadow.\n\n[Footnote: The diagram belonging to this chapter is No. 1 on Plate\nIII. The letters _a b e d_ and _r_ are not reproduced in facsimile\nof the original, but have been replaced by ordinary type in the\nmargin. 5-12. The original text of these lines is reproduced within\nthe diagram.--Compare No 275.]\n\n149.\n\nThe light which falls on a shaded body at the acutest angle receives\nthe highest light, and the darkest portion is that which receives it\nat an obtuse angle and both the light and the shadow form pyramids.\nThe angle _c_ receives the highest grade of light because it is\ndirectly in front of the window _a b_ and the whole horizon of the\nsky _m x_. The angle _a_ differs but little from _c_ because the\nangles which divide it are not so unequal as those below, and only\nthat portion of the horizon is intercepted which lies between _y_\nand _x_. Although it gains as much on the other side its line is\nnevertheless not very strong because one angle is smaller than its\nfellow. The angles _e i_ will have less light because they do not\nsee much of the light _m s_ and the light _v x_ and their angles are\nvery unequal. Yhe angle _k_ and the angle _f_ are each placed\nbetween very unequal angles and therefore have but little light,\nbecause at _k_ it has only the light _p t_, and at _f_ only _t q_;\n_o g_ is the lowest grade of light because this part has no light at\nall from the sky; and thence come the lines which will reconstruct a\npyramid that is the counterpart of the pyramid _c_; and this pyramid\n_l_ is in the first grade of shadow; for this too is placed between\nequal angles directly opposite to each other on either side of a\nstraight line which passes through the centre of the body and goes\nto the centre of the light. The several luminous images cast within\nthe frame of the window at the points _a_ and _b_ make a light which\nsurrounds the derived shadow cast by the solid body at the points 4\nand 6. The shaded images increase from _o g_ and end at 7 and 8.\n\n[Footnote: The diagram belonging to this chapter is No. 2 on Plate\nIII. In the original it is placed between lines 3 and 4, and in the\nreproduction these are shown in part. The semi circle above is\nmarked _orizonte_ (horizon). The number 6 at the left hand side,\noutside the facsimile, is in the place of a figure which has become\nindistinct in the original.]\n\nOn the intensity of shadows as dependent on the distance from the\nlight (150-152).\n\n150.\n\nThe smaller the light that falls upon an object the more shadow it\nwill display. And the light will illuminate a smaller portion of the\nobject in proportion as it is nearer to it; and conversely, a larger\nextent of it in proportion as it is farther off.\n\nA light which is smaller than the object on which it falls will\nlight up a smaller extent of it in proportion as it is nearer to it,\nand the converse, as it is farther from it. But when the light is\nlarger than the object illuminated it will light a larger extent of\nthe object in proportion as it is nearer and the converse when they\nare farther apart.\n\n151.\n\nThat portion of an illuminated object which is nearest to the source\nof light will be the most strongly illuminated.\n\n152.\n\nThat portion of the primary shadow will be least dark which is\nfarthest from the edges.\n\nThe derived shadow will be darker than the primary shadow where it\nis contiguous with it.\n\nOn the proportion of light and shade (153-157).\n\n153.\n\nThat portion of an opaque body will be more in shade or more in\nlight, which is nearer to the dark body, by which it is shaded, or\nto the light that illuminates it.\n\nObjects seen in light and shade show in greater relief than those\nwhich are wholly in light or in shadow.\n\n154.\n\nOF PERSPECTIVE.\n\nThe shaded and illuminated sides of opaque objects will display the\nsame proportion of light and darkness as their objects [Footnote 6:\nThe meaning of _obbietti_ (objects) is explained in no 153, lines\n1-4.--Between the title-line and the next there is, in the\noriginal, a small diagram representing a circle described round a\nsquare.].\n\n155.\n\nOF PAINTING.\n\nThe outlines and form of any part of a body in light and shade are\nindistinct in the shadows and in the high lights; but in the\nportions between the light and the shadows they are highly\nconspicuous.\n\n156.\n\nOF PAINTING.\n\nAmong objects in various degrees of shade, when the light proceeds\nfrom a single source, there will be the same proportion in their\nshadows as in the natural diminution of the light and the same must\nbe understood of the degrees of light.\n\n157.\n\nA single and distinct luminous body causes stronger relief in the\nobject than a diffused light; as may be seen by comparing one side\nof a landscape illuminated by the sun, and one overshadowed by\nclouds, and so illuminated only by the diffused light of the\natmosphere.\n\nTHIRD BOOK ON LIGHT AND SHADE.\n\nDefinition of derived shadow (158. 159).\n\n158.\n\nDerived shadow cannot exist without primary shadow. This is proved\nby the first of this which says: Darkness is the total absence of\nlight, and shadow is an alleviation of darkness and of light, and it\nis more or less dark or light in proportion as the darkness is\nmodified by the light.\n\n159.\n\nShadow is diminution of light.\n\nDarkness is absence of light.\n\nShadow is divided into two kinds, of which the first is called\nprimary shadow, the second is derived shadow. The primary shadow is\nalways the basis of the derived shadow.\n\nThe edges of the derived shadow are straight lines.\n\n[Footnote: The theory of the _ombra_ dirivativa_--a technical\nexpression for which there is no precise English equivalent is\nelaborately treated by Leonardo. But both text and diagrams (as Pl.\nIV, 1-3 and Pl. V) must at once convince the student that the\ndistinction he makes between _ombra primitiva_ and _ombra\ndirivativa_ is not merely justifiable but scientific. _Ombra\ndirivativa_ is by no means a mere abstract idea. This is easily\nproved by repeating the experiment made by Leonardo, and by filling\nwith smoke the room in which the existence of the _ombra dirivativa_\nis investigated, when the shadow becomes visible. Nor is it\ndifficult to perceive how much of Leonardo's teaching depended on\nthis theory. The recognised, but extremely complicated science of\ncast shadows--_percussione dell' ombre dirivative_ as Leonardo\ncalls them--is thus rendered more intelligible if not actually\nsimpler, and we must assume this theory as our chief guide through\nthe investigations which follow.]\n\nThe darkness of the derived shadow diminishes in proportion as it is\nremote from the primary shadow.\n\nDifferent sorts of derived shadows (160-162).\n\n160.\n\nSHADOW AND LIGHT.\n\nThe forms of shadows are three: inasmuch as if the solid body which\ncasts the shadow is equal (in size) to the light, the shadow\nresembles a column without any termination (in length). If the body\nis larger than the light the shadow resembles a truncated and\ninverted pyramid, and its length has also no defined termination.\nBut if the body is smaller than the light, the shadow will resemble\na pyramid and come to an end, as is seen in eclipses of the moon.\n\n161.\n\nOF SIMPLE DERIVED SHADOWS.\n\nThe simple derived shadow is of two kinds: one kind which has its\nlength defined, and two kinds which are undefined; and the defined\nshadow is pyramidal. Of the two undefined, one is a column and the\nother spreads out; and all three have rectilinear outlines. But the\nconverging, that is the pyramidal, shadow proceeds from a body that\nis smaller than the light, and the columnar from a body equal in\nsize to the light, and the spreading shadow from a body larger than\nthe light; &c.\n\nOF COMPOUND DERIVED SHADOWS.\n\nCompound derived shadows are of two kinds; that is columnar and\nspreading.\n\n162.\n\nOF SHADOW.\n\nDerived shadows are of three kinds of which one is spreading, the\nsecond columnar, the third converging to the point where the two\nsides meet and intersect, and beyond this intersection the sides are\ninfinitely prolonged or straight lines. And if you say, this shadow\nmust terminate at the angle where the sides meet and extend no\nfarther, I deny this, because above in the first on shadow I have\nproved: that a thing is completely terminated when no portion of it\ngoes beyond its terminating lines. Now here, in this shadow, we see\nthe converse of this, in as much as where this derived shadow\noriginates we obviously have the figures of two pyramids of shadow\nwhich meet at their angles. Hence, if, as [my] opponent says, the\nfirst pyramid of shadow terminates the derivative shadow at the\nangle whence it starts, then the second pyramid of shadow--so says\nthe adversary--must be caused by the angle and not from the body in\nshadow; and this is disproved with the help of the 2nd of this which\nsays: Shadow is a condition produced by a body casting a shadow, and\ninterposed between this shadow and the luminous body. By this it is\nmade clear that the shadow is not produced by the angle of the\nderived shadow but only by the body casting the shadow; &c. If a\nspherical solid body is illuminated by a light of elongated form the\nshadow produced by the longest portion of this light will have less\ndefined outlines than that which is produced by the breadth of the\nsame light. And this is proved by what was said before, which is:\nThat a shadow will have less defined outlines in proportion as the\nlight which causes it is larger, and conversely, the outlines are\nclearer in proportion as it is smaller.\n\n[Footnote: The two diagrams to this chapter are on Plate IV, No. 1.]\n\nOn the relation of derived and primary shadow (163-165).\n\n163.\n\nThe derived shadow can never resemble the body from which it\nproceeds unless the light is of the same form and size as the body\ncausing the shadow.\n\nThe derived shadow cannot be of the same form as the primary shadow\nunless it is intercepted by a plane parallel to it.\n\n164.\n\nHOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT\nCASTS IT.\n\nIf the rays of light proceed, as experience shows, from a single\npoint and are diffused in a sphere round this point, radiating and\ndispersed through the air, the farther they spread the wider they\nmust spread; and an object placed between the light and a wall is\nalways imaged larger in its shadow, because the rays that strike it\n[Footnote: 7. The following lines are wanting to complete the\nlogical connection.] would, by the time they have reached the wall,\nhave become larger.\n\n165.\n\nAny shadow cast by a body in light and shade is of the same nature\nand character as that which is inseparable from the body. The centre\nof the length of a shadow always corresponds to that of the luminous\nbody [Footnote 6: This second statement of the same idea as in the\nformer sentence, but in different words, does not, in the original,\ncome next to the foregoing; sections 172 and 127 are placed between\nthem.]. It is inevitable that every shadow must have its centre in a\nline with the centre of the light.\n\nOn the shape of derived shadows (166-174).\n\n166.\n\nOF THE PYRAMIDAL SHADOW.\n\nThe pyramidal shadow produced by a columnar body will be narrower\nthan the body itself in proportion as the simple derived shadow is\nintersected farther from the body which casts it.\n\n[Footnote 166: Compare the first diagram to No. 161. If we here\nconceive of the outlines of the pyramid of shadow on the ground as\nprolonged beyond its apex this gives rise to a second pyramid; this\nis what is spoken of at the beginning of No. 166.]\n\n167.\n\nThe cast shadow will be longest when the light is lowest.\n\nThe cast shadow will be shortest when the light is highest.\n\n168.\n\nBoth the primary and derived shadow will be larger when caused by\nthe light of a candle than by diffused light. The difference between\nthe larger and smaller shadows will be in inverse proportion to the\nlarger and smaller lights causing them.\n\n[Footnote: In the diagrams _A_ stands for _celo_ (sky), _B_ for\n_cadela_ (candle).]\n\n169.\n\nALL BODIES, IN PROPORTION AS THEY ARE NEARER TO, OR FARTHER FROM THE\nSOURCE OF LIGHT, WILL PRODUCE LONGER OR SHORTER DERIVED SHADOWS.\n\nAmong bodies of equal size, that one which is illuminated by the\nlargest light will have the shortest shadow. Experiment confirms\nthis proposition. Thus the body _m_ _n_ is surrounded by a larger\namount of light than the body _p q_, as is shown above. Let us say\nthat _v c a b d x_ is the sky, the source of light, and that _s t_\nis a window by which the luminous rays enter, and so _m n_ and _p q_\nare bodies in light and shade as exposed to this light; _m n_ will\nhave a small derived shadow, because its original shadow will be\nsmall; and the derivative light will be large, again, because the\noriginal light _c d_ will be large and _p q_ will have more derived\nshadow because its original shadow will be larger, and its derived\nlight will be smaller than that of the body _m n_ because that\nportion of the hemisphere _a b_ which illuminates it is smaller than\nthe hemisphere _c d_ which illuminates the body _m n_.\n\n[Footnote: The diagram, given on Pl. IV, No. 2, stands in the\noriginal between lines 2 and 7, while the text of lines 3 to 6 is\nwritten on its left side. In the reproduction of this diagram the\nletter _v_ at the outer right-hand end has been omitted.]\n\n170.\n\nThe shadow _m_ bears the same proportion to the shadow _n_ as the\nline _b c_ to the line _f c_.\n\n171.\n\nOF PAINTING.\n\nOf different shadows of equal strength that which is nearest the eye\nwill seem the least strong.\n\nWhy is the shadow _e a b_ in the first grade of strength, _b c_ in\nthe second; _c d_ in the third? The reason is that as from _e a b_\nthe sky is nowhere visible, it gets no light whatever from the sky,\nand so has no direct [primary] light. _b c_ faces the portion of the\nsky _f g_ and is illuminated by it. _c d_ faces the sky at _h k_. _c\nd_, being exposed to a larger extent of sky than _b c_, it is\nreasonable that it should be more lighted. And thus, up to a certain\ndistance, the wall _a d_ will grow lighter for the reasons here\ngiven, until the darkness of the room overpowers the light from the\nwindow.\n\n172.\n\nWhen the light of the atmosphere is restricted [by an opening] and\nilluminates bodies which cast shadows, these bodies being equally\ndistant from the centre of the window, that which is most obliquely\nplaced will cast the largest shadow beyond it.\n\n173.\n\nThese bodies standing apart in a room lighted by a single window\nwill have derivative shadows more or less short according as they\nare more or less opposite to the window. Among the shadows cast by\nbodies of equal mass but at unequal distances from the opening by\nwhich they are illuminated, that shadow will be the longest of the\nbody which is least in the light. And in proportion as one body is\nbetter illuminated than another its shadow will be shorter than\nanother. The proportion _n m_ and _e v k_ bear to _r t_ and _v x_\ncorresponds with that of the shadow _x_ to 4 and _y_.\n\nThe reason why those bodies which are placed most in front of the\nmiddle of the window throw shorter shadows than those obliquely\nsituated is:--That the window appears in its proper form and to the\nobliquely placed ones it appears foreshortened; to those in the\nmiddle, the window shows its full size, to the oblique ones it\nappears smaller; the one in the middle faces the whole hemisphere\nthat is _e f_ and those on the side have only a strip; that is _q r_\nfaces _a b_; and _m n_ faces _c d_; the body in the middle having a\nlarger quantity of light than those at the sides is lighted from a\npoint much below its centre, and thus the shadow is shorter. And the\npyramid _g_ 4 goes into _l y_ exactly as often as _a b_ goes into _e\nf_. The axis of every derivative shadow passes through 6 1/2\n[Footnote 31: _passa per_ 6 1/2 (passes through 6 1/2). The meaning\nof these words is probably this: Each of the three axes of the\nderived shadow intersects the centre (_mezzo_) of the primary shadow\n(_ombra originale_) and, by prolongation upwards crosses six lines.\n\nThis is self evident only in the middle diagram; but it is equally\ntrue of the side figures if we conceive of the lines 4 _f_, _x n v\nm_, _y l k v_, and 4 _e_, as prolonged beyond the semicircle of the\nhorizon.] and is in a straight line with the centre of the primary\nshadow, with the centre of the body casting it and of the derivative\nlight and with the centre of the window and, finally, with the\ncentre of that portion of the source of light which is the celestial\nhemisphere, _y h_ is the centre of the derived shade, _l h_ of the\nprimary shadow, _l_ of the body throwing it, _l k_ of the derived\nlight, _v_ is the centre of the window, _e_ is the final centre of\nthe original light afforded by that portion of the hemisphere of the\nsky which illuminates the solid body.\n\n[Footnote: Compare the diagram on Pl. IV, No. 3. In the original\nthis drawing is placed between lines 3 and 22; the rest, from line 4\nto line 21, is written on the left hand margin.]\n\n174.\n\nTHE FARTHER THE DERIVED SHADOW IS PROLONGED THE LIGHTER IT BECOMES.\n\nYou will find that the proportion of the diameter of the derived\nshadow to that of the primary shadow will be the same as that\nbetween the darkness of the primary shadow and that of the derived\nshadow.\n\n[Footnote 6: Compare No. 177.] Let _a b_ be the diameter of the\nprimary shadow and _c d_ that of the derived shadow, I say that _a\nb_ going, as you see, three times into _d c_, the shadow _d c_ will\nbe three times as light as the shadow _a b_. [Footnote 8: Compare\nNo. 177.]\n\nIf the size of the illuminating body is larger than that of the\nilluminated body an intersection of shadow will occur, beyond which\nthe shadows will run off in two opposite directions as if they were\ncaused by two separate lights.\n\nOn the relative intensity of derived shadows (175-179).\n\n175.\n\nON PAINTING.\n\nThe derived shadow is stronger in proportion as it is nearer to its\nplace of origin.\n\n176.\n\nHOW SHADOWS FADE AWAY AT LONG DISTANCES.\n\nShadows fade and are lost at long distances because the larger\nquantity of illuminated air which lies between the eye and the\nobject seen tints the shadow with its own colour.\n\n177.\n\n_a b_ will be darker than _c d_ in proportion as _c d_ is broader\nthan _a b_.\n\n[Footnote: In the original MS. the word _lume_ (light) is written at\nthe apex of the pyramid.]\n\n178.\n\nIt can be proved why the shadow _o p c h_ is darker in proportion as\nit is nearer to the line _p h_ and is lighter in proportion as it is\nnearer to the line _o c_. Let the light _a b_, be a window, and let\nthe dark wall in which this window is, be _b s_, that is, one of the\nsides of the wall.\n\nThen we may say that the line _p h_ is darker than any other part of\nthe space _o p c h_, because this line faces the whole surface in\nshadow of [Footnote: In the original the diagram is placed between\nlines 27 and 28.] the wall _b s_. The line _o c_ is lighter than the\nother part of this space _o p c h_, because this line faces the\nluminous space _a b_.\n\nWhere the shadow is larger, or smaller, or equal the body which\ncasts it.\n\n[First of the character of divided lights. [Footnote 14: _lumi\ndivisi_. The text here breaks off abruptly.]\n\nOF THE COMPOUND SHADOW _F, R, C, H_ CAUSED BY A SINGLE LIGHT.\n\nThe shadow _f r c h_ is under such conditions as that where it is\nfarthest from its inner side it loses depth in proportion. To prove\nthis:\n\nLet _d a_, be the light and _f n_ the solid body, and let _a e_ be\none of the side walls of the window that is _d a_. Then I\nsay--according to the 2nd [proposition]: that the surface of any\nbody is affected by the tone of the objects surrounding it,--that\nthe side _r c_, which faces the dark wall _a e_ must participate of\nits darkness and, in the same way that the outer surface which faces\nthe light _d a_ participates of the light; thus we get the outlines\nof the extremes on each side of the centre included between them.]\n\nThis is divided into four parts. The first the extremes, which\ninclude the compound shadow, secondly the compound shadow between\nthese extremes.\n\n179.\n\nTHE ACTION OF THE LIGHT AS FROM ITS CENTRE.\n\nIf it were the whole of the light that caused the shadows beyond the\nbodies placed in front of it, it would follow that any body much\nsmaller than the light would cast a pyramidal shadow; but experience\nnot showing this, it must be the centre of the light that produces\nthis effect.\n\n[Footnote: The diagram belonging to this passage is between lines 4\nand 5 in the original. Comp. the reproduction Pl. IV, No. 4. The\ntext and drawing of this chapter have already been published with\ntolerable accuracy. See M. JORDAN: \"_Das Malerbuch des Leonardo da\nVinci_\". Leipzig 1873, P. 90.]\n\nPROOF.\n\nLet _a b_ be the width of the light from a window, which falls on a\nstick set up at one foot from _a c_ [Footnote 6: _bastone_ (stick).\nThe diagram has a sphere in place of a stick.]. And let _a d_ be the\nspace where all the light from the window is visible. At _c e_ that\npart of the window which is between _l b_ cannot be seen. In the\nsame way _a m_ cannot be seen from _d f_ and therefore in these two\nportions the light begins to fail.\n\nShadow as produced by two lights of different size (180. 181).\n\n180.\n\nA body in light and shade placed between two equal lights side by\nside will cast shadows in proportion to the [amount of] light. And\nthe shadows will be one darker than the other in proportion as one\nlight is nearer to the said body than the other on the opposite\nside.\n\nA body placed at an equal distance between two lights will cast two\nshadows, one deeper than the other in proportion, as the light which\ncauses it is brighter than the other.\n\n[Footnote: In the MS. the larger diagram is placed above the first\nline; the smaller one between l. 4 & 5.]\n\n181.\n\nA light which is smaller than the body it illuminates produces\nshadows of which the outlines end within [the surface of] the body,\nand not much compound shadow; and falls on less than half of it. A\nlight which is larger than the body it illuminates, falls on more\nthan half of it, and produces much compound shadow.\n\nThe effect of light at different distances.\n\n182.\n\nOF THE SHADOW CAST BY A BODY PLACED BETWEEN 2 EQUAL LIGHTS.\n\nA body placed between 2 equal lights will cast 2 shadows of itself\nin the direction of the lines of the 2 lights; and if you move this\nbody placing it nearer to one of the lights the shadow cast towards\nthe nearer light will be less deep than that which falls towards the\nmore distant one.\n\nFurther complications in the derived shadows (183-187).\n\n183.\n\nThe greatest depth of shadow is in the simple derived shadow because\nit is not lighted by either of the two lights _a b, c d_.\n\nThe next less deep shadow is the derived shadow _e f n_; and in this\nthe shadow is less by half, because it is illuminated by a single\nlight, that is _c d_.\n\nThis is uniform in natural tone because it is lighted throughout by\none only of the two luminous bodies [10]. But it varies with the\nconditions of shadow, inasmuch as the farther it is away from the\nlight the less it is illuminated by it [13].\n\nThe third degree of depth is the middle shadow [Footnote 15: We\ngather from what follows that _q g r_ here means _ombra media_ (the\nmiddle shadow).]. But this is not uniform in natural tone; because\nthe nearer it gets to the simple derived shadow the deeper it is\n[Footnote 18: Compare lines 10-13], and it is the uniformly gradual\ndiminution by increase of distance which is what modifies it\n[Footnote 20: See Footnote 18]: that is to say the depth of a shadow\nincreases in proportion to the distance from the two lights.\n\nThe fourth is the shadow _k r s_ and this is all the darker in\nnatural tone in proportion as it is nearer to _k s_, because it gets\nless of the light _a o_, but by the accident [of distance] it is\nrendered less deep, because it is nearer to the light _c d_, and\nthus is always exposed to both lights.\n\nThe fifth is less deep in shadow than either of the others because\nit is always entirely exposed to one of the lights and to the whole\nor part of the other; and it is less deep in proportion as it is\nnearer to the two lights, and in proportion as it is turned towards\nthe outer side _x t_; because it is more exposed to the second light\n_a b_.\n\n[Footnote: The diagram to this section is given on Pl. V. To the\nleft is the facsimile of the beginning of the text belonging to it.]\n\n184.\n\nOF SIMPLE SHADOWS.\n\nWhy, at the intersections _a_, _b_ of the two compound shadows _e f_\nand _m e_, is a simple shadow pfoduced as at _e h_ and _m g_, while\nno such simple shadow is produced at the other two intersections _c\nd_ made by the very same compound shadows?\n\nANSWER.\n\nCompound shadow are a mixture of light and shade and simple shadows\nare simply darkness. Hence, of the two lights _n_ and _o_, one falls\non the compound shadow from one side, and the other on the compound\nshadow from the other side, but where they intersect no light falls,\nas at _a b_; therefore it is a simple shadow. Where there is a\ncompound shadow one light or the other falls; and here a difficulty\narises for my adversary since he says that, where the compound\nshadows intersect, both the lights which produce the shadows must of\nnecessity fall and therefore these shadows ought to be neutralised;\ninasmuch as the two lights do not fall there, we say that the shadow\nis a simple one and where only one of the two lights falls, we say\nthe shadow is compound, and where both the lights fall the shadow is\nneutralised; for where both lights fall, no shadow of any kind is\nproduced, but only a light background limiting the shadow. Here I\nshall say that what my adversary said was true: but he only mentions\nsuch truths as are in his favour; and if we go on to the rest he\nmust conclude that my proposition is true. And that is: That if both\nlights fell on the point of intersection, the shadows would be\nneutralised. This I confess to be true if [neither of] the two\nshadows fell in the same spot; because, where a shadow and a light\nfall, a compound shadow is produced, and wherever two shadows or two\nequal lights fall, the shadow cannot vary in any part of it, the\nshadows and the lights both being equal. And this is proved in the\neighth [proposition] on proportion where it is said that if a given\nquantity has a single unit of force and resistance, a double\nquantity will have double force and double resistance.\n\nDEFINITION.\n\nThe intersection _n_ is produced by the shadows caused by the light\n_b_, because this light _b_ produces the shadow _x b_, and the\nshadow _s b_, but the intersection _m_ is produced by the light _a_\nwhich causes the shadow _s a_, and the shadow _x a_.\n\nBut if you uncover both the lights _a b_, then you get the two\nshadows _n m_ both at once, and besides these, two other, simple\nshadows are produced at _r o_ where neither of the two lights falls\nat all. The grades of depth in compound shadows are fewer in\nproportion as the lights falling on, and crossing them are less\nnumerous.\n\n186.\n\nWhy the intersections at _n_ being composed of two compound derived\nshadows, forms a compound shadow and not a simple one, as happens\nwith other intersections of compound shadows. This occurs, according\nto the 2nd [diagram] of this [prop.] which says:--The intersection\nof derived shadows when produced by the intersection of columnar\nshadows caused by a single light does not produce a simple shadow.\nAnd this is the corollary of the 1st [prop.] which says:--The\nintersection of simple derived shadows never results in a deeper\nshadow, because the deepest shadows all added together cannot be\ndarker than one by itself. Since, if many deepest shadows increased\nin depth by their duplication, they could not be called the\n_deepest_ shadows, but only part-shadows. But if such intersections\nare illuminated by a second light placed between the eye and the\nintersecting bodies, then those shadows would become compound\nshadows and be uniformly dark just as much at the intersection as\nthroughout the rest. In the 1st and 2nd above, the intersections _i\nk_ will not be doubled in depth as it is doubled in quantity. But in\nthis 3rd, at the intersections _g n_ they will be double in depth\nand in quantity.\n\n187.\n\nHOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED SHADOW\nWITH THE LIGHT DERIVED FROM THE LUMINOUS BODY.\n\nThe derived shadow of the dark walls on each side of the bright\nlight of the window are what mingle their various degrees of shade\nwith the light derived from the window; and these various depths of\nshade modify every portion of the light, except where it is\nstrongest, at _c_. To prove this let _d a_ be the primary shadow\nwhich is turned towards the point _e_, and darkens it by its derived\nshadow; as may be seen by the triangle _a e d_, in which the\nangle _e_ faces the darkened base _d a e_; the point _v_ faces the\ndark shadow _a s_ which is part of _a d_, and as the whole is\ngreater than a part, _e_ which faces the whole base [of the\ntriangle], will be in deeper shadow than _v_ which only faces part\nof it. In consequence of the conclusion [shown] in the above\ndiagram, _t_ will be less darkened than _v_, because the base of the\n_t_ is part of the base of the _v_; and in the same way it follows\nthat _p_ is less in shadow than _t_, because the base of the _p_ is\npart of the base of the _t_. And _c_ is the terminal point of the\nderived shadow and the chief beginning of the highest light.\n\n[Footnote: The diagram on Pl. IV, No. 5 belongs to this passage; but\nit must be noted that the text explains only the figure on the\nright-hand side.]\n\nFOURTH BOOK ON LIGHT AND SHADE.\n\nOn the shape of the cast shadows (188-191).\n\n188.\n\nThe form of the shadow cast by any body of uniform density can never\nbe the same as that of the body producing it. [Footnote: Comp. the\ndrawing on PI. XXVIII, No. 5.]\n\n189.\n\nNo cast shadow can produce the true image of the body which casts it\non a vertical plane unless the centre of the light is equally\ndistant from all the edges of that body.\n\n190.\n\nIf a window _a b_ admits the sunlight into a room, the sunlight will\nmagnify the size of the window and diminish the shadow of a man in\nsuch a way as that when the man makes that dim shadow of himself,\napproach to that which defines the real size of the window, he will\nsee the shadows where they come into contact, dim and confused from\nthe strength of the light, shutting off and not allowing the solar\nrays to pass; the effect of the shadow of the man cast by this\ncontact will be exactly that figured above.\n\n[Footnote: It is scarcely possible to render the meaning of this\nsentence with strict accuracy; mainly because the grammatical\nconstruction is defective in the most important part--line 4. In the\nvery slight original sketch the shadow touches the upper arch of the\nwindow and the correction, here given is perhaps not justified.]\n\n191.\n\nA shadow is never seen as of uniform depth on the surface which\nintercepts it unless every portion of that surface is equidistant\nfrom the luminous body. This is proved by the 7th which says:--The\nshadow will appear lighter or stronger as it is surrounded by a\ndarker or a lighter background. And by the 8th of this:--The\nbackground will be in parts darker or lighter, in proportion as it\nis farther from or nearer to the luminous body. And:--Of various\nspots equally distant from the luminous body those will always be in\nthe highest light on which the rays fall at the smallest angles: The\noutline of the shadow as it falls on inequalities in the surface\nwill be seen with all the contours similar to those of the body that\ncasts it, if the eye is placed just where the centre of the light\nwas.\n\nThe shadow will look darkest where it is farthest from the body that\ncasts it. The shadow _c d_, cast by the body in shadow _a b_ which\nis equally distant in all parts, is not of equal depth because it is\nseen on a back ground of varying brightness. [Footnote: Compare the\nthree diagrams on Pl. VI, no 1 which, in the original accompany this\nsection.]\n\nOn the outlines of cast shadows (192-195).\n\n192.\n\nThe edges of a derived shadow will be most distinct where it is cast\nnearest to the primary shadow.\n\n193.\n\nAs the derived shadow gets more distant from the primary shadow, the\nmore the cast shadow differs from the primary shadow.\n\n194.\n\nOF SHADOWS WHICH NEVER COME TO AN END.\n\nThe greater the difference between a light and the body lighted by\nit, the light being the larger, the more vague will be the outlines\nof the shadow of that object.\n\nThe derived shadow will be most confused towards the edges of its\ninterception by a plane, where it is remotest from the body casting\nit.\n\n195.\n\nWhat is the cause which makes the outlines of the shadow vague and\nconfused?\n\nWhether it is possible to give clear and definite outlines to the\nedges of shadows.\n\nOn the relative size of shadows (196. 197).\n\n196.\n\nTHE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW, AND\nWHY?\n\nIf an object placed in front of a single light is very close to it\nyou will see that it casts a very large shadow on the opposite wall,\nand the farther you remove the object from the light the smaller\nwill the image of the shadow become.\n\nWHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF\nPROPORTION.\n\nThe disproportion of a shadow which is larger than the body\nproducing it, results from the light being smaller than the body, so\nthat it cannot be at an equal distance from the edges of the body\n[Footnote 11: H. LUDWIG in his edition of the old copies, in the\nVatican library--in which this chapter is included under Nos. 612,\n613 and 614 alters this passage as follows: _quella parte ch'e piu\npropinqua piu cresce che le distanti_, although the Vatican copy\nagrees with the original MS. in having _distante_ in the former and\n_propinque_ in the latter place. This supposed amendment seems to me\nto invert the facts. Supposing for instance, that on Pl. XXXI No. 3.\n_f_ is the spot where the light is that illuminates the figure there\nrepresented, and that the line behind the figure represents a wall\non which the shadow of the figure is thrown. It is evident, that in\nthat case the nearest portion, in this case the under part of the\nthigh, is very little magnified in the shadow, and the remoter\nparts, for instance the head, are more magnified.]; and the portions\nwhich are most remote are made larger than the nearer portions for\nthis reason [Footnote 12: See Footnote 11].\n\nWHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS\nILL-DEFINED OUTLINES.\n\nThe atmosphere which surrounds a light is almost like light itself\nfor brightness and colour; but the farther off it is the more it\nloses this resemblance. An object which casts a large shadow and is\nnear to the light, is illuminated both by that light by the luminous\natmosphere; hence this diffused light gives the shadow ill-defined\nedges.\n\n197.\n\nA luminous body which is long and narrow in shape gives more\nconfused outlines to the derived shadow than a spherical light, and\nthis contradicts the proposition next following: A shadow will have\nits outlines more clearly defined in proportion as it is nearer to\nthe primary shadow or, I should say, the body casting the shadow;\n[Footnote 14: The lettering refers to the lower diagram, Pl. XLI,\nNo. 5.] the cause of this is the elongated form of the luminous body\n_a c_, &c. [Footnote 16: See Footnote 14].\n\nEffects on cast shadows by the tone of the back ground.\n\n198.\n\nOF MODIFIED SHADOWS.\n\nModified shadows are those which are cast on light walls or other\nilluminated objects.\n\nA shadow looks darkest against a light background. The outlines of a\nderived shadow will be clearer as they are nearer to the primary\nshadow. A derived shadow will be most defined in shape where it is\nintercepted, where the plane intercepts it at the most equal angle.\n\nThose parts of a shadow will appear darkest which have darker\nobjects opposite to them. And they will appear less dark when they\nface lighter objects. And the larger the light object opposite, the\nmore the shadow will be lightened.\n\nAnd the larger the surface of the dark object the more it will\ndarken the derived shadow where it is intercepted.\n\nA disputed proposition.\n\n199.\n\nOF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE\nSURFACE.\n\nCertain mathematicians have maintained that a triangle, of which the\nbase is turned to the light, casts no shadow on a plane; and this\nthey prove by saying [5] that no spherical body smaller than the\nlight can reach the middle with the shadow. The lines of radiant\nlight are straight lines [6]; therefore, suppose the light to be _g\nh_ and the triangle _l m n_, and let the plane be _i k_; they say\nthe light _g_ falls on the side of the triangle _l n_, and the\nportion of the plane _i q_. Thus again _h_ like _g_ falls on the\nside _l m_, and then on _m n_ and the plane _p k_; and if the whole\nplane thus faces the lights _g h_, it is evident that the triangle\nhas no shadow; and that which has no shadow can cast none. This, in\nthis case appears credible. But if the triangle _n p g_ were not\nilluminated by the two lights _g_ and _h_, but by _i p_ and _g_ and\n_k_ neither side is lighted by more than one single light: that is\n_i p_ is invisible to _h g_ and _k_ will never be lighted by _g_;\nhence _p q_ will be twice as light as the two visible portions that\nare in shadow.\n\n[Footnote: 5--6. This passage is so obscure that it would be rash to\noffer an explanation. Several words seem to have been omitted.]\n\nOn the relative depth of cast shadows (200-202).\n\n200.\n\nA spot is most in the shade when a large number of darkened rays\nfall upon it. The spot which receives the rays at the widest angle\nand by darkened rays will be most in the dark; a will be twice as\ndark as b, because it originates from twice as large a base at an\nequal distance. A spot is most illuminated when a large number of\nluminous rays fall upon it. d is the beginning of the shadow _d f_,\nand tinges _c_ but _a_ little; _d e_ is half of the shadow _d f_ and\ngives a deeper tone where it is cast at _b_ than at _f_. And the\nwhole shaded space _e_ gives its tone to the spot _a_. [Footnote:\nThe diagram here referred to is on Pl. XLI, No. 2.]\n\n201.\n\n_A n_ will be darker than _c r_ in proportion to the number of times\nthat _a b_ goes into _c d_.\n\n202.\n\nThe shadow cast by an object on a plane will be smaller in\nproportion as that object is lighted by feebler rays. Let _d e_ be\nthe object and _d c_ the plane surface; the number of times that _d\ne_ will go into _f g_ gives the proportion of light at _f h_ to _d\nc_. The ray of light will be weaker in proportion to its distance\nfrom the hole through which it falls.\n\nFIFTH BOOK ON LIGHT AND SHADE.\n\nPrinciples of reflection (203. 204).\n\n203.\n\nOF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED.\n\nIf the object is the mountain here figured, and the light is at the\npoint _a_, I say that from _b d_ and also from _c f_ there will be\nno light but from reflected rays. And this results from the fact\nthat rays of light can only act in straight lines; and the same is\nthe case with the secondary or reflected rays.\n\n204.\n\nThe edges of the derived shadow are defined by the hues of the\nilluminated objects surrounding the luminous body which produces the\nshadow.\n\nOn reverberation.\n\n205.\n\nOF REVERBERATION.\n\nReverberation is caused by bodies of a bright nature with a flat and\nsemi opaque surface which, when the light strikes upon them, throw\nit back again, like the rebound of a ball, to the former object.\n\nWHERE THERE CAN BE NO REFLECTED LIGHTS.\n\nAll dense bodies have their surfaces occupied by various degrees of\nlight and shade. The lights are of two kinds, one called original,\nthe other borrowed. Original light is that which is inherent in the\nflame of fire or the light of the sun or of the atmosphere. Borrowed\nlight will be reflected light; but to return to the promised\ndefinition: I say that this luminous reverberation is not produced\nby those portions of a body which are turned towards darkened\nobjects, such as shaded spots, fields with grass of various height,\nwoods whether green or bare; in which, though that side of each\nbranch which is turned towards the original light has a share of\nthat light, nevertheless the shadows cast by each branch separately\nare so numerous, as well as those cast by one branch on the others,\nthat finally so much shadow is the result that the light counts for\nnothing. Hence objects of this kind cannot throw any reflected light\non opposite objects.\n\nReflection on water (206. 207).\n\n206.\n\nPERSPECTIVE.\n\nThe shadow or object mirrored in water in motion, that is to say in\nsmall wavelets, will always be larger than the external object\nproducing it.\n\n207.\n\nIt is impossible that an object mirrored on water should correspond\nin form to the object mirrored, since the centre of the eye is above\nthe surface of the water.\n\nThis is made plain in the figure here given, which demonstrates that\nthe eye sees the surface _a b_, and cannot see it at _l f_, and at\n_r t_; it sees the surface of the image at _r t_, and does not see\nit in the real object _c d_. Hence it is impossible to see it, as\nhas been said above unless the eye itself is situated on the surface\nof the water as is shown below [13].\n\n[Footnote: _A_ stands for _ochio_ [eye], _B_ for _aria_ [air], _C_\nfor _acqua_ [water], _D_ for _cateto_ [cathetus].--In the original\nMS. the second diagram is placed below line 13.]\n\nExperiments with the mirror (208-210).\n\n208.\n\nTHE MIRROR.\n\nIf the illuminated object is of the same size as the luminous body\nand as that in which the light is reflected, the amount of the\nreflected light will bear the same proportion to the intermediate\nlight as this second light will bear to the first, if both bodies\nare smooth and white.\n\n209.\n\nDescribe how it is that no object has its limitation in the mirror\nbut in the eye which sees it in the mirror. For if you look at your\nface in the mirror, the part resembles the whole in as much as the\npart is everywhere in the mirror, and the whole is in every part of\nthe same mirror; and the same is true of the whole image of any\nobject placed opposite to this mirror, &c.\n\n210.\n\nNo man can see the image of another man in a mirror in its proper\nplace with regard to the objects; because every object falls on [the\nsurface of] the mirror at equal angles. And if the one man, who sees\nthe other in the mirror, is not in a direct line with the image he\nwill not see it in the place where it really falls; and if he gets\ninto the line, he covers the other man and puts himself in the place\noccupied by his image. Let _n o_ be the mirror, _b_ the eye of your\nfriend and _d_ your own eye. Your friend's eye will appear to you at\n_a_, and to him it will seem that yours is at _c_, and the\nintersection of the visual rays will occur at _m_, so that either of\nyou touching _m_ will touch the eye of the other man which shall be\nopen. And if you touch the eye of the other man in the mirror it\nwill seem to him that you are touching your own.\n\nAppendix:--On shadows in movement (211. 212).\n\n211.\n\nOF THE SHADOW AND ITS MOTION.\n\nWhen two bodies casting shadows, and one in front of the other, are\nbetween a window and the wall with some space between them, the\nshadow of the body which is nearest to the plane of the wall will\nmove if the body nearest to the window is put in transverse motion\nacross the window. To prove this let _a_ and _b_ be two bodies\nplaced between the window _n m_ and the plane surface _o p_ with\nsufficient space between them as shown by the space _a b_. I say\nthat if the body _a_ is moved towards _s_ the shadow of the body _b_\nwhich is at _c_ will move towards _d_.\n\n212.\n\nOF THE MOTION OF SHADOWS.\n\nThe motion of a shadow is always more rapid than that of the body\nwhich produces it if the light is stationary. To prove this let _a_\nbe the luminous body, and _b_ the body casting the shadow, and _d_\nthe shadow. Then I say that in the time while the solid body moves\nfrom _b_ to _c_, the shadow _d_ will move to _e_; and this\nproportion in the rapidity of the movements made in the same space\nof time, is equal to that in the length of the space moved over.\nThus, given the proportion of the space moved over by the body _b_\nto _c_, to that moved over by the shadow _d_ to _e_, the proportion\nin the rapidity of their movements will be the same.\n\nBut if the luminous body is also in movement with a velocity equal\nto that of the solid body, then the shadow and the body that casts\nit will move with equal speed. And if the luminous body moves more\nrapidly than the solid body, the motion of the shadow will be slower\nthan that of the body casting it.\n\nBut if the luminous body moves more slowly than the solid body, then\nthe shadow will move more rapidly than that body.\n\nSIXTH BOOK ON LIGHT AND SHADE.\n\nThe effect of rays passing through holes (213. 214).\n\n213.\n\nPERSPECTIVE.\n\nIf you transmit the rays of the sun through a hole in the shape of a\nstar you will see a beautiful effect of perspective in the spot\nwhere the sun's rays fall.\n\n[Footnote: In this and the following chapters of MS. C the order of\nthe original paging has been adhered to, and is shown in\nparenthesis. Leonardo himself has but rarely worked out the subject\nof these propositions. The space left for the purpose has\noccasionally been made use of for quite different matter. Even the\nnumerous diagrams, most of them very delicately sketched, lettered\nand numbered, which occur on these pages, are hardly ever explained,\nwith the exception of those few which are here given.]\n\n214.\n\nNo small hole can so modify the convergence of rays of light as to\nprevent, at a long distance, the transmission of the true form of\nthe luminous body causing them. It is impossible that rays of light\npassing through a parallel [slit], should not display the form of\nthe body causing them, since all the effects produced by a luminous\nbody are [in fact] the reflection of that body: The moon, shaped\nlike a boat, if transmitted through a hole is figured in the surface\n[it falls on] as a boatshaped object. [Footnote 8: In the MS. a\nblank space is left after this question.] Why the eye sees bodies at\na distance, larger than they measure on the vertical plane?.\n\n[Footnote: This chapter, taken from another MS. may, as an\nexception, be placed here, as it refers to the same subject as the\npreceding section.]\n\nOn gradation of shadows (215. 216).\n\n215.\n\nAlthough the breadth and length of lights and shadow will be\nnarrower and shorter in foreshortening, the quality and quantity of\nthe light and shade is not increased nor diminished.\n\n[3]The function of shade and light when diminished by\nforeshortening, will be to give shadow and to illuminate an object\nopposite, according to the quality and quantity in which they fall\non the body.\n\n[5]In proportion as a derived shadow is nearer to its penultimate\nextremities the deeper it will appear, _g z_ beyond the intersection\nfaces only the part of the shadow [marked] _y z_; this by\nintersection takes the shadow from _m n_ but by direct line it takes\nthe shadow _a m_ hence it is twice as deep as _g z_. _Y x_, by\nintersection takes the shadow _n o_, but by direct line the shadow\n_n m a_, therefore _x y_ is three times as dark as _z g_; _x f_, by\nintersection faces _o b_ and by direct line _o n m a_, therefore we\nmust say that the shadow between _f x_ will be four times as dark as\nthe shadow _z g_, because it faces four times as much shadow.\n\nLet _a b_ be the side where the primary shadow is, and _b c_ the\nprimary light, _d_ will be the spot where it is intercepted,_f g_\nthe derived shadow and _f e_ the derived light.\n\nAnd this must be at the beginning of the explanation.\n\n[Footnote: In the original MS. the text of No. 252 precedes the one\ngiven here. In the text of No. 215 there is a blank space of about\nfour lines between the lines 2 and 3. The diagram given on Pl. VI,\nNo. 2 is placed between lines 4 and 5. Between lines 5 and 6 there\nis another space of about three lines and one line left blank\nbetween lines 8 and 9. The reader will find the meaning of the whole\npassage much clearer if he first reads the final lines 11--13.\nCompare also line 4 of No. 270.]\n\nOn relative proportion of light and shadows (216--221).\n\n216.\n\nThat part of the surface of a body on which the images [reflection]\nfrom other bodies placed opposite fall at the largest angle will\nassume their hue most strongly. In the diagram below, 8 is a larger\nangle than 4, since its base _a n_ is larger than _e n_ the base of\n4. This diagram below should end at _a n_ 4 8. [4]That portion of\nthe illuminated surface on which a shadow is cast will be brightest\nwhich lies contiguous to the cast shadow. Just as an object which is\nlighted up by a greater quantity of luminous rays becomes brighter,\nso one on which a greater quantity of shadow falls, will be darker.\n\nLet 4 be the side of an illuminated surface 4 8, surrounding the\ncast shadow _g e_ 4. And this spot 4 will be lighter than 8, because\nless shadow falls on it than on 8. Since 4 faces only the shadow _i\nn_; and 8 faces and receives the shadow _a e_ as well as _i n_ which\nmakes it twice as dark. And the same thing happens when you put the\natmosphere and the sun in the place of shade and light.\n\n[12] The distribution of shadow, originating in, and limited by,\nplane surfaces placed near to each other, equal in tone and directly\nopposite, will be darker at the ends than at the beginning, which\nwill be determined by the incidence of the luminous rays. You will\nfind the same proportion in the depth of the derived shadows _a n_\nas in the nearness of the luminous bodies _m b_, which cause them;\nand if the luminous bodies were of equal size you would still\nfarther find the same proportion in the light cast by the luminous\ncircles and their shadows as in the distance of the said luminous\nbodies.\n\n[Footnote: The diagram originally placed between lines 3 and 4 is on\nPl. VI, No. 3. In the diagram given above line 14 of the original,\nand here printed in the text, the words _corpo luminoso_ [luminous\nbody] are written in the circle _m_, _luminoso_ in the circle _b_\nand _ombroso_ [body in shadow] in the circle _o_.]\n\n217.\n\nTHAT PART OF THE REFLECTION WILL BE BRIGHTEST WHERE THE REFLECTED\nRAYS ARE SHORTEST.\n\n[2] The darkness occasioned by the casting of combined shadows will\nbe in conformity with its cause, which will originate and terminate\nbetween two plane surfaces near together, alike in tone and directly\nopposite each other.\n\n[4] In proportion as the source of light is larger, the luminous and\nshadow rays will be more mixed together. This result is produced\nbecause wherever there is a larger quantity of luminous rays, there\nis most light, but where there are fewer there is least light,\nconsequently the shadow rays come in and mingle with them.\n\n[Footnote: Diagrams are inserted before lines 2 and 4.]\n\n218.\n\nIn all the proportions I lay down it must be understood that the\nmedium between the bodies is always the same. [2] The smaller the\nluminous body the more distinct will the transmission of the shadows\nbe.\n\n[3] When of two opposite shadows, produced by the same body, one is\ntwice as dark as the other though similar in form, one of the two\nlights causing them must have twice the diameter that the other has\nand be at twice the distance from the opaque body. If the object is\nlowly moved across the luminous body, and the shadow is intercepted\nat some distance from the object, there will be the same relative\nproportion between the motion of the derived shadow and the motion\nof the primary shadow, as between the distance from the object to\nthe light, and that from the object to the spot where the shadow is\nintercepted; so that though the object is moved slowly the shadow\nmoves fast.\n\n[Footnote: There are diagrams inserted before lines 2 and 3 but they\nare not reproduced here. The diagram above line 6 is written upon as\nfollows: at _A lume_ (light), at _B obbietto_ (body), at _C ombra\nd'obbietto_ (shadow of the object).]\n\n219.\n\nA luminous body will appear less brilliant when surrounded by a\nbright background.\n\n[2] I have found that the stars which are nearest to the horizon\nlook larger than the others because light falls upon them from a\nlarger proportion of the solar body than when they are above us; and\nhaving more light from the sun they give more light, and the bodies\nwhich are most luminous appear the largest. As may be seen by the\nsun through a mist, and overhead; it appears larger where there is\nno mist and diminished through mist. No portion of the luminous body\nis ever visible from any spot within the pyramid of pure derived\nshadow.\n\n[Footnote: Between lines 1 and 2 there is in the original a large\ndiagram which does not refer to this text. ]\n\n220.\n\nA body on which the solar rays fall between the thin branches of\ntrees far apart will cast but a single shadow.\n\n[2] If an opaque body and a luminous one are (both) spherical the\nbase of the pyramid of rays will bear the same proportion to the\nluminous body as the base of the pyramid of shade to the opaque\nbody.\n\n[4] When the transmitted shadow is intercepted by a plane surface\nplaced opposite to it and farther away from the luminous body than\nfrom the object [which casts it] it will appear proportionately\ndarker and the edges more distinct.\n\n[Footnote: The diagram which, in the original, is placed above line\n2, is similar to the one, here given on page 73 (section 120).--The\ndiagram here given in the margin stands, in the original, between\nlines 3 and 4.]\n\n221.\n\nA body illuminated by the solar rays passing between the thick\nbranches of trees will produce as many shadows as there are branches\nbetween the sun and itself.\n\nWhere the shadow-rays from an opaque pyramidal body are intercepted\nthey will cast a shadow of bifurcate outline and various depth at\nthe points. A light which is broader than the apex but narrower than\nthe base of an opaque pyramidal body placed in front of it, will\ncause that pyramid to cast a shadow of bifurcate form and various\ndegrees of depth.\n\nIf an opaque body, smaller than the light, casts two shadows and if\nit is the same size or larger, casts but one, it follows that a\npyramidal body, of which part is smaller, part equal to, and part\nlarger than, the luminous body, will cast a bifurcate shadow.\n\n[Footnote: Between lines 2 and 3 there are in the original two large\ndiagrams.]\n\n_IV._\n\n_Perspective of Disappearance._\n\n_The theory of the_ \"Prospettiva de' perdimenti\" _would, in many\nimportant details, be quite unintelligible if it had not been led up\nby the principles of light and shade on which it is based. The word_\n\"Prospettiva\" _in the language of the time included the principles\nof optics; what Leonardo understood by_ \"Perdimenti\" _will be\nclearly seen in the early chapters, Nos._ 222--224. _It is in the\nvery nature of the case that the farther explanations given in the\nsubsequent chapters must be limited to general rules. The sections\ngiven as_ 227--231 _\"On indistinctness at short distances\" have, it\nis true, only an indirect bearing on the subject; but on the other\nhand, the following chapters,_ 232--234, _\"On indistinctness at\ngreat distances,\" go fully into the matter, and in chapters_\n235--239, _which treat \"Of the importance of light and shade in the\nPerspective of Disappearance\", the practical issues are distinctly\ninsisted on in their relation to the theory. This is naturally\nfollowed by the statements as to \"the effect of light or dark\nbackgrounds on the apparent size of bodies\"_ (_Nos._ 240--250). _At\nthe end I have placed, in the order of the original, those sections\nfrom the MS._ C _which treat of the \"Perspective of Disappearance\"\nand serve to some extent to complete the treatment of the subject_\n(251--262).\n\nDefinition (222. 223).\n\n222.\n\nOF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES.\n\nIf the real outlines of opaque bodies are indistinguishable at even\na very short distance, they will be more so at long distances; and,\nsince it is by its outlines that we are able to know the real form\nof any opaque body, when by its remoteness we fail to discern it as\na whole, much more must we fail to discern its parts and outlines.\n\n223.\n\nOF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS.\n\nAmong opaque objects of equal size the apparent diminution of size\nwill be in proportion to their distance from the eye of the\nspectator; but it is an inverse proportion, since, where the\ndistance is greater, the opaque body will appear smaller, and the\nless the distance the larger will the object appear. And this is the\nfundamental principle of linear perspective and it\nfollows:--[11]every object as it becomes more remote loses first\nthose parts which are smallest. Thus of a horse, we should lose the\nlegs before the head, because the legs are thinner than the head;\nand the neck before the body for the same reason. Hence it follows\nthat the last part of the horse which would be discernible by the\neye would be the mass of the body in an oval form, or rather in a\ncylindrical form and this would lose its apparent thickness before\nits length--according to the 2nd rule given above, &c. [Footnote 23:\nCompare line 11.].\n\nIf the eye remains stationary the perspective terminates in the\ndistance in a point. But if the eye moves in a straight [horizontal]\nline the perspective terminates in a line and the reason is that\nthis line is generated by the motion of the point and our sight;\ntherefore it follows that as we move our sight [eye], the point\nmoves, and as we move the point, the line is generated, &c.\n\nAn illustration by experiment.\n\n224.\n\nEvery visible body, in so far as it affects the eye, includes three\nattributes; that is to say: mass, form and colour; and the mass is\nrecognisable at a greater distance from the place of its actual\nexistence than either colour or form. Again, colour is discernible\nat a greater distance than form, but this law does not apply to\nluminous bodies.\n\nThe above proposition is plainly shown and proved by experiment;\nbecause: if you see a man close to you, you discern the exact\nappearance of the mass and of the form and also of the colouring; if\nhe goes to some distance you will not recognise who he is, because\nthe character of the details will disappear, if he goes still\nfarther you will not be able to distinguish his colouring, but he\nwill appear as a dark object, and still farther he will appear as a\nvery small dark rounded object. It appears rounded because distance\nso greatly diminishes the various details that nothing remains\nvisible but the larger mass. And the reason is this: We know very\nwell that all the images of objects reach the senses by a small\naperture in the eye; hence, if the whole horizon _a d_ is admitted\nthrough such an aperture, the object _b c_ being but a very small\nfraction of this horizon what space can it fill in that minute image\nof so vast a hemisphere? And because luminous bodies have more power\nin darkness than any others, it is evident that, as the chamber of\nthe eye is very dark, as is the nature of all colored cavities, the\nimages of distant objects are confused and lost in the great light\nof the sky; and if they are visible at all, appear dark and black,\nas every small body must when seen in the diffused light of the\natmosphere.\n\n[Footnote: The diagram belonging to this passage is placed between\nlines 5 and 6; it is No. 4 on Pl. VI. ]\n\nA guiding rule.\n\n225.\n\nOF THE ATMOSPHERE THAT INTERPOSES BETWEEN THE EYE AND VISIBLE\nOBJECTS.\n\nAn object will appear more or less distinct at the same distance, in\nproportion as the atmosphere existing between the eye and that\nobject is more or less clear. Hence, as I know that the greater or\nless quantity of the air that lies between the eye and the object\nmakes the outlines of that object more or less indistinct, you must\ndiminish the definiteness of outline of those objects in proportion\nto their increasing distance from the eye of the spectator.\n\nAn experiment.\n\n226.\n\nWhen I was once in a place on the sea, at an equal distance from the\nshore and the mountains, the distance from the shore looked much\ngreater than that from the mountains.\n\nOn indistinctness at short distances (227-231).\n\n227.\n\nIf you place an opaque object in front of your eye at a distance of\nfour fingers' breadth, if it is smaller than the space between the\ntwo eyes it will not interfere with your seeing any thing that may\nbe beyond it. No object situated beyond another object seen by the\neye can be concealed by this [nearer] object if it is smaller than\nthe space from eye to eye.\n\n228.\n\nThe eye cannot take in a luminous angle which is too close to it.\n\n229.\n\nThat part of a surface will be better lighted on which the light\nfalls at the greater angle. And that part, on which the shadow falls\nat the greatest angle, will receive from those rays least of the\nbenefit of the light.\n\n230.\n\nOF THE EYE.\n\nThe edges of an object placed in front of the pupil of the eye will\nbe less distinct in proportion as they are closer to the eye. This\nis shown by the edge of the object _n_ placed in front of the pupil\n_d_; in looking at this edge the pupil also sees all the space _a c_\nwhich is beyond the edge; and the images the eye receives from that\nspace are mingled with the images of the edge, so that one image\nconfuses the other, and this confusion hinders the pupil from\ndistinguishing the edge.\n\n231.\n\nThe outlines of objects will be least clear when they are nearest to\nthe eye, and therefore remoter outlines will be clearer. Among\nobjects which are smaller than the pupil of the eye those will be\nless distinct which are nearer to the eye.\n\nOn indistinctness at great distances (232-234).\n\n232.\n\nObjects near to the eye will appear larger than those at a distance.\n\nObjects seen with two eyes will appear rounder than if they are seen\nwith only one.\n\nObjects seen between light and shadow will show the most relief.\n\n233.\n\nOF PAINTING.\n\nOur true perception of an object diminishes in proportion as its\nsize is diminished by distance.\n\n234.\n\nPERSPECTIVE.\n\nWhy objects seen at a distance appear large to the eye and in the\nimage on the vertical plane they appear small.\n\nPERSPECTIVE.\n\nI ask how far away the eye can discern a non-luminous body, as, for\ninstance, a mountain. It will be very plainly visible if the sun is\nbehind it; and could be seen at a greater or less distance according\nto the sun's place in the sky.\n\n[Footnote: The clue to the solution of this problem (lines 1-3) is\ngiven in lines 4-6, No. 232. Objects seen with both eyes appear\nsolid since they are seen from two distinct points of sight\nseparated by the distance between the eyes, but this solidity cannot\nbe represented in a flat drawing. Compare No. 535.]\n\nThe importance of light and shade in the perspective of\ndisappearance (235-239).\n\n235.\n\nAn opaque body seen in a line in which the light falls will reveal\nno prominences to the eye. For instance, let _a_ be the solid body\nand _c_ the light; _c m_ and _c n_ will be the lines of incidence of\nthe light, that is to say the lines which transmit the light to the\nobject _a_. The eye being at the point _b_, I say that since the\nlight _c_ falls on the whole part _m n_ the portions in relief on\nthat side will all be illuminated. Hence the eye placed at _c_\ncannot see any light and shade and, not seeing it, every portion\nwill appear of the same tone, therefore the relief in the prominent\nor rounded parts will not be visible.\n\n236.\n\nOF PAINTING.\n\nWhen you represent in your work shadows which you can only discern\nwith difficulty, and of which you cannot distinguish the edges so\nthat you apprehend them confusedly, you must not make them sharp or\ndefinite lest your work should have a wooden effect.\n\n237.\n\nOF PAINTING.\n\nYou will observe in drawing that among the shadows some are of\nundistinguishable gradation and form, as is shown in the 3rd\n[proposition] which says: Rounded surfaces display as many degrees\nof light and shade as there are varieties of brightness and darkness\nreflected from the surrounding objects.\n\n238.\n\nOF LIGHT AND SHADE.\n\nYou who draw from nature, look (carefully) at the extent, the\ndegree, and the form of the lights and shadows on each muscle; and\nin their position lengthwise observe towards which muscle the axis\nof the central line is directed.\n\n239.\n\nAn object which is [so brilliantly illuminated as to be] almost as\nbright as light will be visible at a greater distance, and of larger\napparent size than is natural to objects so remote.\n\nThe effect of light or dark backgrounds on the apparent size of\nobjects (240-250).\n\n240.\n\nA shadow will appear dark in proportion to the brilliancy of the\nlight surrounding it and conversely it will be less conspicuous\nwhere it is seen against a darker background.\n\n241.\n\nOF ORDINARY PERSPECTIVE.\n\nAn object of equal breadth and colour throughout, seen against a\nbackground of various colours will appear unequal in breadth.\n\nAnd if an object of equal breadth throughout, but of various\ncolours, is seen against a background of uniform colour, that object\nwill appear of various breadth. And the more the colours of the\nbackground or of the object seen against the ground vary, the\ngreater will the apparent variations in the breadth be though the\nobjects seen against the ground be of equal breadth [throughout].\n\n242.\n\nA dark object seen against a bright background will appear smaller\nthan it is.\n\nA light object will look larger when it is seen against a background\ndarker than itself.\n\n243.\n\nOF LIGHT.\n\nA luminous body when obscured by a dense atmosphere will appear\nsmaller; as may be seen by the moon or sun veiled by mists.\n\nOF LIGHT.\n\nOf several luminous bodies of equal size and brilliancy and at an\nequal distance, that will look the largest which is surrounded by\nthe darkest background.\n\nOF LIGHT.\n\nI find that any luminous body when seen through a dense and thick\nmist diminishes in proportion to its distance from the eye. Thus it\nis with the sun by day, as well as the moon and the other eternal\nlights by night. And when the air is clear, these luminaries appear\nlarger in proportion as they are farther from the eye.\n\n244.\n\nThat portion of a body of uniform breadth which is against a lighter\nbackground will look narrower [than the rest].\n\n[4] _e_ is a given object, itself dark and of uniform breadth; _a b_\nand _c d_ are two backgrounds one darker than the other; _b c_ is a\nbright background, as it might be a spot lighted by the sun through\nan aperture in a dark room. Then I say that the object _e g_ will\nappear larger at _e f_ than at _g h_; because _e f_ has a darker\nbackground than _g h_; and again at _f g_ it will look narrower from\nbeing seen by the eye _o_, on the light background _b c_. [Footnote\n12: The diagram to which the text, lines 1-11, refers, is placed in\nthe original between lines 3 and 4, and is given on Pl. XLI, No. 3.\nLines 12 to 14 are explained by the lower of the two diagrams on Pl.\nXLI, No. 4. In the original these are placed after line 14.] That\npart of a luminous body, of equal breadth and brilliancy throughout,\nwill look largest which is seen against the darkest background; and\nthe luminous body will seem on fire.\n\n245.\n\nWHY BODIES IN LIGHT AND SHADE HAVE THEIR OUTLINES ALTERED BY THE\nCOLOUR AND BRIGHTNESS OF THE OBJECTS SERVING AS A BACKGROUND TO\nTHEM.\n\nIf you look at a body of which the illuminated portion lies and ends\nagainst a dark background, that part of the light which will look\nbrightest will be that which lies against the dark [background] at\n_d_. But if this brighter part lies against a light background, the\nedge of the object, which is itself light, will be less distinct\nthan before, and the highest light will appear to be between the\nlimit of the background _m f_ and the shadow. The same thing is seen\nwith regard to the dark [side], inasmuch as that edge of the shaded\nportion of the object which lies against a light background, as at\n_l_, it looks much darker than the rest. But if this shadow lies\nagainst a dark background, the edge of the shaded part will appear\nlighter than before, and the deepest shade will appear between the\nedge and the light at the point _o_.\n\n[Footnote: In the original diagram _o_ is inside the shaded surface\nat the level of _d_.]\n\n246.\n\nAn opaque body will appear smaller when it is surrounded by a highly\nluminous background, and a light body will appear larger when it is\nseen against a darker background. This may be seen in the height of\nbuildings at night, when lightning flashes behind them; it suddenly\nseems, when it lightens, as though the height of the building were\ndiminished. For the same reason such buildings look larger in a\nmist, or by night than when the atmosphere is clear and light.\n\n247.\n\nON LIGHT BETWEEN SHADOWS\n\nWhen you are drawing any object, remember, in comparing the grades\nof light in the illuminated portions, that the eye is often deceived\nby seeing things lighter than they are. And the reason lies in our\ncomparing those parts with the contiguous parts. Since if two\n[separate] parts are in different grades of light and if the less\nbright is conterminous with a dark portion and the brighter is\nconterminous with a light background--as the sky or something\nequally bright--, then that which is less light, or I should say\nless radiant, will look the brighter and the brighter will seem the\ndarker.\n\n248.\n\nOf objects equally dark in themselves and situated at a considerable\nand equal distance, that will look the darkest which is farthest\nabove the earth.\n\n249.\n\nTO PROVE HOW IT IS THAT LUMINOUS BODIES APPEAR LARGER, AT A\nDISTANCE, THAN THEY ARE.\n\nIf you place two lighted candles side by side half a braccio apart,\nand go from them to a distance 200 braccia you will see that by the\nincreased size of each they will appear as a single luminous body\nwith the light of the two flames, one braccio wide.\n\nTO PROVE HOW YOU MAY SEE THE REAL SIZE OF LUMINOUS BODIES.\n\nIf you wish to see the real size of these luminous bodies, take a\nvery thin board and make in it a hole no bigger than the tag of a\nlace and place it as close to your eye as possible, so that when you\nlook through this hole, at the said light, you can see a large space\nof air round it. Then by rapidly moving this board backwards and\nforwards before your eye you will see the light increase [and\ndiminish].\n\nPropositions on perspective of disappearance from MS. C. (250-262).\n\n250.\n\nOf several bodies of equal size and equally distant from the eye,\nthose will look the smallest which are against the lightest\nbackground.\n\nEvery visible object must be surrounded by light and shade. A\nperfectly spherical body surrounded by light and shade will appear\nto have one side larger than the other in proportion as one is more\nhighly lighted than the other.\n\n251.\n\nPERSPECTIVE.\n\nNo visible object can be well understood and comprehended by the\nhuman eye excepting from the difference of the background against\nwhich the edges of the object terminate and by which they are\nbounded, and no object will appear [to stand out] separate from that\nbackground so far as the outlines of its borders are concerned. The\nmoon, though it is at a great distance from the sun, when, in an\neclipse, it comes between our eyes and the sun, appears to the eyes\nof men to be close to the sun and affixed to it, because the sun is\nthen the background to the moon.\n\n252.\n\nA luminous body will appear more brilliant in proportion as it is\nsurrounded by deeper shadow. [Footnote: The diagram which, in the\noriginal, is placed after this text, has no connection with it.]\n\n253.\n\nThe straight edges of a body will appear broken when they are\nconterminous with a dark space streaked with rays of light.\n[Footnote: Here again the diagrams in the original have no\nconnection with the text.]\n\n254.\n\nOf several bodies, all equally large and equally distant, that which\nis most brightly illuminated will appear to the eye nearest and\nlargest. [Footnote: Here again the diagrams in the original have no\nconnection with the text.]\n\n255.\n\nIf several luminous bodies are seen from a great distance although\nthey are really separate they will appear united as one body.\n\n256.\n\nIf several objects in shadow, standing very close together, are seen\nagainst a bright background they will appear separated by wide\nintervals.\n\n257.\n\nOf several bodies of equal size and tone, that which is farthest\nwill appear the lightest and smallest.\n\n258.\n\nOf several objects equal in size, brightness of background and\nlength that which has the flattest surface will look the largest. A\nbar of iron equally thick throughout and of which half is red hot,\naffords an example, for the red hot part looks thicker than the\nrest.\n\n259.\n\nOf several bodies of equal size and length, and alike in form and in\ndepth of shade, that will appear smallest which is surrounded by the\nmost luminous background.\n\n260.\n\nDIFFERENT PORTIONS OF A WALL SURFACE WILL BE DARKER OR BRIGHTER IN\nPROPORTION AS THE LIGHT OR SHADOW FALLS ON THEM AT A LARGER ANGLE.\n\nThe foregoing proposition can be clearly proved in this way. Let us\nsay that _m q_ is the luminous body, then _f g_ will be the opaque\nbody; and let _a e_ be the above-mentioned plane on which the said\nangles fall, showing [plainly] the nature and character of their\nbases. Then: _a_ will be more luminous than _b_; the base of the\nangle _a_ is larger than that of _b_ and it therefore makes a\ngreater angle which will be _a m q_; and the pyramid _b p m_ will be\nnarrower and _m o c_ will be still finer, and so on by degrees, in\nproportion as they are nearer to _e_, the pyramids will become\nnarrower and darker. That portion of the wall will be the darkest\nwhere the breadth of the pyramid of shadow is greater than the\nbreadth of the pyramid of light.\n\nAt the point _a_ the pyramid of light is equal in strength to the\npyramid of shadow, because the base _f g_ is equal to the base _r\nf_. At the point _d_ the pyramid of light is narrower than the\npyramid of shadow by so much as the base _s f_ is less than the base\n_f g_.\n\nDivide the foregoing proposition into two diagrams, one with the\npyramids of light and shadow, the other with the pyramids of light\n[only].\n\n261.\n\nAmong shadows of equal depth those which are nearest to the eye will\nlook least deep.\n\n262.\n\nThe more brilliant the light given by a luminous body, the deeper\nwill the shadows be cast by the objects it illuminates.\n\n_V._\n\n_Theory of colours._\n\n_Leonardo's theory of colours is even more intimately connected with\nhis principles of light and shade than his Perspective of\nDisappearance and is in fact merely an appendix or supplement to\nthose principles, as we gather from the titles to sections_ 264,\n267_, and _276_, while others again_ (_Nos._ 281, 282_) are headed_\nProspettiva.\n\n_A very few of these chapters are to be found in the oldest copies\nand editions of the Treatise on Painting, and although the material\nthey afford is but meager and the connection between them but\nslight, we must still attribute to them a special theoretical value\nas well as practical utility--all the more so because our knowledge\nof the theory and use of colours at the time of the Renaissance is\nstill extremely limited._\n\nThe reciprocal effects of colours on objects placed opposite each\nother (263-272).\n\n263.\n\nOF PAINTING.\n\nThe hue of an illuminated object is affected by that of the luminous\nbody.\n\n264.\n\nOF SHADOW.\n\nThe surface of any opaque body is affected by the colour of\nsurrounding objects.\n\n265.\n\nA shadow is always affected by the colour of the surface on which it\nis cast.\n\n266.\n\nAn image produced in a mirror is affected by the colour of the\nmirror.\n\n267.\n\nOF LIGHT AND SHADE.\n\nEvery portion of the surface of a body is varied [in hue] by the\n[reflected] colour of the object that may be opposite to it.\n\nEXAMPLE.\n\nIf you place a spherical body between various objects that is to say\nwith [direct] sunlight on one side of it, and on the other a wall\nilluminated by the sun, which wall may be green or of any other\ncolour, while the surface on which it is placed may be red, and the\ntwo lateral sides are in shadow, you will see that the natural\ncolour of that body will assume something of the hue reflected from\nthose objects. The strongest will be [given by] the luminous body;\nthe second by the illuminated wall, the third by the shadows. There\nwill still be a portion which will take a tint from the colour of\nthe edges.\n\n268.\n\nThe surface of every opaque body is affected by the colour of the\nobjects surrounding it. But this effect will be strong or weak in\nproportion as those objects are more or less remote and more or less\nstrongly [coloured].\n\n269.\n\nOF PAINTING.\n\nThe surface of every opaque body assumes the hues reflected from\nsurrounding objects.\n\nThe surface of an opaque body assumes the hues of surrounding\nobjects more strongly in proportion as the rays that form the images\nof those objects strike the surface at more equal angles.\n\nAnd the surface of an opaque body assumes a stronger hue from the\nsurrounding objects in proportion as that surface is whiter and the\ncolour of the object brighter or more highly illuminated.\n\n270.\n\nOF THE RAYS WHICH CONVEY THROUGH THE AIR THE IMAGES OF OBJECTS.\n\nAll the minutest parts of the image intersect each other without\ninterfering with each other. To prove this let _r_ be one of the\nsides of the hole, opposite to which let _s_ be the eye which sees\nthe lower end _o_ of the line _n o_. The other extremity cannot\ntransmit its image to the eye _s_ as it has to strike the end _r_\nand it is the same with regard to _m_ at the middle of the line. The\ncase is the same with the upper extremity _n_ and the eye _u_. And\nif the end _n_ is red the eye _u_ on that side of the holes will not\nsee the green colour of _o_, but only the red of _n_ according to\nthe 7th of this where it is said: Every form projects images from\nitself by the shortest line, which necessarily is a straight line,\n&c.\n\n[Footnote: 13. This probably refers to the diagram given under No.\n66.]\n\n271.\n\nOF PAINTING.\n\nThe surface of a body assumes in some degree the hue of those around\nit. The colours of illuminated objects are reflected from the\nsurfaces of one to the other in various spots, according to the\nvarious positions of those objects. Let _o_ be a blue object in full\nlight, facing all by itself the space _b c_ on the white sphere _a b\ne d e f_, and it will give it a blue tinge, _m_ is a yellow body\nreflected onto the space _a b_ at the same time as _o_ the blue\nbody, and they give it a green colour (by the 2nd [proposition] of\nthis which shows that blue and yellow make a beautiful green &c.)\nAnd the rest will be set forth in the Book on Painting. In that Book\nit will be shown, that, by transmitting the images of objects and\nthe colours of bodies illuminated by sunlight through a small round\nperforation and into a dark chamber onto a plane surface, which\nitself is quite white, &c.\n\nBut every thing will be upside down.\n\nCombination of different colours in cast shadows.\n\n272.\n\nThat which casts the shadow does not face it, because the shadows\nare produced by the light which causes and surrounds the shadows.\nThe shadow caused by the light _e_, which is yellow, has a blue\ntinge, because the shadow of the body _a_ is cast upon the pavement\nat _b_, where the blue light falls; and the shadow produced by the\nlight _d_, which is blue, will be yellow at _c_, because the yellow\nlight falls there and the surrounding background to these shadows _b\nc_ will, besides its natural colour, assume a hue compounded of\nyellow and blue, because it is lighted by the yellow light and by\nthe blue light both at once.\n\nShadows of various colours, as affected by the lights falling on\nthem. That light which causes the shadow does not face it.\n\n[Footnote: In the original diagram we find in the circle _e_\n\"_giallo_\" (yellow) and the cirle _d_ \"_azurro\"_ (blue) and also\nunder the circle of shadow to the left \"_giallo_\" is written and\nunder that to the right \"_azurro_\".\n\nIn the second diagram where four circles are placed in a row we find\nwritten, beginning at the left hand, \"_giallo_\" (yellow), \"_azurro_\"\n(blue), \"_verde_\" (green), \"_rosso_\" (red).]\n\nThe effect of colours in the camera obscura (273-274).\n\n273.\n\nThe edges of a colour(ed object) transmitted through a small hole\nare more conspicuous than the central portions.\n\nThe edges of the images, of whatever colour, which are transmitted\nthrough a small aperture into a dark chamber will always be stronger\nthan the middle portions.\n\n274.\n\nOF THE INTERSECTIONS OF THE IMAGES IN THE PUPIL OF THE EYE.\n\nThe intersections of the images as they enter the pupil do not\nmingle in confusion in the space where that intersection unites\nthem; as is evident, since, if the rays of the sun pass through two\npanes of glass in close contact, of which one is blue and the other\nyellow, the rays, in penetrating them, do not become blue or yellow\nbut a beautiful green. And the same thing would happen in the eye,\nif the images which were yellow or green should mingle where they\n[meet and] intersect as they enter the pupil. As this does not\nhappen such a mingling does not exist.\n\nOF THE NATURE OF THE RAYS COMPOSED OF THE IMAGES OF OBJECTS, AND OF\nTHEIR INTERSECTIONS.\n\nThe directness of the rays which transmit the forms and colours of\nthe bodies whence they proceed does not tinge the air nor can they\naffect each other by contact where they intersect. They affect only\nthe spot where they vanish and cease to exist, because that spot\nfaces and is faced by the original source of these rays, and no\nother object, which surrounds that original source can be seen by\nthe eye where these rays are cut off and destroyed, leaving there\nthe spoil they have conveyed to it. And this is proved by the 4th\n[proposition], on the colour of bodies, which says: The surface of\nevery opaque body is affected by the colour of surrounding objects;\nhence we may conclude that the spot which, by means of the rays\nwhich convey the image, faces--and is faced by the cause of the\nimage, assumes the colour of that object.\n\nOn the colours of derived shadows (275. 276).\n\n275.\n\nANY SHADOW CAST BY AN OPAQUE BODY SMALLER THAN THE LIGHT CAUSING THE\nSHADOW WILL THROW A DERIVED SHADOW WHICH IS TINGED BY THE COLOUR OF\nTHE LIGHT.\n\nLet _n_ be the source of the shadow _e f_; it will assume its hue.\nLet _o_ be the source of _h e_ which will in the same way be tinged\nby its hue and so also the colour of _v h_ will be affected by _p_\nwhich causes it; and the shadow of the triangle _z k y_ will be\naffected by the colour of _q_, because it is produced by it. [7] In\nproportion as _c d_ goes into _a d_, will _n r s_ be darker than\n_m_; and the rest of the space will be shadowless [11]. _f g_ is\nthe highest light, because here the whole light of the window _a d_\nfalls; and thus on the opaque body _m e_ is in equally high light;\n_z k y_ is a triangle which includes the deepest shadow, because the\nlight _a d_ cannot reach any part of it. _x h_ is the 2nd grade of\nshadow, because it receives only 1/3 of the light from the window,\nthat is _c d_. The third grade of shadow is _h e_, where two thirds\nof the light from the window is visible. The last grade of shadow is\n_b d e f_, because the highest grade of light from the window falls\nat _f_.\n\n[Footnote: The diagram Pl. III, No. 1 belongs to this chapter as\nwell as the text given in No. 148. Lines 7-11 (compare lines 8-12 of\nNo. 148) which are written within the diagram, evidently apply to\nboth sections and have therefore been inserted in both.]\n\n276.\n\nOF THE COLOURS OF SIMPLE DERIVED SHADOWS.\n\nThe colour of derived shadows is always affected by that of the body\ntowards which they are cast. To prove this: let an opaque body be\nplaced between the plane _s c t d_ and the blue light _d e_ and the\nred light _a b_, then I say that _d e_, the blue light, will fall on\nthe whole surface _s c t d_ excepting at _o p_ which is covered by\nthe shadow of the body _q r_, as is shown by the straight lines _d q\no e r p_. And the same occurs with the light _a b_ which falls on\nthe whole surface _s c t d_ excepting at the spot obscured by the\nshadow _q r_; as is shown by the lines _d q o_, and _e r p_. Hence\nwe may conclude that the shadow _n m_ is exposed to the blue light\n_d e_; but, as the red light _a b_ cannot fall there, _n m_ will\nappear as a blue shadow on a red background tinted with blue,\nbecause on the surface _s c t d_ both lights can fall. But in the\nshadows only one single light falls; for this reason these shadows\nare of medium depth, since, if no light whatever mingled with the\nshadow, it would be of the first degree of darkness &c. But in the\nshadow at _o p_ the blue light does not fall, because the body _q r_\ninterposes and intercepts it there. Only the red light _a b_ falls\nthere and tinges the shadow of a red hue and so a ruddy shadow\nappears on the background of mingled red and blue.\n\nThe shadow of _q r_ at _o p_ is red, being caused by the blue light\n_d e_; and the shadow of _q r_ at _o' p'_ is blue being caused by\nthe red light _a b_. Hence we say that the blue light in this\ninstance causes a red derived shadow from the opaque body _q' r'_,\nwhile the red light causes the same body to cast a blue derived\nshadow; but the primary shadow [on the dark side of the body itself]\nis not of either of those hues, but a mixture of red and blue.\n\nThe derived shadows will be equal in depth if they are produced by\nlights of equal strength and at an equal distance; this is proved.\n[Footnote 53: The text is unfinished in the original.]\n\n[Footnote: In the original diagram Leonardo has written within the\ncircle _q r corpo obroso_ (body in shadow); at the spot marked _A,\nluminoso azzurro_ (blue luminous body); at _B, luminoso rosso_ (red\nluminous body). At _E_ we read _ombra azzurra_ (blue tinted shadow)\nand at _D ombra rossa_ (red tinted shadow).]\n\nOn the nature of colours (277. 278).\n\n277.\n\nNo white or black is transparent.\n\n278.\n\nOF PAINTING.\n\n[Footnote 2: See Footnote 3] Since white is not a colour but the\nneutral recipient of every colour [Footnote 3: _il bianco non e\ncolore ma e inpotentia ricettiva d'ogni colore_ (white is not a\ncolour, but the neutral recipient of every colour). LEON BATT.\nALBERTI \"_Della pittura_\" libro I, asserts on the contrary: \"_Il\nbianco e'l nero non sono veri colori, ma sono alteratione delli\naltri colori_\" (ed. JANITSCHEK, p. 67; Vienna 1877).], when it is\nseen in the open air and high up, all its shadows are bluish; and\nthis is caused, according to the 4th [prop.], which says: the\nsurface of every opaque body assumes the hue of the surrounding\nobjects. Now this white [body] being deprived of the light of the\nsun by the interposition of some body between the sun and itself,\nall that portion of it which is exposed to the sun and atmosphere\nassumes the colour of the sun and atmosphere; the side on which the\nsun does not fall remains in shadow and assumes the hue of the\natmosphere. And if this white object did not reflect the green of\nthe fields all the way to the horizon nor get the brightness of the\nhorizon itself, it would certainly appear simply of the same hue as\nthe atmosphere.\n\nOn gradations in the depth of colours (279. 280).\n\n279.\n\nSince black, when painted next to white, looks no blacker than when\nnext to black; and white when next to black looks no whiter than\nwhite, as is seen by the images transmitted through a small hole or\nby the edges of any opaque screen ...\n\n280.\n\nOF COLOURS.\n\nOf several colours, all equally white, that will look whitest which\nis against the darkest background. And black will look intensest\nagainst the whitest background.\n\nAnd red will look most vivid against the yellowest background; and\nthe same is the case with all colours when surrounded by their\nstrongest contrasts.\n\nOn the reflection of colours (281-283).\n\n281.\n\nPERSPECTIVE.\n\nEvery object devoid of colour in itself is more or less tinged by\nthe colour [of the object] placed opposite. This may be seen by\nexperience, inasmuch as any object which mirrors another assumes the\ncolour of the object mirrored in it. And if the surface thus\npartially coloured is white the portion which has a red reflection\nwill appear red, or any other colour, whether bright or dark.\n\nPERSPECTIVE.\n\nEvery opaque and colourless body assumes the hue of the colour\nreflected on it; as happens with a white wall.\n\n282.\n\nPERSPECTIVE.\n\nThat side of an object in light and shade which is towards the light\ntransmits the images of its details more distinctly and immediately\nto the eye than the side which is in shadow.\n\nPERSPECTIVE.\n\nThe solar rays reflected on a square mirror will be thrown back to\ndistant objects in a circular form.\n\nPERSPECTIVE.\n\nAny white and opaque surface will be partially coloured by\nreflections from surrounding objects.\n\n[Footnote 281. 282: The title line of these chapters is in the\noriginal simply _\"pro\"_, which may be an abbreviation for either\n_Propositione_ or _Prospettiva_--taking Prospettiva of course in its\nwidest sense, as we often find it used in Leonardo's writings. The\ntitle _\"pro\"_ has here been understood to mean _Prospettiva_, in\naccordance with the suggestion afforded by page 10b of this same\nMS., where the first section is headed _Prospettiva_ in full (see\nNo. 94), while the four following sections are headed merely _\"pro\"_\n(see No. 85).]\n\n283.\n\nWHAT PORTION OF A COLOURED SURFACE OUGHT IN REASON TO BE THE MOST\nINTENSE.\n\nIf _a_ is the light, and _b_ illuminated by it in a direct line,\n_c_, on which the light cannot fall, is lighted only by reflection\nfrom _b_ which, let us say, is red. Hence the light reflected from\nit, will be affected by the hue of the surface causing it and will\ntinge the surface _c_ with red. And if _c_ is also red you will see\nit much more intense than _b_; and if it were yellow you would see\nthere a colour between yellow and red.\n\nOn the use of dark and light colours in painting (284--286).\n\n284.\n\nWHY BEAUTIFUL COLOURS MUST BE IN THE [HIGHEST] LIGHT.\n\nSince we see that the quality of colour is known [only] by means of\nlight, it is to be supposed that where there is most light the true\ncharacter of a colour in light will be best seen; and where there is\nmost shadow the colour will be affected by the tone of that. Hence,\nO Painter! remember to show the true quality of colours in bright\nlights.\n\n285.\n\nAn object represented in white and black will display stronger\nrelief than in any other way; hence I would remind you O Painter! to\ndress your figures in the lightest colours you can, since, if you\nput them in dark colours, they will be in too slight relief and\ninconspicuous from a distance. And the reason is that the shadows of\nall objects are dark. And if you make a dress dark there is little\nvariety in the lights and shadows, while in light colours there are\nmany grades.\n\n286.\n\nOF PAINTING.\n\nColours seen in shadow will display more or less of their natural\nbrilliancy in proportion as they are in fainter or deeper shadow.\n\nBut if these same colours are situated in a well-lighted place, they\nwill appear brighter in proportion as the light is more brilliant.\n\nTHE ADVERSARY.\n\nThe variety of colours in shadow must be as great as that of the\ncolours in the objects in that shadow.\n\nTHE ANSWER.\n\nColours seen in shadow will display less variety in proportion as\nthe shadows in which they lie are deeper. And evidence of this is to\nbe had by looking from an open space into the doorways of dark and\nshadowy churches, where the pictures which are painted in various\ncolours all look of uniform darkness.\n\nHence at a considerable distance all the shadows of different\ncolours will appear of the same darkness.\n\nIt is the light side of an object in light and shade which shows the\ntrue colour.\n\nOn the colours of the rainbow (287. 288).\n\n287.\n\nTreat of the rainbow in the last book on Painting, but first write\nthe book on colours produced by the mixture of other colours, so as\nto be able to prove by those painters' colours how the colours of\nthe rainbow are produced.\n\n288.\n\nWHETHER THE COLOURS OF THE RAINBOW ARE PRODUCED BY THE SUN.\n\nThe colours of the rainbow are not produced by the sun, for they\noccur in many ways without the sunshine; as may be seen by holding a\nglass of water up to the eye; when, in the glass--where there are\nthose minute bubbles always seen in coarse glass--each bubble, even\nthough the sun does not fall on it, will produce on one side all the\ncolours of the rainbow; as you may see by placing the glass between\nthe day light and your eye in such a way as that it is close to the\neye, while on one side the glass admits the [diffused] light of the\natmosphere, and on the other side the shadow of the wall on one side\nof the window; either left or right, it matters not which. Then, by\nturning the glass round you will see these colours all round the\nbubbles in the glass &c. And the rest shall be said in its place.\n\nTHAT THE EYE HAS NO PART IN PRODUCING THE COLOURS OF THE RAINBOW.\n\nIn the experiment just described, the eye would seem to have some\nshare in the colours of the rainbow, since these bubbles in the\nglass do not display the colours except through the medium of the\neye. But, if you place the glass full of water on the window sill,\nin such a position as that the outer side is exposed to the sun's\nrays, you will see the same colours produced in the spot of light\nthrown through the glass and upon the floor, in a dark place, below\nthe window; and as the eye is not here concerned in it, we may\nevidently, and with certainty pronounce that the eye has no share in\nproducing them.\n\nOF THE COLOURS IN THE FEATHERS OF CERTAIN BIRDS.\n\nThere are many birds in various regions of the world on whose\nfeathers we see the most splendid colours produced as they move, as\nwe see in our own country in the feathers of peacocks or on the\nnecks of ducks or pigeons, &c.\n\nAgain, on the surface of antique glass found underground and on the\nroots of turnips kept for some time at the bottom of wells or other\nstagnant waters [we see] that each root displays colours similar to\nthose of the real rainbow. They may also be seen when oil has been\nplaced on the top of water and in the solar rays reflected from the\nsurface of a diamond or beryl; again, through the angular facet of a\nberyl every dark object against a background of the atmosphere or\nany thing else equally pale-coloured is surrounded by these rainbow\ncolours between the atmosphere and the dark body; and in many other\ncircumstances which I will not mention, as these suffice for my\npurpose.\n\n_VI._\n\n_'Prospettiva de' colri' (Perspective of Colour)_\n\n_and_\n\n_'Prospettiva aerea' (Aerial Perspective)._\n\n_Leonardo distinctly separates these branches of his subject, as may\nbe seen in the beginning of No._ 295. _Attempts have been made to\ncast doubts on the results which Leonardo arrived at by experiment\non the perspective of colour, but not with justice, as may be seen\nfrom the original text of section_ 294.\n\n_The question as to the composition of the atmosphere, which is\ninseparable from a discussion on Aerial Perspective, forms a\nseparate theory which is treated at considerable length. Indeed the\nauthor enters into it so fully that we cannot escape the conviction\nthat he must have dwelt with particular pleasure on this part of his\nsubject, and that he attached great importance to giving it a\ncharacter of general applicability._\n\nGeneral rules (289--291).\n\n289.\n\nThe variety of colour in objects cannot be discerned at a great\ndistance, excepting in those parts which are directly lighted up by\nthe solar rays.\n\n290.\n\nAs to the colours of objects: at long distances no difference is\nperceptible in the parts in shadow.\n\n291.\n\nOF THE VISIBILITY OF COLOURS.\n\nWhich colour strikes most? An object at a distance is most\nconspicuous, when it is lightest, and the darkest is least visible.\n\nAn exceptional case.\n\n292.\n\nOf the edges [outlines] of shadows. Some have misty and ill defined\nedges, others distinct ones.\n\nNo opaque body can be devoid of light and shade, except it is in a\nmist, on ground covered with snow, or when snow is falling on the\nopen country which has no light on it and is surrounded with\ndarkness.\n\nAnd this occurs [only] in spherical bodies, because in other bodies\nwhich have limbs and parts, those sides of limbs which face each\nother reflect on each other the accidental [hue and tone] of their\nsurface.\n\nAn experiment.\n\n293.\n\nALL COLOURS ARE AT A DISTANCE UNDISTINGUISHABLE AND UNDISCERNIBLE.\n\nAll colours at a distance are undistinguishable in shadow, because\nan object which is not in the highest light is incapable of\ntransmitting its image to the eye through an atmosphere more\nluminous than itself; since the lesser brightness must be absorbed\nby the greater. For instance: We, in a house, can see that all the\ncolours on the surface of the walls are clearly and instantly\nvisible when the windows of the house are open; but if we were to go\nout of the house and look in at the windows from a little distance\nto see the paintings on those walls, instead of the paintings we\nshould see an uniform deep and colourless shadow.\n\nThe practice of the prospettiva de colori.\n\n294.\n\nHOW A PAINTER SHOULD CARRY OUT THE PERSPECTIVE OF COLOUR IN\nPRACTICE.\n\nIn order to put into practice this perspective of the variation and\nloss or diminution of the essential character of colours, observe at\nevery hundred braccia some objects standing in the landscape, such\nas trees, houses, men and particular places. Then in front of the\nfirst tree have a very steady plate of glass and keep your eye very\nsteady, and then, on this plate of glass, draw a tree, tracing it\nover the form of that tree. Then move it on one side so far as that\nthe real tree is close by the side of the tree you have drawn; then\ncolour your drawing in such a way as that in colour and form the two\nmay be alike, and that both, if you close one eye, seem to be\npainted on the glass and at the same distance. Then, by the same\nmethod, represent a second tree, and a third, with a distance of a\nhundred braccia between each. And these will serve as a standard and\nguide whenever you work on your own pictures, wherever they may\napply, and will enable you to give due distance in those works. [14]\nBut I have found that as a rule the second is 4/5 of the first when\nit is 20 braccia beyond it.\n\n[Footnote: This chapter is one of those copied in the Manuscript of\nthe Vatican library Urbinas 1270, and the original text is rendered\nhere with no other alterations, but in the orthography. H. LUDWIG,\nin his edition of this copy translates lines 14 and 15 thus: \"_Ich\nfinde aber als Regel, dass der zweite um vier Funftel des ersten\nabnimmt, wenn er namlich zwanzig Ellen vom ersten entfernt ist\n(?)\"_. He adds in his commentary: \"_Das Ende der Nummer ist wohl\njedenfalls verstummelt_\". However the translation given above shows\nthat it admits of a different rendering.]\n\nThe rules of aerial perspective (295--297).\n\n295.\n\nOF AERIAL PERSPECTIVE.\n\nThere is another kind of perspective which I call Aerial\nPerspective, because by the atmosphere we are able to distinguish\nthe variations in distance of different buildings, which appear\nplaced on a single line; as, for instance, when we see several\nbuildings beyond a wall, all of which, as they appear above the top\nof the wall, look of the same size, while you wish to represent them\nin a picture as more remote one than another and to give the effect\nof a somewhat dense atmosphere. You know that in an atmosphere of\nequal density the remotest objects seen through it, as mountains, in\nconsequence of the great quantity of atmosphere between your eye and\nthem--appear blue and almost of the same hue as the atmosphere\nitself [Footnote 10: _quado il sole e per leuante_ (when the sun is\nin the East). Apparently the author refers here to morning light in\ngeneral. H. LUDWIG however translates this passage from the Vatican\ncopy \"_wenn namlich die Sonne (dahinter) im Osten steht_\".] when the\nsun is in the East [Footnote 11: See Footnote 10]. Hence you must\nmake the nearest building above the wall of its real colour, but the\nmore distant ones make less defined and bluer. Those you wish should\nlook farthest away you must make proportionately bluer; thus, if one\nis to be five times as distant, make it five times bluer. And by\nthis rule the buildings which above a [given] line appear of the\nsame size, will plainly be distinguished as to which are the more\nremote and which larger than the others.\n\n296.\n\nThe medium lying between the eye and the object seen, tinges that\nobject with its colour, as the blueness of the atmosphere makes the\ndistant mountains appear blue and red glass makes objects seen\nbeyond it, look red. The light shed round them by the stars is\nobscured by the darkness of the night which lies between the eye and\nthe radiant light of the stars.\n\n297.\n\nTake care that the perspective of colour does not disagree with the\nsize of your objects, hat is to say: that the colours diminish from\ntheir natural [vividness] in proportion as the objects at various\ndistances dimmish from their natural size.\n\nOn the relative density of the atmosphere (298--290).\n\n298.\n\nWHY THE ATMOSPHERE MUST BE REPRESENTED AS PALER TOWARDS THE LOWER\nPORTION.\n\nBecause the atmosphere is dense near the earth, and the higher it is\nthe rarer it becomes. When the sun is in the East if you look\ntowards the West and a little way to the South and North, you will\nsee that this dense atmosphere receives more light from the sun than\nthe rarer; because the rays meet with greater resistance. And if the\nsky, as you see it, ends on a low plain, that lowest portion of the\nsky will be seen through a denser and whiter atmosphere, which will\nweaken its true colour as seen through that medium, and there the\nsky will look whiter than it is above you, where the line of sight\ntravels through a smaller space of air charged with heavy vapour.\nAnd if you turn to the East, the atmosphere will appear darker as\nyou look lower down because the luminous rays pass less freely\nthrough the lower atmosphere.\n\n299.\n\nOF THE MODE OF TREATING REMOTE OBJECTS IN PAINTING.\n\nIt is easy to perceive that the atmosphere which lies closest to the\nlevel ground is denser than the rest, and that where it is higher\nup, it is rarer and more transparent. The lower portions of large\nand lofty objects which are at a distance are not much seen, because\nyou see them along a line which passes through a denser and thicker\nsection of the atmosphere. The summits of such heights are seen\nalong a line which, though it starts from your eye in a dense\natmosphere, still, as it ends at the top of those lofty objects,\nceases in a much rarer atmosphere than exists at their base; for\nthis reason the farther this line extends from your eye, from point\nto point the atmosphere becomes more and more rare. Hence, O\nPainter! when you represent mountains, see that from hill to hill\nthe bases are paler than the summits, and in proportion as they\nrecede beyond each other make the bases paler than the summits;\nwhile, the higher they are the more you must show of their true form\nand colour.\n\nOn the colour of the atmosphere (300-307).\n\n300.\n\nOF THE COLOUR OF THE ATMOSPHERE.\n\nI say that the blueness we see in the atmosphere is not intrinsic\ncolour, but is caused by warm vapour evaporated in minute and\ninsensible atoms on which the solar rays fall, rendering them\nluminous against the infinite darkness of the fiery sphere which\nlies beyond and includes it. And this may be seen, as I saw it by\nany one going up [Footnote 5: With regard to the place spoken of as\n_M'oboso_ (compare No. 301 line 20) its identity will be discussed\nunder Leonardo's Topographical notes in Vol. II.] Monboso, a peak of\nthe Alps which divide France from Italy. The base of this mountain\ngives birth to the four rivers which flow in four different\ndirections through the whole of Europe. And no mountain has its base\nat so great a height as this, which lifts itself almost above the\nclouds; and snow seldom falls there, but only hail in the summer,\nwhen the clouds are highest. And this hail lies [unmelted] there, so\nthat if it were not for the absorption of the rising and falling\nclouds, which does not happen twice in an age, an enormous mass of\nice would be piled up there by the hail, and in the middle of July I\nfound it very considerable. There I saw above me the dark sky, and\nthe sun as it fell on the mountain was far brighter here than in the\nplains below, because a smaller extent of atmosphere lay between the\nsummit of the mountain and the sun. Again as an illustration of the\ncolour of the atmosphere I will mention the smoke of old and dry\nwood, which, as it comes out of a chimney, appears to turn very\nblue, when seen between the eye and the dark distance. But as it\nrises, and comes between the eye and the bright atmosphere, it at\nonce shows of an ashy grey colour; and this happens because it no\nlonger has darkness beyond it, but this bright and luminous space.\nIf the smoke is from young, green wood, it will not appear blue,\nbecause, not being transparent and being full of superabundant\nmoisture, it has the effect of condensed clouds which take distinct\nlights and shadows like a solid body. The same occurs with the\natmosphere, which, when overcharged with moisture appears white, and\nthe small amount of heated moisture makes it dark, of a dark blue\ncolour; and this will suffice us so far as concerns the colour of\nthe atmosphere; though it might be added that, if this transparent\nblue were the natural colour of the atmosphere, it would follow that\nwherever a larger mass air intervened between the eye and the\nelement of fire, the azure colour would be more intense; as we see\nin blue glass and in sapphires, which are darker in proportion as\nthey are larger. But the atmosphere in such circumstances behaves in\nan opposite manner, inasmuch as where a greater quantity of it lies\nbetween the eye and the sphere of fire, it is seen much whiter. This\noccurs towards the horizon. And the less the extent of atmosphere\nbetween the eye and the sphere of fire, the deeper is the blue\ncolour, as may be seen even on low plains. Hence it follows, as I\nsay, that the atmosphere assumes this azure hue by reason of the\nparticles of moisture which catch the rays of the sun. Again, we may\nnote the difference in particles of dust, or particles of smoke, in\nthe sun beams admitted through holes into a dark chamber, when the\nformer will look ash grey and the thin smoke will appear of a most\nbeautiful blue; and it may be seen again in in the dark shadows of\ndistant mountains when the air between the eye and those shadows\nwill look very blue, though the brightest parts of those mountains\nwill not differ much from their true colour. But if any one wishes\nfor a final proof let him paint a board with various colours, among\nthem an intense black; and over all let him lay a very thin and\ntransparent [coating of] white. He will then see that this\ntransparent white will nowhere show a more beautiful blue than over\nthe black--but it must be very thin and finely ground.\n\n[Footnote 7: _reta_ here has the sense of _malanno_.]\n\n301.\n\nExperience shows us that the air must have darkness beyond it and\nyet it appears blue. If you produce a small quantity of smoke from\ndry wood and the rays of the sun fall on this smoke, and if you then\nplace behind the smoke a piece of black velvet on which the sun does\nnot shine, you will see that all the smoke which is between the eye\nand the black stuff will appear of a beautiful blue colour. And if\ninstead of the velvet you place a white cloth smoke, that is too\nthick smoke, hinders, and too thin smoke does not produce, the\nperfection of this blue colour. Hence a moderate amount of smoke\nproduces the finest blue. Water violently ejected in a fine spray\nand in a dark chamber where the sun beams are admitted produces\nthese blue rays and the more vividly if it is distilled water, and\nthin smoke looks blue. This I mention in order to show that the\nblueness of the atmosphere is caused by the darkness beyond it, and\nthese instances are given for those who cannot confirm my experience\non Monboso.\n\n302.\n\nWhen the smoke from dry wood is seen between the eye of the\nspectator and some dark space [or object], it will look blue. Thus\nthe sky looks blue by reason of the darkness beyond it. And if you\nlook towards the horizon of the sky, you will see the atmosphere is\nnot blue, and this is caused by its density. And thus at each\ndegree, as you raise your eyes above the horizon up to the sky over\nyour head, you will see the atmosphere look darker [blue] and this\nis because a smaller density of air lies between your eye and the\n[outer] darkness. And if you go to the top of a high mountain the\nsky will look proportionately darker above you as the atmosphere\nbecomes rarer between you and the [outer] darkness; and this will be\nmore visible at each degree of increasing height till at last we\nshould find darkness.\n\nThat smoke will look bluest which rises from the driest wood and\nwhich is nearest to the fire and is seen against the darkest\nbackground, and with the sunlight upon it.\n\n303.\n\nA dark object will appear bluest in proportion as it has a greater\nmass of luminous atmosphere between it and the eye. As may be seen\nin the colour of the sky.\n\n304.\n\nThe atmosphere is blue by reason of the darkness above it because\nblack and white make blue.\n\n305.\n\nIn the morning the mist is denser above than below, because the sun\ndraws it upwards; hence tall buildings, even if the summit is at the\nsame distance as the base have the summit invisible. Therefore,\nalso, the sky looks darkest [in colour] overhead, and towards the\nhorizon it is not blue but rather between smoke and dust colour.\n\nThe atmosphere, when full of mist, is quite devoid of blueness, and\nonly appears of the colour of clouds, which shine white when the\nweather is fine. And the more you turn to the west the darker it\nwill be, and the brighter as you look to the east. And the verdure\nof the fields is bluish in a thin mist, but grows grey in a dense\none.\n\nThe buildings in the west will only show their illuminated side,\nwhere the sun shines, and the mist hides the rest. When the sun\nrises and chases away the haze, the hills on the side where it lifts\nbegin to grow clearer, and look blue, and seem to smoke with the\nvanishing mists; and the buildings reveal their lights and shadows;\nthrough the thinner vapour they show only their lights and through\nthe thicker air nothing at all. This is when the movement of the\nmist makes it part horizontally, and then the edges of the mist will\nbe indistinct against the blue of the sky, and towards the earth it\nwill look almost like dust blown up. In proportion as the atmosphere\nis dense the buildings of a city and the trees in a landscape will\nlook fewer, because only the tallest and largest will be seen.\n\nDarkness affects every thing with its hue, and the more an object\ndiffers from darkness, the more we see its real and natural colour.\nThe mountains will look few, because only those will be seen which\nare farthest apart; since, at such a distance, the density increases\nto such a degree that it causes a brightness by which the darkness\nof the hills becomes divided and vanishes indeed towards the top.\nThere is less [mist] between lower and nearer hills and yet little\nis to be distinguished, and least towards the bottom.\n\n306.\n\nThe surface of an object partakes of the colour of the light which\nilluminates it; and of the colour of the atmosphere which lies\nbetween the eye and that object, that is of the colour of the\ntransparent medium lying between the object and the eye; and among\ncolours of a similar character the second will be of the same tone\nas the first, and this is caused by the increased thickness of the\ncolour of the medium lying between the object and the eye.\n\n307. OF PAINTING.\n\nOf various colours which are none of them blue that which at a great\ndistance will look bluest is the nearest to black; and so,\nconversely, the colour which is least like black will at a great\ndistance best preserve its own colour.\n\nHence the green of fields will assume a bluer hue than yellow or\nwhite will, and conversely yellow or white will change less than\ngreen, and red still less.\n\n_VII._\n\n_On the Proportions and on the Movements of the Human Figure._\n\n_Leonardo's researches on the proportions and movements of the human\nfigure must have been for the most part completed and written before\nthe year_ 1498; _for LUCA PACIOLO writes, in the dedication to\nLudovico il Moro, of his book_ Divina Proportione, _which was\npublished in that year:_ \"Leonardo da venci ... hauedo gia co tutta\ndiligetia al degno libro de pictura e movimenti humani posto fine\".\n\n_The selection of Leonardo's axioms contained in the Vatican copy\nattributes these words to the author:_ \"e il resto si dira nella\nuniversale misura del huomo\". (_MANZI, p. 147; LUDWIG, No. 264_).\n_LOMAZZO, again, in his_ Idea del Tempio della Pittura Milano 1590,\ncap. IV, _says:_ \"Lionardo Vinci ... dimostro anco in figura tutte\nle proporzioni dei membri del corpo umano\".\n\n_The Vatican copy includes but very few sections of the_ \"Universale\nmisura del huomo\" _and until now nothing has been made known of the\noriginal MSS. on the subject which have supplied the very extensive\nmaterials for this portion of the work. The collection at Windsor,\nbelonging to her Majesty the Queen, includes by far the most\nimportant part of Leonardo's investigations on this subject,\nconstituting about half of the whole of the materials here\npublished; and the large number of original drawings adds greatly to\nthe interest which the subject itself must command. Luca Paciolo\nwould seem to have had these MSS. (which I have distinguished by the\ninitials W. P.) in his mind when he wrote the passage quoted above.\nStill, certain notes of a later date--such as Nos. 360, 362 and 363,\nfrom MS. E, written in 1513--14, sufficiently prove that Leonardo did\nnot consider his earlier studies on the Proportions and Movements of\nthe Human Figure final and complete, as we might suppose from Luca\nPaciolo's statement. Or else he took the subject up again at a\nsubsequent period, since his former researches had been carried on\nat Milan between 1490 and 1500. Indeed it is highly probable that\nthe anatomical studies which he was pursuing zvith so much zeal\nbetween 1510--16 should have led him to reconsider the subject of\nProportion.\n\nPreliminary observations (308. 309).\n\n308.\n\nEvery man, at three years old is half the full height he will grow\nto at last.\n\n309.\n\nIf a man 2 braccia high is too small, one of four is too tall, the\nmedium being what is admirable. Between 2 and 4 comes 3; therefore\ntake a man of 3 braccia in height and measure him by the rule I will\ngive you. If you tell me that I may be mistaken, and judge a man to\nbe well proportioned who does not conform to this division, I answer\nthat you must look at many men of 3 braccia, and out of the larger\nnumber who are alike in their limbs choose one of those who are most\ngraceful and take your measurements. The length of the hand is 1/3\nof a braccio [8 inches] and this is found 9 times in man. And the\nface [Footnote 7: The account here given of the _braccio_ is of\nimportance in understanding some of the succeeding chapters. _Testa_\nmust here be understood to mean the face. The statements in this\nsection are illustrated in part on Pl. XI.] is the same, and from\nthe pit of the throat to the shoulder, and from the shoulder to the\nnipple, and from one nipple to the other, and from each nipple to\nthe pit of the throat.\n\nProportions of the head and face (310-318).\n\n310.\n\nThe space between the parting of the lips [the mouth] and the base\nof the nose is one-seventh of the face.\n\nThe space from the mouth to the bottom of the chin _c d_ is the\nfourth part of the face and equal to the width of the mouth.\n\nThe space from the chin to the base of the nose _e f_ is the third\npart of the face and equal to the length of the nose and to the\nforehead.\n\nThe distance from the middle of the nose to the bottom of the chin\n_g h_, is half the length of the face.\n\nThe distance from the top of the nose, where the eyebrows begin, to\nthe bottom of the chin, _i k_, is two thirds of the face.\n\nThe space from the parting of the lips to the top of the chin _l m_,\nthat is where the chin ends and passes into the lower lip of the\nmouth, is the third of the distance from the parting of the lips to\nthe bottom of the chin and is the twelfth part of the face. From the\ntop to the bottom of the chin _m n_ is the sixth part of the face\nand is the fifty fourth part of a man's height.\n\nFrom the farthest projection of the chin to the throat _o p_ is\nequal to the space between the mouth and the bottom of the chin, and\na fourth of the face.\n\nThe distance from the top of the throat to the pit of the throat\nbelow _q r_ is half the length of the face and the eighteenth part\nof a man's height.\n\nFrom the chin to the back of the neck _s t_, is the same distance as\nbetween the mouth and the roots of the hair, that is three quarters\nof the head.\n\nFrom the chin to the jaw bone _v x_ is half the head and equal to\nthe thickness of the neck in profile.\n\nThe thickness of the head from the brow to the nape is once and 3/4\nthat of the neck.\n\n[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No.\nI. The two upper sketches of heads, Pl. VII, No. 2, belong to lines\n11-14, and in the original are placed immediately below the sketches\nreproduced on Pl. VII, No. 1.]\n\n311.\n\nThe distance from the attachment of one ear to the other is equal to\nthat from the meeting of the eyebrows to the chin, and in a fine\nface the width of the mouth is equal to the length from the parting\nof the lips to the bottom of the chin.\n\n312.\n\nThe cut or depression below the lower lip of the mouth is half way\nbetween the bottom of the nose and the bottom of the chin.\n\nThe face forms a square in itself; that is its width is from the\nouter corner of one eye to the other, and its height is from the\nvery top of the nose to the bottom of the lower lip of the mouth;\nthen what remains above and below this square amounts to the height\nof such another square, _a_ _b_ is equal to the space between _c_\n_d_; _d_ _n_ in the same way to _n_ _c_, and likewise _s_ _r_, _q_\n_p_, _h_ _k_ are equal to each other.\n\nIt is as far between _m_ and _s_ as from the bottom of the nose to\nthe chin. The ear is exactly as long as the nose. It is as far from\n_x_ to _j_ as from the nose to the chin. The parting of the mouth\nseen in profile slopes to the angle of the jaw. The ear should be as\nhigh as from the bottom of the nose to the top of the eye-lid. The\nspace between the eyes is equal to the width of an eye. The ear is\nover the middle of the neck, when seen in profile. The distance from\n4 to 5 is equal to that from s_ to _r_.\n\n[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also\ngiven in facsimile.]\n\n313.\n\n(_a_ _b_) is equal to (_c_ _d_).\n\n[Footnote: See Pl. VII, No. 3. Reference may also be made here to\ntwo pen and ink drawings of heads in profile with figured\nmeasurements, of which there is no description in the MS. These are\ngiven on Pl. XVII, No. 2.--A head, to the left, with part of the\ntorso [W. P. 5a], No. 1 on the same plate is from MS. A 2b and in\nthe original occurs on a page with wholly irrelevant text on matters\nof natural history. M. RAVAISSON in his edition of the Paris MS. A\nhas reproduced this head and discussed it fully [note on page 12];\nhe has however somewhat altered the original measurements. The\ncomplicated calculations which M. RAVAISSON has given appear to me\nin no way justified. The sketch, as we see it, can hardly have been\nintended for any thing more than an experimental attempt to\nascertain relative proportions. We do not find that Leonardo made\nuse of circular lines in any other study of the proportions of the\nhuman head. At the same time we see that the proportions of this\nsketch are not in accordance with the rules which he usually\nobserved (see for instance No. 310).]\n\nThe head _a_ _f_ 1/6 larger than _n_ _f_.\n\n315.\n\nFrom the eyebrow to the junction of the lip with the chin, and the\nangle of the jaw and the upper angle where the ear joins the temple\nwill be a perfect square. And each side by itself is half the head.\n\nThe hollow of the cheek bone occurs half way between the tip of the\nnose and the top of the jaw bone, which is the lower angle of the\nsetting on of the ear, in the frame here represented.\n\nFrom the angle of the eye-socket to the ear is as far as the length\nof the ear, or the third of the face.\n\n[Footnote: See Pl. IX. The text, in the original is written behind\nthe head. The handwriting would seem to indicate a date earlier than\n1480. On the same leaf there is a drawing in red chalk of two\nhorsemen of which only a portion of the upper figure is here\nvisible. The whole leaf measures 22 1/2 centimetres wide by 29 long,\nand is numbered 127 in the top right-hand corner.]\n\n316.\n\nFrom _a_ to _b_--that is to say from the roots of the hair in front\nto the top of the head--ought to be equal to _c_ _d_;--that is from\nthe bottom of the nose to the meeting of the lips in the middle of\nthe mouth. From the inner corner of the eye _m_ to the top of the\nhead _a_ is as far as from _m_ down to the chin _s_. _s_ _c_ _f_ _b_\nare all at equal distances from each other.\n\n[Footnote: The drawing in silver-point on bluish tinted paper--Pl.\nX--which belongs to this chapter has been partly drawn over in ink\nby Leonardo himself.]\n\n317.\n\nFrom the top of the head to the bottom of the chin is 1/9, and from\nthe roots of the hair to the chin is 1/9 of the distance from the\nroots of the hair to the ground. The greatest width of the face is\nequal to the space between the mouth and the roots of the hair and\nis 1/12 of the whole height. From the top of the ear to the top of\nthe head is equal to the distance from the bottom of the chin to the\nlachrymatory duct of the eye; and also equal to the distance from\nthe angle of the chin to that of the jaw; that is the 1/16 of the\nwhole. The small cartilage which projects over the opening of the\near towards the nose is half-way between the nape and the eyebrow;\nthe thickness of the neck in profile is equal to the space between\nthe chin and the eyes, and to the space between the chin and the\njaw, and it is 1/18 of the height of the man.\n\n318.\n\n_a b_, _c d_, _e f_, _g h_, _i k_ are equal to each other in size\nexcepting that _d f_ is accidental.\n\n[Footnote: See Pl. XI.]\n\nProportions of the head seen in front (319-321).\n\n319.\n\n_a n o f_ are equal to the mouth.\n\n_a c_ and _a f_ are equal to the space between one eye and the\nother.\n\n_n m o f q r_ are equal to half the width of the eye lids, that is\nfrom the inner [lachrymatory] corner of the eye to its outer corner;\nand in like manner the division between the chin and the mouth; and\nin the same way the narrowest part of the nose between the eyes. And\nthese spaces, each in itself, is the 19th part of the head, _n o_ is\nequal to the length of the eye or of the space between the eyes.\n\n_m c_ is 1/3 of _n m_ measuring from the outer corner of the eyelids\nto the letter _c_. _b s_ will be equal to the width of the nostril.\n\n[Footnote: See Pl. XII.]\n\n320.\n\nThe distance between the centres of the pupils of the eyes is 1/3 of\nthe face. The space between the outer corners of the eyes, that is\nwhere the eye ends in the eye socket which contains it, thus the\nouter corners, is half the face.\n\nThe greatest width of the face at the line of the eyes is equal to\nthe distance from the roots of the hair in front to the parting of\nthe lips.\n\n[Footnote: There are, with this section, two sketches of eyes, not\nreproduced here.]\n\n321.\n\nThe nose will make a double square; that is the width of the nose at\nthe nostrils goes twice into the length from the tip of the nose to\nthe eyebrows. And, in the same way, in profile the distance from the\nextreme side of the nostril where it joins the cheek to the tip of\nthe nose is equal to the width of the nose in front from one nostril\nto the other. If you divide the whole length of the nose--that is\nfrom the tip to the insertion of the eyebrows, into 4 equal parts,\nyou will find that one of these parts extends from the tip of the\nnostrils to the base of the nose, and the upper division lies\nbetween the inner corner of the eye and the insertion of the\neyebrows; and the two middle parts [together] are equal to the\nlength of the eye from the inner to the outer corner.\n\n[Footnote: The two bottom sketches on Pl. VII, No. 4 face the six\nlines of this section,--With regard to the proportions of the head\nin profile see No. 312.]\n\n322.\n\nThe great toe is the sixth part of the foot, taking the measure in\nprofile, on the inside of the foot, from where this toe springs from\nthe ball of the sole of the foot to its tip _a b_; and it is equal\nto the distance from the mouth to the bottom of the chin. If you\ndraw the foot in profile from the outside, make the little toe begin\nat three quarters of the length of the foot, and you will find the\nsame distance from the insertion of this toe as to the farthest\nprominence of the great toe.\n\n323.\n\nFor each man respectively the distance between _a b_ is equal to _c\nd_.\n\n324.\n\nRelative proportion of the hand and foot.\n\nThe foot is as much longer than the hand as the thickness of the arm\nat the wrist where it is thinnest seen facing.\n\nAgain, you will find that the foot is as much longer than the hand\nas the space between the inner angle of the little toe to the last\nprojection of the big toe, if you measure along the length of the\nfoot.\n\nThe palm of the hand without the fingers goes twice into the length\nof the foot without the toes.\n\nIf you hold your hand with the fingers straight out and close\ntogether you will find it to be of the same width as the widest part\nof the foot, that is where it is joined onto the toes.\n\nAnd if you measure from the prominence of the inner ancle to the end\nof the great toe you will find this measure to be as long as the\nwhole hand.\n\nFrom the top angle of the foot to the insertion of the toes is equal\nto the hand from wrist joint to the tip of the thumb.\n\nThe smallest width of the hand is equal to the smallest width of the\nfoot between its joint into the leg and the insertion of the toes.\n\nThe width of the heel at the lower part is equal to that of the arm\nwhere it joins the hand; and also to the leg where it is thinnest\nwhen viewed in front.\n\nThe length of the longest toe, from its first division from the\ngreat toe to its tip is the fourth of the foot from the centre of\nthe ancle bone to the tip, and it is equal to the width of the\nmouth. The distance between the mouth and the chin is equal to that\nof the knuckles and of the three middle fingers and to the length of\ntheir first joints if the hand is spread, and equal to the distance\nfrom the joint of the thumb to the outset of the nails, that is the\nfourth part of the hand and of the face.\n\nThe space between the extreme poles inside and outside the foot\ncalled the ancle or ancle bone _a b_ is equal to the space between\nthe mouth and the inner corner of the eye.\n\n325.\n\nThe foot, from where it is attached to the leg, to the tip of the\ngreat toe is as long as the space between the upper part of the chin\nand the roots of the hair _a b_; and equal to five sixths of the\nface.\n\n326.\n\n_a d_ is a head's length, _c b_ is a head's length. The four smaller\ntoes are all equally thick from the nail at the top to the bottom,\nand are 1/13 of the foot.\n\n[Footnote: See Pl. XIV, No. 1, a drawing of a foot with the text in\nthree lines below it.]\n\n327.\n\nThe whole length of the foot will lie between the elbow and the\nwrist and between the elbow and the inner angle of the arm towards\nthe breast when the arm is folded. The foot is as long as the whole\nhead of a man, that is from under the chin to the topmost part of\nthe head[Footnote 2: _nel modo che qui i figurato_. See Pl. VII, No.\n4, the upper figure. The text breaks off at the end of line 2 and\nthe text given under No. 321 follows below. It may be here remarked\nthat the second sketch on W. P. 311 has in the original no\nexplanatory text.] in the way here figured.\n\nProportions of the leg (328-331).\n\n328.\n\nThe greatest thickness of the calf of the leg is at a third of its\nheight _a b_, and is a twentieth part thicker than the greatest\nthickness of the foot.\n\n_a c_ is half of the head, and equal to _d b_ and to the insertion\nof the five toes _e f_. _d k_ diminishes one sixth in the leg _g h_.\n_g h_ is 1/3 of the head; _m n_ increases one sixth from _a e_ and\nis 7/12 of the head, _o p_ is 1/10 less than _d k_ and is 6/17 of\nthe head. _a_ is at half the distance between _b q_, and is 1/4 of\nthe man. _r_ is half way between _s_ and _b_[Footnote 11: _b_ is\nhere and later on measured on the right side of the foot as seen by\nthe spectator.]. The concavity of the knee outside _r_ is higher\nthan that inside _a_. The half of the whole height of the leg from\nthe foot _r_, is half way between the prominence _s_ and the ground\n_b_. _v_ is half way between _t_ and _b_. The thickness of the thigh\nseen in front is equal to the greatest width of the face, that is\n2/3 of the length from the chin to the top of the head; _z r_ is 5/6\nof 7 to _v_; _m n_ is equal to 7 _v_ and is 1/4 of _r b_, _x y_ goes\n3 times into _r b_, and into _r s_.\n\n[Footnote 22-35: The sketch illustrating these lines is on Pl. XIII,\nNo. 2.]\n\n[Footnote 22: a b _entra in_ c f 6 _e_ 6 _in_ c n. Accurate\nmeasurement however obliges us to read 7 for 6.] _a b_ goes six\ntimes into _c f_ and six times into _c n_ and is equal to _g h_; _i\nk l m_ goes 4 times into _d f_, and 4 times into _d n_ and is 3/7 of\nthe foot; _p q r s_ goes 3 times into _d f, and 3 times into _b n_;\n[Footnote: 25. _y_ is not to be found on the diagram and _x_ occurs\ntwice; this makes the passage very obscure.] _x y_ is 1/8 of _x f_\nand is equal to _n q_. 3 7 is 1/9 of _n f_; 4 5 is 1/10 of _n f_\n[Footnote: 22-27. Compare with this lines 18-24 of No. 331, and the\nsketch of a leg in profile Pl. XV.].\n\nI want to know how much a man increases in height by standing on\ntip-toe and how much _p g_ diminishes by stooping; and how much it\nincreases at _n q_ likewise in bending the foot.\n\n[Footnote 34: _e f_ 4 _dal cazo_. By reading _i_ for _e_ the sense\nof this passage is made clear.] _e f_ is four times in the distance\nbetween the genitals and the sole of the foot; [Footnote 35: 2 is\nnot to be found in the sketch which renders the passage obscure. The\ntwo last lines are plainly legible in the facsimile.] 3 7 is six\ntimes from 3 to 2 and is equal to _g h_ and _i k_.\n\n[Footnote: The drawing of a leg seen in front Pl. XIII, No. 1\nbelongs to the text from lines 3-21. The measurements in this\nsection should be compared with the text No. 331, lines 1-13, and\nthe sketch of a leg seen in front on Pl. XV.]\n\n329.\n\nThe length of the foot from the end of the toes to the heel goes\ntwice into that from the heel to the knee, that is where the leg\nbone [fibula] joins the thigh bone [femur].\n\n330.\n\n_a n b_ are equal; _c n d_ are equal; _n c_ makes two feet; _n d_\nmakes 2 feet.\n\n[Footnote: See the lower sketch, Pl. XIV, No. 1.]\n\n331.\n\n_m n o_ are equal. The narrowest width of the leg seen in front goes\n8 times from the sole of the foot to the joint of the knee, and is\nthe same width as the arm, seen in front at the wrist, and as the\nlongest measure of the ear, and as the three chief divisions into\nwhich we divide the face; and this measurement goes 4 times from the\nwrist joint of the hand to the point of the elbow. [14] The foot is\nas long as the space from the knee between _a_ and _b_; and the\npatella of the knee is as long as the leg between _r_ and _s_.\n\n[18] The least thickness of the leg in profile goes 6 times from the\nsole of the foot to the knee joint and is the same width as the\nspace between the outer corner of the eye and the opening of the\near, and as the thickest part of the arm seen in profile and between\nthe inner corner of the eye and the insertion of the hair.\n\n_a b c_ [_d_] are all relatively of equal length, _c d_ goes twice\nfrom the sole of the foot to the centre of the knee and the same\nfrom the knee to the hip.\n\n[28]_a b c_ are equal; _a_ to _b_ is 2 feet--that is to say\nmeasuring from the heel to the tip of the great toe.\n\n[Footnote: See Pl. XV. The text of lines 2-17 is to the left of the\nfront view of the leg, to which it refers. Lines 18-27 are in the\nmiddle column and refer to the leg seen in profile and turned to the\nleft, on the right hand side of the writing. Lines 20-30 are above,\nto the left and apply to the sketch below them.\n\nSome farther remarks on the proportion of the leg will be found in\nNo. 336, lines 6, 7.]\n\nOn the central point of the whole body.\n\n332.\n\nIn kneeling down a man will lose the fourth part of his height.\n\nWhen a man kneels down with his hands folded on his breast the navel\nwill mark half his height and likewise the points of the elbows.\n\nHalf the height of a man who sits--that is from the seat to the top\nof the head--will be where the arms fold below the breast, and\nbelow the shoulders. The seated portion--that is from the seat to\nthe top of the head--will be more than half the man's [whole height]\nby the length of the scrotum.\n\n[Footnote: See Pl. VIII, No. 2.]\n\nThe relative proportions of the torso and of the whole figure.\n\n333.\n\nThe cubit is one fourth of the height of a man and is equal to the\ngreatest width of the shoulders. From the joint of one shoulder to\nthe other is two faces and is equal to the distance from the top of\nthe breast to the navel. [Footnote 9: _dalla detta somita_. It would\nseem more accurate to read here _dal detto ombilico_.] From this\npoint to the genitals is a face's length.\n\n[Footnote: Compare with this the sketches on the other page of the\nsame leaf. Pl. VIII, No. 2.]\n\nThe relative proportions of the head and of the torso.\n\n334.\n\nFrom the roots of the hair to the top of the breast _a b_ is the\nsixth part of the height of a man and this measure is equal.\n\nFrom the outside part of one shoulder to the other is the same\ndistance as from the top of the breast to the navel and this measure\ngoes four times from the sole of the foot to the lower end of the\nnose.\n\nThe [thickness of] the arm where it springs from the shoulder in\nfront goes 6 times into the space between the two outside edges of\nthe shoulders and 3 times into the face, and four times into the\nlength of the foot and three into the hand, inside or outside.\n\n[Footnote: The three sketches Pl. XIV, No. 2 belong to this text.]\n\nThe relative proportions of the torso and of the leg (335. 336).\n\n335.\n\n_a b c_ are equal to each other and to the space from the armpit of\nthe shoulder to the genitals and to the distance from the tip of the\nfingers of the hand to the joint of the arm, and to the half of the\nbreast; and you must know that _c b_ is the third part of the height\nof a man from the shoulders to the ground; _d e f_ are equal to each\nother and equal to the greatest width of the shoulders.\n\n[Footnote: See Pl. XVI, No. 1.]\n\n336.\n\n--Top of the chin--hip--the insertion of the middle finger. The end\nof the calf of the leg on the inside of the thigh.--The end of the\nswelling of the shin bone of the leg. [6] The smallest thickness of\nthe leg goes 3 times into the thigh seen in front.\n\n[Footnote: See Pl. XVII, No. 2, middle sketch.]\n\nThe relative proportions of the torso and of the foot.\n\n337.\n\nThe torso _a b_ in its thinnest part measures a foot; and from _a_\nto _b_ is 2 feet, which makes two squares to the seat--its thinnest\npart goes 3 times into the length, thus making 3 squares.\n\n[Footnote: See Pl, VII, No. 2, the lower sketch.]\n\nThe proportions of the whole figure (338-341).\n\n338.\n\nA man when he lies down is reduced to 1/9 of his height.\n\n339.\n\nThe opening of the ear, the joint of the shoulder, that of the hip\nand the ancle are in perpendicular lines; _a n_ is equal to _m o_.\n\n[Footnote: See Pl. XVI, No. 2, the upper sketch.]\n\n340.\n\nFrom the chin to the roots of the hair is 1/10 of the whole figure.\nFrom the joint of the palm of the hand to the tip of the longest\nfinger is 1/10. From the chin to the top of the head 1/8; and from\nthe pit of the stomach to the top of the breast is 1/6, and from the\npit below the breast bone to the top of the head 1/4. From the chin\nto the nostrils 1/3 Part of the face, the same from the nostrils to\nthe brow and from the brow to the roots of the hair, and the foot is\n1/6, the elbow 1/4, the width of the shoulders 1/4.\n\n341.\n\nThe width of the shoulders is 1/4 of the whole. From the joint of\nthe shoulder to the hand is 1/3, from the parting of the lips to\nbelow the shoulder-blade is one foot.\n\nThe greatest thickness of a man from the breast to the spine is one\n8th of his height and is equal to the space between the bottom of\nthe chin and the top of the head.\n\nThe greatest width is at the shoulders and goes 4.\n\nThe torso from the front and back.\n\n342.\n\nThe width of a man under the arms is the same as at the hips.\n\nA man's width across the hips is equal to the distance from the top\nof the hip to the bottom of the buttock, when a man stands equally\nbalanced on both feet; and there is the same distance from the top\nof the hip to the armpit. The waist, or narrower part above the hips\nwill be half way between the arm pits and the bottom of the buttock.\n\n[Footnote: The lower sketch Pl. XVI, No. 2, is drawn by the side of\nline 1.]\n\nVitruvius' scheme of proportions.\n\n343.\n\nVitruvius, the architect, says in his work on architecture that the\nmeasurements of the human body are distributed by Nature as follows:\nthat is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms\nmake 1 cubit; 4 cubits make a man's height. And 4 cubits make one\npace and 24 palms make a man; and these measures he used in his\nbuildings. If you open your legs so much as to decrease your height\n1/14 and spread and raise your arms till your middle fingers touch\nthe level of the top of your head you must know that the centre of\nthe outspread limbs will be in the navel and the space between the\nlegs will be an equilateral triangle.\n\nThe length of a man's outspread arms is equal to his height.\n\nFrom the roots of the hair to the bottom of the chin is the tenth of\na man's height; from the bottom of the chin to the top of his head\nis one eighth of his height; from the top of the breast to the top\nof his head will be one sixth of a man. From the top of the breast\nto the roots of the hair will be the seventh part of the whole man.\nFrom the nipples to the top of the head will be the fourth part of a\nman. The greatest width of the shoulders contains in itself the\nfourth part of the man. From the elbow to the tip of the hand will\nbe the fifth part of a man; and from the elbow to the angle of the\narmpit will be the eighth part of the man. The whole hand will be\nthe tenth part of the man; the beginning of the genitals marks the\nmiddle of the man. The foot is the seventh part of the man. From the\nsole of the foot to below the knee will be the fourth part of the\nman. From below the knee to the beginning of the genitals will be\nthe fourth part of the man. The distance from the bottom of the chin\nto the nose and from the roots of the hair to the eyebrows is, in\neach case the same, and like the ear, a third of the face.\n\n[Footnote: See Pl. XVIII. The original leaf is 21 centimetres wide\nand 33 1/2 long. At the ends of the scale below the figure are\nwritten the words _diti_ (fingers) and _palmi_ (palms). The passage\nquoted from Vitruvius is Book III, Cap. 1, and Leonardo's drawing is\ngiven in the editions of Vitruvius by FRA GIOCONDO (Venezia 1511,\nfol., Firenze 1513, 8vo.) and by CESARIANO (Como 1521).]\n\nThe arm and head.\n\n344.\n\nFrom _b_ to _a_ is one head, as well as from _c_ to _a_ and this\nhappens when the elbow forms a right angle.\n\n[Footnote: See Pl. XLI, No. 1.]\n\nProportions of the arm (345-349).\n\n345.\n\nFrom the tip of the longest finger of the hand to the shoulder joint\nis four hands or, if you will, four faces.\n\n_a b c_ are equal and each interval is 2 heads.\n\n[Footnote: Lines 1-3 are given on Pl. XV below the front view of the\nleg; lines 4 and 5 are below again, on the left side. The lettering\nrefers to the bent arm near the text.]\n\n346.\n\nThe hand from the longest finger to the wrist joint goes 4 times\nfrom the tip of the longest finger to the shoulder joint.\n\n347.\n\n_a b c_ are equal to each other and to the foot and to the space\nbetween the nipple and the navel _d e_ will be the third part of the\nwhole man.\n\n_f g_ is the fourth part of a man and is equal to _g h_ and measures\na cubit.\n\n[Footnote: See Pl. XIX, No. 1. 1. _mamolino_ (=_bambino_, little\nchild) may mean here the navel.]\n\n348.\n\n_a b_ goes 4 times into _a c_ and 9 into _a m_. The greatest\nthickness of the arm between the elbow and the hand goes 6 times\ninto _a m_ and is equal to _r f_. The greatest thickness of the arm\nbetween the shoulder and the elbow goes 4 times into _c m_, and is\nequal to _h n g_. The smallest thickness of the arm above the elbow\n_x y_ is not the base of a square, but is equal to half the space\n_h_ 3 which is found between the inner joint of the arm and the\nwrist joint.\n\n[11]The width of the wrist goes 12 times into the whole arm; that is\nfrom the tip of the fingers to the shoulder joint; that is 3 times\ninto the hand and 9 into the arm.\n\nThe arm when bent is 4 heads.\n\nThe arm from the shoulder to the elbow in bending increases in\nlength, that is in the length from the shoulder to the elbow, and\nthis increase is equal to the thickness of the arm at the wrist when\nseen in profile. And the space between the bottom of the chin and\nthe parting of the lips, is equal to the thickness of the 2 middle\nfingers, and to the width of the mouth and to the space between the\nroots of the hair on the forehead and the top of the head [Footnote:\n_Queste cose_. This passage seems to have been written on purpose to\nrectify the foregoing lines. The error is explained by the\naccompanying sketch of the bones of the arm.]. All these distances\nare equal to each other, but they are not equal to the\nabove-mentioned increase in the arm.\n\nThe arm between the elbow and wrist never increases by being bent or\nextended.\n\nThe arm, from the shoulder to the inner joint when extended.\n\nWhen the arm is extended, _p n_ is equal to _n a_. And when it is\nbent _n a_ diminishes 1/6 of its length and _p n_ does the same. The\nouter elbow joint increases 1/7 when bent; and thus by being bent it\nincreases to the length of 2 heads. And on the inner side, by\nbending, it is found that whereas the arm from where it joins the\nside to the wrist, was 2 heads and a half, in bending it loses the\nhalf head and measures only two: one from the [shoulder] joint to\nthe end [by the elbow], and the other to the hand.\n\nThe arm when folded will measure 2 faces up to the shoulder from the\nelbow and 2 from the elbow to the insertion of the four fingers on\nthe palm of the hand. The length from the base of the fingers to the\nelbow never alters in any position of the arm.\n\nIf the arm is extended it decreases by 1/3 of the length between _b_\nand _h_; and if--being extended--it is bent, it will increase the\nhalf of _o e_. [Footnote 59-61: The figure sketched in the margin is\nhowever drawn to different proportions.] The length from the\nshoulder to the elbow is the same as from the base of the thumb,\ninside, to the elbow _a b c_.\n\n[Footnote 62-64: The arm sketch on the margin of the MS. is\nidentically the same as that given below on Pl. XX which may\ntherefore be referred to in this place. In line 62 we read therefore\n_z c_ for _m n_.] The smallest thickness of the arm in profile _z c_\ngoes 6 times between the knuckles of the hand and the dimple of the\nelbow when extended and 14 times in the whole arm and 42 in the\nwhole man [64]. The greatest thickness of the arm in profile is\nequal to the greatest thickness of the arm in front; but the first\nis placed at a third of the arm from the shoulder joint to the elbow\nand the other at a third from the elbow towards the hand.\n\n[Footnote: Compare Pl. XVII. Lines 1-10 and 11-15 are written in two\ncolumns below the extended arm, and at the tips of the fingers we\nfind the words: _fine d'unghie_ (ends of the nails). Part of the\ntext--lines 22 to 25--is visible by the side of the sketches on Pl.\nXXXV, No. 1.]\n\n349.\n\nFrom the top of the shoulder to the point of the elbow is as far as\nfrom that point to the joints of the four fingers with the palm of\nthe hand, and each is 2 faces.\n\n[5]_a e_ is equal to the palm of the hand, _r f_ and _o g_ are equal\nto half a head and each goes 4 times into _a b_ and _b c_. From _c_\nto _m_ is 1/2 a head; _m n_ is 1/3 of a head and goes 6 times into\n_c b_ and into _b a_; _a b_ loses 1/7 of its length when the arm is\nextended; _c b_ never alters; _o_ will always be the middle point\nbetween _a_ and _s_.\n\n_y l_ is the fleshy part of the arm and measures one head; and when\nthe arm is bent this shrinks 2/5 of its length; _o a_ in bending\nloses 1/6 and so does _o r_.\n\n_a b_ is 1/7 of _r c_. _f s_ will be 1/8 of _r c_, and each of those\n2 measurements is the largest of the arm; _k h_ is the thinnest part\nbetween the shoulder and the elbow and it is 1/8 of the whole arm _r\nc_; _o p_ is 1/5 of _r l_; _c z_ goes 13 times into _r c_.\n\n[Footnote: See Pl. XX where the text is also seen from lines 5-23.]\n\nThe movement of the arm (350-354).\n\n350.\n\nIn the innermost bend of the joints of every limb the reliefs are\nconverted into a hollow, and likewise every hollow of the innermost\nbends becomes a convexity when the limb is straightened to the\nutmost. And in this very great mistakes are often made by those who\nhave insufficient knowledge and trust to their own invention and do\nnot have recourse to the imitation of nature; and these variations\noccur more in the middle of the sides than in front, and more at the\nback than at the sides.\n\n351.\n\nWhen the arm is bent at an angle at the elbow, it will produce some\nangle; the more acute the angle is, the more will the muscles within\nthe bend be shortened; while the muscles outside will become of\ngreater length than before. As is shown in the example; _d c e_ will\nshrink considerably; and _b n_ will be much extended.\n\n[Footnote: See Pl. XIX, No. 2.]\n\n352.\n\nOF PAINTING.\n\nThe arm, as it turns, thrusts back its shoulder towards the middle\nof the back.\n\n353.\n\nThe principal movements of the hand are 10; that is forwards,\nbackwards, to right and to left, in a circular motion, up or down,\nto close and to open, and to spread the fingers or to press them\ntogether.\n\n354.\n\nOF THE MOTIONS OF THE FINGERS.\n\nThe movements of the fingers principally consist in extending and\nbending them. This extension and bending vary in manner; that is,\nsometimes they bend altogether at the first joint; sometimes they\nbend, or extend, half way, at the 2nd joint; and sometimes they bend\nin their whole length and in all the three joints at once. If the 2\nfirst joints are hindered from bending, then the 3rd joint can be\nbent with greater ease than before; it can never bend of itself, if\nthe other joints are free, unless all three joints are bent. Besides\nall these movements there are 4 other principal motions of which 2\nare up and down, the two others from side to side; and each of these\nis effected by a single tendon. From these there follow an infinite\nnumber of other movements always effected by two tendons; one tendon\nceasing to act, the other takes up the movement. The tendons are\nmade thick inside the fingers and thin outside; and the tendons\ninside are attached to every joint but outside they are not.\n\n[Footnote 26: This head line has, in the original, no text to\nfollow.] Of the strength [and effect] of the 3 tendons inside the\nfingers at the 3 joints.\n\nThe movement of the torso (355-361).\n\n355.\n\nObserve the altered position of the shoulder in all the movements of\nthe arm, going up and down, inwards and outwards, to the back and to\nthe front, and also in circular movements and any others.\n\nAnd do the same with reference to the neck, hands and feet and the\nbreast above the lips &c.\n\n356.\n\nThree are the principal muscles of the shoulder, that is _b c d_,\nand two are the lateral muscles which move it forward and backward,\nthat is _a o_; _a_ moves it forward, and _o_ pulls it back; and bed\nraises it; _a b c_ moves it upwards and forwards, and _c d o_\nupwards and backwards. Its own weight almost suffices to move it\ndownwards.\n\nThe muscle _d_ acts with the muscle _c_ when the arm moves forward;\nand in moving backward the muscle _b_ acts with the muscle _c_.\n\n[Footnote: See Pl. XXI. In the original the lettering has been\nwritten in ink upon the red chalk drawing and the outlines of the\nfigures have in most places been inked over.]\n\n357.\n\nOF THE LOINS, WHEN BENT.\n\nThe loins or backbone being bent. The breasts are are always lower\nthan the shoulderblades of the back.\n\nIf the breast bone is arched the breasts are higher than the\nshoulderblades.\n\nIf the loins are upright the breast will always be found at the same\nlevel as the shoulderblades.\n\n[Footnote: See Pl. XXII, No. 1.]\n\n358.\n\n_a b_ the tendon and ankle in raising the heel approach each other\nby a finger's breadth; in lowering it they separate by a finger's\nbreadth.\n\n[Footnote: See Pl. XXII, No. 2. Compare this facsimile and text with\nPl. III, No. 2, and p. 152 of MANZI'S edition. Also with No. 274 of\nLUDWIG'S edition of the Vatican Copy.]\n\n359.\n\nJust so much as the part _d a_ of the nude figure decreases in this\nposition so much does the opposite part increase; that is: in\nproportion as the length of the part _d a_ diminishes the normal\nsize so does the opposite upper part increase beyond its [normal]\nsize. The navel does not change its position to the male organ; and\nthis shrinking arises because when a figure stands on one foot, that\nfoot becomes the centre [of gravity] of the superimposed weight.\nThis being so, the middle between the shoulders is thrust above it\nout of it perpendicular line, and this line, which forms the central\nline of the external parts of the body, becomes bent at its upper\nextremity [so as to be] above the foot which supports the body; and\nthe transverse lines are forced into such angles that their ends are\nlower on the side which is supported. As is shown at _a b c_.\n\n[Footnote: See Pl. XXII, No. 3.]\n\n360.\n\nOF PAINTING.\n\nNote in the motions and attitudes of figures how the limbs vary, and\ntheir feeling, for the shoulderblades in the motions of the arms and\nshoulders vary the [line of the] back bone very much. And you will\nfind all the causes of this in my book of Anatomy.\n\n361.\n\nOF [CHANGE OF] ATTITUDE.\n\nThe pit of the throat is over the feet, and by throwing one arm\nforward the pit of the throat is thrown off that foot. And if the\nleg is thrown forward the pit of the throat is thrown forward; and.\nso it varies in every attitude.\n\n362.\n\nOF PAINTING.\n\nIndicate which are the muscles, and which the tendons, which become\nprominent or retreat in the different movements of each limb; or\nwhich do neither [but are passive]. And remember that these\nindications of action are of the first importance and necessity in\nany painter or sculptor who professes to be a master &c.\n\nAnd indicate the same in a child, and from birth to decrepitude at\nevery stage of its life; as infancy, childhood, boyhood, youth &c.\n\nAnd in each express the alterations in the limbs and joints, which\nswell and which grow thinner.\n\n363.\n\nO Anatomical Painter! beware lest the too strong indication of the\nbones, sinews and muscles, be the cause of your becoming wooden in\nyour painting by your wish to make your nude figures display all\ntheir feeling. Therefore, in endeavouring to remedy this, look in\nwhat manner the muscles clothe or cover their bones in old or lean\npersons; and besides this, observe the rule as to how these same\nmuscles fill up the spaces of the surface that extend between them,\nwhich are the muscles which never lose their prominence in any\namount of fatness; and which too are the muscles of which the\nattachments are lost to sight in the very least plumpness. And in\nmany cases several muscles look like one single muscle in the\nincrease of fat; and in many cases, in growing lean or old, one\nsingle muscle divides into several muscles. And in this treatise,\neach in its place, all their peculiarities will be explained--and\nparticularly as to the spaces between the joints of each limb &c.\nAgain, do not fail [to observe] the variations in the forms of the\nabove mentioned muscles, round and about the joints of the limbs of\nany animal, as caused by the diversity of the motions of each limb;\nfor on some side of those joints the prominence of these muscles is\nwholly lost in the increase or diminution of the flesh of which\nthese muscles are composed, &c.\n\n[Footnote: DE ROSSI remarks on this chapter, in the Roman edition of\nthe Trattato, p. 504: \"_Non in questo luogo solo, ma in altri ancora\nosserver\u00e0 il lettore, che Lionardo va fungendo quelli che fanno\nabuso della loro dottrina anatomica, e sicuramente con ci\u00f2 ha in\nmira il suo rivale Bonarroti, che di anatomia facea tanta pompa_.\"\nNote, that Leonardo wrote this passage in Rome, probably under the\nimmediate impression of MICHAELANGELO'S paintings in the Sistine\nChapel and of RAPHAEL'S Isaiah in Sant' Agostino.]\n\n364.\n\nOF THE DIFFERENT MEASUREMENTS OF BOYS AND MEN.\n\nThere is a great difference in the length between the joints in men\nand boys for, in man, from the top of the shoulder [by the neck] to\nthe elbow, and from the elbow to the tip of the thumb and from one\nshoulder to the other, is in each instance two heads, while in a boy\nit is but one because Nature constructs in us the mass which is the\nhome of the intellect, before forming that which contains the vital\nelements.\n\n365.\n\nOF PAINTING.\n\nWhich are the muscles which subdivide in old age or in youth, when\nbecoming lean? Which are the parts of the limbs of the human frame\nwhere no amount of fat makes the flesh thicker, nor any degree of\nleanness ever diminishes it?\n\nThe thing sought for in this question will be found in all the\nexternal joints of the bones, as the shoulder, elbow, wrists,\nfinger-joints, hips, knees, ankle-bone and toes and the like; all of\nwhich shall be told in its place. The greatest thickness acquired by\nany limb is at the part of the muscles which is farthest from its\nattachments.\n\nFlesh never increases on those portions of the limb where the bones\nare near to the surface.\n\nAt _b r d a c e f_ the increase or diminution of the flesh never\nmakes any considerable difference. Nature has placed in front of man\nall those parts which feel most pain under a blow; and these are the\nshin of the leg, the forehead, and the nose. And this was done for\nthe preservation of man, since, if such pain were not felt in these\nparts, the number of blows to which they would be exposed must be\nthe cause of their destruction.\n\nDescribe why the bones of the arm and leg are double near the hand\nand foot [respectively].\n\nAnd where the flesh is thicker or thinner in the bending of the\nlimbs.\n\n366.\n\nOF PAINTING.\n\nEvery part of the whole must be in proportion to the whole. Thus, if\na man is of a stout short figure he will be the same in all his\nparts: that is with short and thick arms, wide thick hands, with\nshort fingers with their joints of the same character, and so on\nwith the rest. I would have the same thing understood as applying to\nall animals and plants; in diminishing, [the various parts] do so in\ndue proportion to the size, as also in enlarging.\n\n367.\n\nOF THE AGREEMENT OF THE PROPORTION OF THE LIMBS.\n\nAnd again, remember to be very careful in giving your figures limbs,\nthat they must appear to agree with the size of the body and\nlikewise to the age. Thus a youth has limbs that are not very\nmuscular not strongly veined, and the surface is delicate and round,\nand tender in colour. In man the limbs are sinewy and muscular,\nwhile in old men the surface is wrinkled, rugged and knotty, and the\nsinews very prominent.\n\nHOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN,\nAS TO SIZE.\n\nLittle children have all the joints slender and the portions between\nthem are thick; and this happens because nothing but the skin covers\nthe joints without any other flesh and has the character of sinew,\nconnecting the bones like a ligature. And the fat fleshiness is laid\non between one joint and the next, and between the skin and the\nbones. But, since the bones are thicker at the joints than between\nthem, as a mass grows up the flesh ceases to have that superfluity\nwhich it had, between the skin and the bones; whence the skin clings\nmore closely to the bone and the limbs grow more slender. But since\nthere is nothing over the joints but the cartilaginous and sinewy\nskin this cannot dry up, and, not drying up, cannot shrink. Thus,\nand for this reason, children are slender at the joints and fat\nbetween the joints; as may be seen in the joints of the fingers,\narms, and shoulders, which are slender and dimpled, while in man on\nthe contrary all the joints of the fingers, arms, and legs are\nthick; and wherever children have hollows men have prominences.\n\nThe movement of the human figure (368-375).\n\n368.\n\nOf the manner of representing the 18 actions of man. Repose,\nmovement, running, standing, supported, sitting, leaning, kneeling,\nlying down, suspended. Carrying or being carried, thrusting,\npulling, striking, being struck, pressing down and lifting up.\n\n[As to how a figure should stand with a weight in its hand [Footnote\n8: The original text ends here.] Remember].\n\n369.\n\nA sitting man cannot raise himself if that part of his body which is\nfront of his axis [centre of gravity] does not weigh more than that\nwhich is behind that axis [or centre] without using his arms.\n\nA man who is mounting any slope finds that he must involuntarily\nthrow the most weight forward, on the higher foot, rather than\nbehind--that is in front of the axis and not behind it. Hence a man\nwill always, involuntarily, throw the greater weight towards the\npoint whither he desires to move than in any other direction.\n\nThe faster a man runs, the more he leans forward towards the point\nhe runs to and throws more weight in front of his axis than behind.\nA man who runs down hill throws the axis onto his heels, and one who\nruns up hill throws it into the points of his feet; and a man\nrunning on level ground throws it first on his heels and then on the\npoints of his feet.\n\nThis man cannot carry his own weight unless, by drawing his body\nback he balances the weight in front, in such a way as that the foot\non which he stands is the centre of gravity.\n\n[Footnote: See Pl. XXII, No. 4.]\n\n370.\n\nHow a man proceeds to raise himself to his feet, when he is sitting\non level ground.\n\n371.\n\nA man when walking has his head in advance of his feet.\n\nA man when walking across a long level plain first leans [rather]\nbackwards and then as much forwards.\n\n[Footnote 3-6: He strides forward with the air of a man going down\nhill; when weary, on the contrary he walks like a man going up\nhill.]\n\n372.\n\nA man when running throws less weight on his legs than when standing\nstill. And in the same way a horse which is running feels less the\nweight of the man he carries. Hence many persons think it wonderful\nthat, in running, the horse can rest on one single foot. From this\nit may be stated that when a weight is in progressive motion the\nmore rapid it is the less is the perpendicular weight towards the\ncentre.\n\n373.\n\nIf a man, in taking a jump from firm ground, can leap 3 braccia, and\nwhen he was taking his leap it were to recede 1/3 of a braccio, that\nwould be taken off his former leap; and so if it were thrust forward\n1/3 of a braccio, by how much would his leap be increased?\n\n374.\n\nOF DRAWING.\n\nWhen a man who is running wants to neutralise the impetus that\ncarries him on he prepares a contrary impetus which is generated by\nhis hanging backwards. This can be proved, since, if the impetus\ncarries a moving body with a momentum equal to 4 and the moving body\nwants to turn and fall back with a momentum of 4, then one momentum\nneutralises the other contrary one, and the impetus is neutralised.\n\nOf walking up and down (375-379)\n\n375.\n\nWhen a man wants to stop running and check the impetus he is forced\nto hang back and take short quick steps. [Footnote: Lines 5-31 refer\nto the two upper figures, and the lower figure to the right is\nexplained by the last part of the chapter.] The centre of gravity of\na man who lifts one of his feet from the ground always rests on the\ncentre of the sole of the foot [he stands on].\n\nA man, in going up stairs involuntarily throws so much weight\nforward and on the side of the upper foot as to be a counterpoise to\nthe lower leg, so that the labour of this lower leg is limited to\nmoving itself.\n\nThe first thing a man does in mounting steps is to relieve the leg\nhe is about to lift of the weight of the body which was resting on\nthat leg; and besides this, he gives to the opposite leg all the\nrest of the bulk of the whole man, including [the weight of] the\nother leg; he then raises the other leg and sets the foot upon the\nstep to which he wishes to raise himself. Having done this he\nrestores to the upper foot all the weight of the body and of the leg\nitself, and places his hand on his thigh and throws his head forward\nand repeats the movement towards the point of the upper foot,\nquickly lifting the heel of the lower one; and with this impetus he\nlifts himself up and at the same time extends the arm which rested\non his knee; and this extension of the arm carries up the body and\nthe head, and so straightens the spine which was curved.\n\n[32] The higher the step is which a man has to mount, the farther\nforward will he place his head in advance of his upper foot, so as\nto weigh more on _a_ than on _b_; this man will not be on the step\n_m_. As is shown by the line _g f_.\n\n[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left\nbelongs to the four first lines.]\n\n376.\n\nI ask the weight [pressure] of this man at every degree of motion on\nthese steps, what weight he gives to _b_ and to _c_.\n\n[Footnote 8: These lines are, in the original, written in ink]\nObserve the perpendicular line below the centre of gravity of the\nman.\n\n[Footnote: See Pl. XXIII, No. 2.]\n\n377.\n\nIn going up stairs if you place your hands on your knees all the\nlabour taken by the arms is removed from the sinews at the back of\nthe knees.\n\n[Footnote: See Pl. XXIII, No. 3.]\n\n378.\n\nThe sinew which guides the leg, and which is connected with the\npatella of the knee, feels it a greater labour to carry the man\nupwards, in proportion as the leg is more bent; and the muscle which\nacts upon the angle made by the thigh where it joins the body has\nless difficulty and has a less weight to lift, because it has not\nthe [additional] weight of the thigh itself. And besides this it has\nstronger muscles, being those which form the buttock.\n\n379.\n\nA man coming down hill takes little steps, because the weight rests\nupon the hinder foot, while a man mounting takes wide steps, because\nhis weight rests on the foremost foot.\n\n[Footnote: See Pl. XXIII, No. 4.]\n\nOn the human body in action (380-388).\n\n380.\n\nOF THE HUMAN BODY IN ACTION.\n\nWhen you want to represent a man as moving some weight consider what\nthe movements are that are to be represented by different lines;\nthat is to say either from below upwards, with a simple movement, as\na man does who stoops forward to take up a weight which he will lift\nas he straightens himself. Or as a man does who wants to squash\nsomething backwards, or to force it forwards or to pull it downwards\nwith ropes passed through pullies [Footnote 10: Compare the sketch\non page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that\nthe weight of a man pulls in proportion as his centre of gravity is\ndistant from his fulcrum, and to this is added the force given by\nhis legs and bent back as he raises himself.\n\n381.\n\nAgain, a man has even a greater store of strength in his legs than\nhe needs for his own weight; and to see if this is true, make a man\nstand on the shore-sand and then put another man on his back, and\nyou will see how much he will sink in. Then take the man from off\nhis back and make him jump straight up as high as he can, and you\nwill find that the print of his feet will be made deeper by the jump\nthan from having the man on his back. Hence, here, by 2 methods it\nis proved that a man has double the strength he requires to support\nhis own body.\n\n382.\n\nOF PAINTING.\n\nIf you have to draw a man who is in motion, or lifting or pulling,\nor carrying a weight equal to his own, in what way must you set on\nhis legs below his body?\n\n[Footnote: In the MS. this question remains unanswered.]\n\n383.\n\nOF THE STRENGTH OF MAN.\n\nA man pulling a [dead] weight balanced against himself cannot pull\nmore than his own weight. And if he has to raise it he will [be able\nto] raise as much more than his weight as his strength may be more\nthan that of other men. [Footnote 7: The stroke at the end of this\nline finishes in the original in a sort of loop or flourish, and a\nsimilar flourish occurs at the end of the previous passage written\non the same page. M. RAVAISSON regards these as numbers (compare the\nphotograph of page 30b in his edition of MS. A). He remarks: \"_Ce\nchiffre_ 8 _et, a la fin de l'alinea precedent, le chiffre_ 7 _sont,\ndans le manuscrit, des renvois_.\"] The greatest force a man can\napply, with equal velocity and impetus, will be when he sets his\nfeet on one end of the balance [or lever] and then presses his\nshoulders against some stable body. This will raise a weight at the\nother end of the balance [lever], equal to his own weight and [added\nto that] as much weight as he can carry on his shoulders.\n\n384.\n\nNo animal can simply move [by its dead weight] a greater weight than\nthe sum of its own weight outside the centre of his fulcrum.\n\n385.\n\nA man who wants to send an arrow very far from the bow must be\nstanding entirely on one foot and raising the other so far from the\nfoot he stands on as to afford the requisite counterpoise to his\nbody which is thrown on the front foot. And he must not hold his arm\nfully extended, and in order that he may be more able to bear the\nstrain he must hold a piece of wood which there is in all crossbows,\nextending from the hand to the breast, and when he wishes to shoot\nhe suddenly leaps forward at the same instant and extends his arm\nwith the bow and releases the string. And if he dexterously does\nevery thing at once it will go a very long way.\n\n386.\n\nWhen two men are at the opposite ends of a plank that is balanced,\nand if they are of equal weight, and if one of them wants to make a\nleap into the air, then his leap will be made down from his end of\nthe plank and the man will never go up again but must remain in his\nplace till the man at the other end dashes up the board.\n\n[Footnote: See Pl. XXIV, No. 3.]\n\n387.\n\nOf delivering a blow to the right or left.\n\n[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage.\nThe rest of the sketches and notes on that page are of a\nmiscellaneous nature.]\n\n388.\n\nWhy an impetus is not spent at once [but diminishes] gradually in\nsome one direction? [Footnote 1: The paper has been damaged at the\nend of line 1.] The impetus acquired in the line _a b c d_ is spent\nin the line _d e_ but not so completely but that some of its force\nremains in it and to this force is added the momentum in the line _d\ne_ with the force of the motive power, and it must follow than the\nimpetus multiplied by the blow is greater that the simple impetus\nproduced by the momentum _d e_.\n\n[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original,\nbetween lines 7 and 8. Compare also the sketches on Pl. LIV.] A man\nwho has to deal a great blow with his weapon prepares himself with\nall his force on the opposite side to that where the spot is which\nhe is to hit; and this is because a body as it gains in velocity\ngains in force against the object which impedes its motion.\n\nOn hair falling down in curls.\n\n389.\n\nObserve the motion of the surface of the water which resembles that\nof hair, and has two motions, of which one goes on with the flow of\nthe surface, the other forms the lines of the eddies; thus the water\nforms eddying whirlpools one part of which are due to the impetus of\nthe principal current and the other to the incidental motion and\nreturn flow.\n\n[Footnote: See Pl. XXV. Where also the text of this passage is given\nin facsimile.]\n\nOn draperies (390--392).\n\n390.\n\nOF THE NATURE OF THE FOLDS IN DRAPERY.\n\nThat part of a fold which is farthest from the ends where it is\nconfined will fall most nearly in its natural form.\n\nEvery thing by nature tends to remain at rest. Drapery, being of\nequal density and thickness on its wrong side and on its right, has\na tendency to lie flat; therefore when you give it a fold or plait\nforcing it out of its flatness note well the result of the\nconstraint in the part where it is most confined; and the part which\nis farthest from this constraint you will see relapses most into the\nnatural state; that is to say lies free and flowing.\n\nEXAMPLE.\n\n[Footnote 13: _a c sia_. In the original text _b_ is written instead\nof _c_--an evident slip of the pen.] Let _a b c_ be the fold of the\ndrapery spoken of above, _a c_ will be the places where this folded\ndrapery is held fast. I maintain that the part of the drapery which\nis farthest from the plaited ends will revert most to its natural\nform.\n\nTherefore, _b_ being farthest from _a_ and _c_ in the fold _a b c_\nit will be wider there than anywhere else.\n\n[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from\nWindsor Pl. XXX for farther illustration of what is here stated.]\n\n391.\n\nOF SMALL FOLDS IN DRAPERIES.\n\nHow figures dressed in a cloak should not show the shape so much as\nthat the cloak looks as if it were next the flesh; since you surely\ncannot wish the cloak to be next the flesh, for you must suppose\nthat between the flesh and the cloak there are other garments which\nprevent the forms of the limbs appearing distinctly through the\ncloak. And those limbs which you allow to be seen you must make\nthicker so that the other garments may appear to be under the cloak.\nBut only give something of the true thickness of the limbs to a\nnymph [Footnote 9: _Una nifa_. Compare the beautiful drawing of a\nNymph, in black chalk from the Windsor collection, Pl. XXVI.] or an\nangel, which are represented in thin draperies, pressed and clinging\nto the limbs of the figures by the action of the wind.\n\n392.\n\nYou ought not to give to drapery a great confusion of many folds,\nbut rather only introduce them where they are held by the hands or\nthe arms; the rest you may let fall simply where it is its nature to\nflow; and do not let the nude forms be broken by too many details\nand interrupted folds. How draperies should be drawn from nature:\nthat is to say if youwant to represent woollen cloth draw the folds\nfrom that; and if it is to be silk, or fine cloth or coarse, or of\nlinen or of crape, vary the folds in each and do not represent\ndresses, as many do, from models covered with paper or thin leather\nwhich will deceive you greatly.\n\n[Footnote: The little pen and ink drawing from Windsor (W. 102),\ngiven on Pl. XXVIII, No. 7, clearly illustrates the statement made\nat the beginning of this passage; the writing of the cipher 19 on\nthe same page is in Leonardo's hand; the cipher 21 is certainly\nnot.]\n\n_VIII._\n\n_Botany for Painters and Elements of Landscape Painting._\n\n_The chapters composing this portion of the work consist of\nobservations on Form, Light and Shade in Plants, and particularly in\nTrees summed up in certain general rules by which the author intends\nto guide the artist in the pictorial representation of landscape._\n\n_With these the first principles of a_ Theory of Landscape painting\n_are laid down--a theory as profoundly thought out in its main\nlines as it is lucidly worked out in its details. In reading these\nchapters the conviction is irresistible that such a_ Botany for\npainters _is or ought to be of similar importance in the practice of\npainting as the principles of the Proportions and Movements of the\nhuman figure_ i. e. Anatomy for painters.\n\n_There can be no doubt that Leonardo, in laying down these rules,\ndid not intend to write on Botany in the proper scientific\nsense--his own researches on that subject have no place here; it\nneed only be observed that they are easily distinguished by their\ncharacter and contents from those which are here collected and\narranged under the title 'Botany for painters'. In some cases where\nthis division might appear doubtful,--as for instance in No._\n402--_the Painter is directly addressed and enjoined to take the\nrule to heart as of special importance in his art._\n\n_The original materials are principally derived from MS._ G, _in\nwhich we often find this subject treated on several pages in\nsuccession without any of that intermixture of other matters, which\nis so frequent in Leonardo's writings. This MS., too, is one of the\nlatest; when it was written, the great painter was already more than\nsixty years of age, so we can scarcely doubt that he regarded all he\nwrote as his final views on the subject. And the same remark applies\nto the chapters from MSS._ E _and_ M _which were also written\nbetween_ 1513--15.\n\n_For the sake of clearness, however, it has been desirable to\nsacrifice--with few exceptions--the original order of the passages\nas written, though it was with much reluctance and only after long\nhesitation that I resigned myself to this necessity. Nor do I mean\nto impugn the logical connection of the author's ideas in his MS.;\nbut it will be easily understood that the sequence of disconnected\nnotes, as they occurred to Leonardo and were written down from time\nto time, might be hardly satisfactory as a systematic arrangement of\nhis principles. The reader will find in the Appendix an exact\naccount of the order of the chapters in the original MS. and from\nthe data there given can restore them at will. As the materials are\nhere arranged, the structure of the tree as regards the growth of\nthe branches comes first_ (394-411) _and then the insertion of the\nleaves on the stems_ (412-419). _Then follow the laws of Light and\nShade as applied, first, to the leaves (420-434), and, secondly, to\nthe whole tree and to groups of trees_ (435-457). _After the remarks\non the Light and Shade in landscapes generally_ (458-464), _we find\nspecial observations on that of views of towns and buildings_\n(465-469). _To the theory of Landscape Painting belong also the\npassages on the effect of Wind on Trees_ (470-473) _and on the Light\nand Shade of Clouds_ (474-477), _since we find in these certain\ncomparisons with the effect of Light and Shade on Trees_ (e. g.: _in\nNo._ 476, 4. 5; _and No._ 477, 9. 12). _The chapters given in the\nAppendix Nos._ 478 _and_ 481 _have hardly any connection with the\nsubjects previously treated._\n\nClassification of trees.\n\n393.\n\nTREES.\n\nSmall, lofty, straggling, thick, that is as to foliage, dark, light,\nrusset, branched at the top; some directed towards the eye, some\ndownwards; with white stems; this transparent in the air, that not;\nsome standing close together, some scattered.\n\nThe relative thickness of the branches to the trunk (393--396).\n\n394.\n\nAll the branches of a tree at every stage of its height when put\ntogether are equal in thickness to the trunk [below them].\n\nAll the branches of a water [course] at every stage of its course,\nif they are of equal rapidity, are equal to the body of the main\nstream.\n\n395.\n\nEvery year when the boughs of a plant [or tree] have made an end of\nmaturing their growth, they will have made, when put together, a\nthickness equal to that of the main stem; and at every stage of its\nramification you will find the thickness of the said main stem; as:\n_i k_, _g h_, _e f_, _c d_, _a b_, will always be equal to each\nother; unless the tree is pollard--if so the rule does not hold\ngood.\n\nAll the branches have a direction which tends to the centre of the\ntree _m_.\n\n[Footnote: The two sketches of leafless trees one above another on\nthe left hand side of Pl. XXVII, No. 1, belong to this passage.]\n\n396.\n\nIf the plant n grows to the thickness shown at m, its branches will\ncorrespond [in thickness] to the junction a b in consequence of the\ngrowth inside as well as outside.\n\nThe branches of trees or plants have a twist wherever a minor branch\nis given off; and this giving off the branch forms a fork; this said\nfork occurs between two angles of which the largest will be that\nwhich is on the side of the larger branch, and in proportion, unless\naccident has spoilt it.\n\n[Footnote: The sketches illustrating this are on the right hand side\nof PI. XXVII, No. I, and the text is also given there in facsimile.]\n\n397.\n\nThere is no boss on branches which has not been produced by some\nbranch which has failed.\n\nThe lower shoots on the branches of trees grow more than the upper\nones and this occurs only because the sap that nourishes them, being\nheavy, tends downwards more than upwards; and again, because those\n[branches] which grow downwards turn away from the shade which\nexists towards the centre of the plant. The older the branches are,\nthe greater is the difference between their upper and their lower\nshoots and in those dating from the same year or epoch.\n\n[Footnote: The sketch accompanying this in the MS. is so effaced\nthat an exact reproduction was impossible.]\n\n398.\n\nOF THE SCARS ON TREES.\n\nThe scars on trees grow to a greater thickness than is required by\nthe sap of the limb which nourishes them.\n\n399.\n\nThe plant which gives out the smallest ramifications will preserve\nthe straightest line in the course of its growth.\n\n[Footnote: This passage is illustrated by two partly effaced\nsketches. One of these closely resembles the lower one given under\nNo. 408, the other also represents short closely set boughs on an\nupright trunk.]\n\n400.\n\nOF THE RAMIFICATION.\n\nThe beginning of the ramification [the shoot] always has the central\nline [axis] of its thickness directed to the central line [axis] of\nthe plant itself.\n\n401.\n\nIn starting from the main stem the branches always form a base with\na prominence as is shown at _a b c d_.\n\n402.\n\nWHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT.\n\nWhen the branches which grow the second year above the branch of the\npreceding year, are not of equal thickness above the antecedent\nbranches, but are on one side, then the vigour of the lower branch\nis diverted to nourish the one above it, although it may be somewhat\non one side.\n\nBut if the ramifications are equal in their growth, the veins of the\nmain stem will be straight [parallel] and equidistant at every\ndegree of the height of the plant.\n\nWherefore, O Painter! you, who do not know these laws! in order to\nescape the blame of those who understand them, it will be well that\nyou should represent every thing from nature, and not despise such\nstudy as those do who work [only] for money.\n\nThe direction of growth (403-407).\n\n403.\n\nOF THE RAMIFICATIONS OF PLANTS.\n\nThe plants which spread very much have the angles of the spaces\nwhich divide their branches more obtuse in proportion as their point\nof origin is lower down; that is nearer to the thickest and oldest\nportion of the tree. Therefore in the youngest portions of the tree\nthe angles of ramification are more acute. [Footnote: Compare the\nsketches on the lower portion of Pl. XXVII, No. 2.]\n\n404.\n\nThe tips of the boughs of plants [and trees], unless they are borne\ndown by the weight of their fruits, turn towards the sky as much as\npossible.\n\nThe upper side of their leaves is turned towards the sky that it may\nreceive the nourishment of the dew which falls at night.\n\nThe sun gives spirit and life to plants and the earth nourishes them\nwith moisture. [9] With regard to this I made the experiment of\nleaving only one small root on a gourd and this I kept nourished\nwith water, and the gourd brought to perfection all the fruits it\ncould produce, which were about 60 gourds of the long kind, andi set\nmy mind diligently [to consider] this vitality and perceived that\nthe dews of night were what supplied it abundantly with moisture\nthrough the insertion of its large leaves and gave nourishment to\nthe plant and its offspring--or the seeds which its offspring had\nto produce--[21].\n\nThe rule of the leaves produced on the last shoot of the year will\nbe that they will grow in a contrary direction on the twin branches;\nthat is, that the insertion of the leaves turns round each branch in\nsuch a way, as that the sixth leaf above is produced over the sixth\nleaf below, and the way they turn is that if one turns towards its\ncompanion to the right, the other turns to the left, the leaf\nserving as the nourishing breast for the shoot or fruit which grows\nthe following year.\n\n[Footnote: A French translation of lines 9-12 was given by M.\nRAVAISSON in the _Gazette des Beaux Arts_, Oct. 1877; his paper also\ncontains some valuable information as to botanical science in the\nancient classical writers and at the time of the Renaissance.]\n\n405.\n\nThe lowest branches of those trees which have large leaves and heavy\nfruits, such as nut-trees, fig-trees and the like, always droop\ntowards the ground.\n\nThe branches always originate above [in the axis of] the leaves.\n\n406.\n\nThe upper shoots of the lateral branches of plants lie closer to the\nparent branch than the lower ones.\n\n407.\n\nThe lowest branches, after they have formed the angle of their\nseparation from the parent stem, always bend downwards so as not to\ncrowd against the other branches which follow them on the same stem\nand to be better able to take the air which nourishes them. As is\nshown by the angle _b a c_; the branch _a c_ after it has made the\ncorner of the angle _a c_ bends downwards to _c d_ and the lesser\nshoot _c_ dries up, being too thin.\n\nThe main branch always goes below, as is shown by the branch _f n\nm_, which does not go to _f n o_.\n\nThe forms of trees (408--411).\n\n408.\n\nThe elm always gives a greater length to the last branches of the\nyear's growth than to the lower ones; and Nature does this because\nthe highest branches are those which have to add to the size of the\ntree; and those at the bottom must get dry because they grow in the\nshade and their growth would be an impediment to the entrance of the\nsolar rays and the air among the main branches of the tree.\n\nThe main branches of the lower part bend down more than those above,\nso as to be more oblique than those upper ones, and also because\nthey are larger and older.\n\n409.\n\nIn general almost all the upright portions of trees curve somewhat\nturning the convexity towards the South; and their branches are\nlonger and thicker and more abundant towards the South than towards\nthe North. And this occurs because the sun draws the sap towards\nthat surface of the tree which is nearest to it.\n\nAnd this may be observed if the sun is not screened off by other\nplants.\n\n410.\n\nThe cherry-tree is of the character of the fir tree as regards its\nramification placed in stages round its main stem; and its branches\nspring, 4 or five or 6 [together] opposite each other; and the tips\nof the topmost shoots form a pyramid from the middle upwards; and\nthe walnut and oak form a hemisphere from the middle upwards.\n\n411.\n\nThe bough of the walnut which is only hit and beaten when it has\nbrought to perfection...\n\n[Footnote: The end of the text and the sketch in red chalk belonging\nto it, are entirely effaced.]\n\nThe insertion of the leaves (412--419).\n\n412.\n\nOF THE INSERTION OF THE BRANCHES ON PLANTS.\n\nSuch as the growth of the ramification of plants is on their\nprincipal branches, so is that of the leaves on the shoots of the\nsame plant. These leaves have [Footnote 6: _Quattro modi_ (four\nmodes). Only three are described in the text, the fourth is only\nsuggested by a sketch.\n\nThis passage occurs in MANZI'S edition of the Trattato, p. 399, but\nwithout the sketches and the text is mutilated in an important part.\nThe whole passage has been commented on, from MANZI'S version, in\nPart I of the _Nuovo Giornale Botanico Italiano_, by Prof. G.\nUZIELLI (Florence 1869, Vol. I). He remarks as to the 'four modes':\n\"_Leonardo, come si vede nelle linie sententi da solo tre esempli.\nQuesta ed altre inessattezze fanno desiderare, sia esaminato di\nnuovo il manoscritto Vaticano_\". This has since been done by D.\nKNAPP of Tubingen, and his accurate copy has been published by H.\nLUDWIG, the painter. The passage in question occurs in his edition\nas No. 833; and there also the drawings are wanting. The space for\nthem has been left vacant, but in the Vatican copy '_niente_' has\nbeen written on the margin; and in it, as well as in LUDWIG'S and\nMANZI'S edition, the text is mutilated.] four modes of growing one\nabove another. The first, which is the most general, is that the\nsixth always originates over the sixth below [Footnote 8: _la sesta\ndi sotto. \"Disposizione 2/5 o 1/5. Leonardo osservo probabilmente\nsoltanto la prima\"_ (UZIELLl).]; the second is that two third ones\nabove are over the two third ones below [Footnote 10: _terze di\nsotto: \"Intende qui senza dubbio parlare di foglie decussate, in cui\nil terzo verticello e nel piano del primo\"_ (UZIELLI).]; and the\nthird way is that the third above is over the third below [Footnote\n11: 3a _di sotto: \"Disposizione 1/2\"_ (UZIELLI).].\n\n[Footnote: See the four sketches on the upper portion of the page\nreproduced as fig. 2 on P1. XXVII.]\n\n413.\n\nA DESCRIPTION OF THE ELM.\n\nThe ramification of the elm has the largest branch at the top. The\nfirst and the last but one are smaller, when the main trunk is\nstraight.\n\nThe space between the insertion of one leaf to the rest is half the\nextreme length of the leaf or somewhat less, for the leaves are at\nan interval which is about the 3rd of the width of the leaf.\n\nThe elm has more leaves near the top of the boughs than at the base;\nand the broad [surface] of the leaves varies little as to [angle\nand] aspect.\n\n[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under\nthe number of the page is the word '_olmo_' (elm).]\n\n414.\n\nIn the walnut tree the leaves which are distributed on the shoots of\nthis year are further apart from each other and more numerous in\nproportion as the branch from which this shoot springs is a young\none. And they are inserted more closely and less in number when the\nshoot that bears them springs from an old branch. Its fruits are\nborne at the ends of the shoots. And its largest boughs are the\nlowest on the boughs they spring from. And this arises from the\nweight of its sap which is more apt to descend than to rise, and\nconsequently the branches which spring from them and rise towards\nthe sky are small and slender [20]; and when the shoot turns towards\nthe sky its leaves spread out from it [at an angle] with an equal\ndistribution of their tips; and if the shoot turns to the horizon\nthe leaves lie flat; and this arises from the fact that leaves\nwithout exception, turn their underside to the earth [29].\n\nThe shoots are smaller in proportion as they spring nearer to the\nbase of the bough they spring from.\n\n[Footnote: See the two sketches on Pl XXVII, No. 4. The second\nrefers to the passage lines 20-30.]\n\n415.\n\nOF THE INSERTION OF THE LEAVES ON THE BRANCHES.\n\nThe thickness of a branch never diminishes within the space between\none leaf and the next excepting by so much as the thickness of the\nbud which is above the leaf and this thickness is taken off from the\nbranch above [the node] as far as the next leaf.\n\nNature has so placed the leaves of the latest shoots of many plants\nthat the sixth leaf is always above the first, and so on in\nsuccession, if the rule is not [accidentally] interfered with; and\nthis occurs for two useful ends in the plant: First that as the\nshoot and the fruit of the following year spring from the bud or eye\nwhich lies above and in close contact with the insertion of the leaf\n[in the axil], the water which falls upon the shoot can run down to\nnourish the bud, by the drop being caught in the hollow [axil] at\nthe insertion of the leaf. And the second advantage is, that as\nthese shoots develop in the following year one will not cover the\nnext below, since the 5 come forth on five different sides; and the\nsixth which is above the first is at some distance.\n\n416.\n\nOF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE.\n\nThe ramifications of any tree, such as the elm, are wide and slender\nafter the manner of a hand with spread fingers, foreshortened. And\nthese are seen in the distribution [thus]: the lower portions are\nseen from above; and those that are above are seen from below; and\nthose in the middle, some from below and some from above. The upper\npart is the extreme [top] of this ramification and the middle\nportion is more foreshortened than any other of those which are\nturned with their tips towards you. And of those parts of the middle\nof the height of the tree, the longest will be towards the top of\nthe tree and will produce a ramification like the foliage of the\ncommon willow, which grows on the banks of rivers.\n\nOther ramifications are spherical, as those of such trees as put\nforth their shoots and leaves in the order of the sixth being placed\nabove the first. Others are thin and light like the willow and\nothers.\n\n417.\n\nYou will see in the lower branches of the elder, which puts forth\nleaves two and two placed crosswise [at right angles] one above\nanother, that if the stem rises straight up towards the sky this\norder never fails; and its largest leaves are on the thickest part\nof the stem and the smallest on the slenderest part, that is towards\nthe top. But, to return to the lower branches, I say that the leaves\non these are placed on them crosswise like [those on] the upper\nbranches; and as, by the law of all leaves, they are compelled to\nturn their upper surface towards the sky to catch the dew at night,\nit is necessary that those so placed should twist round and no\nlonger form a cross.\n\n[Footnote: See Pl. XXVII, No. 5.]\n\n418.\n\nA leaf always turns its upper side towards the sky so that it may\nthe better receive, on all its surface, the dew which drops gently\nfrom the atmosphere. And these leaves are so distributed on the\nplant as that one shall cover the other as little as possible, but\nshall lie alternately one above another as may be seen in the ivy\nwhich covers the walls. And this alternation serves two ends; that\nis, to leave intervals by which the air and sun may penetrate\nbetween them. The 2nd reason is that the drops which fall from the\nfirst leaf may fall onto the fourth or--in other trees--onto the\nsixth.\n\n419.\n\nEvery shoot and every fruit is produced above the insertion [in the\naxil] of its leaf which serves it as a mother, giving it water from\nthe rain and moisture from the dew which falls at night from above,\nand often it protects them against the too great heat of the rays of\nthe sun.\n\nLIGHT ON BRANCHES AND LEAVES (420--422).\n\n420.\n\nThat part of the body will be most illuminated which is hit by the\nluminous ray coming between right angles.\n\n[Footnote: See Pl. XXVIII, No. 1.]\n\n421.\n\nYoung plants have more transparent leaves and a more lustrous bark\nthan old ones; and particularly the walnut is lighter coloured in\nMay than in September.\n\n422.\n\nOF THE ACCIDENTS OF COLOURING IN TREES.\n\nThe accidents of colour in the foliage of trees are 4. That is:\nshadow, light, lustre [reflected light] and transparency.\n\nOF THE VISIBILITY OF THESE ACCIDENTS.\n\nThese accidents of colour in the foliage of trees become confused at\na great distance and that which has most breadth [whether light or\nshade, &c.] will be most conspicuous.\n\nThe proportions of light and shade in a leaf (423-426).\n\n423.\n\nOF THE SHADOWS OF A LEAF.\n\nSometimes a leaf has three accidents [of light] that is: shade,\nlustre [reflected light] and transparency [transmitted light]. Thus,\nif the light were at _n_ as regards the leaf _s_, and the eye at\n_m_, it would see _a_ in full light, _b_ in shadow and _c_\ntransparent.\n\n424.\n\nA leaf with a concave surface seen from the under side and\nup-side-down will sometimes show itself as half in shade, and half\ntransparent. Thus, if _o p_ is the leaf and the light _m_ and the\neye _n_, this will see _o_ in shadow because the light does not fall\nupon it between equal angles, neither on the upper nor the under\nside, and _p_ is lighted on the upper side and the light is\ntransmitted to its under side. [Footnote: See Pl. XXVIII, No. 2, the\nupper sketch on the page. In the original they are drawn in red\nchalk.]\n\n425.\n\nAlthough those leaves which have a polished surface are to a great\nextent of the same colour on the right side and on the reverse, it\nmay happen that the side which is turned towards the atmosphere will\nhave something of the colour of the atmosphere; and it will seem to\nhave more of this colour of the atmosphere in proportion as the eye\nis nearer to it and sees it more foreshortened. And, without\nexception the shadows show as darker on the upper side than on the\nlower, from the contrast offered by the high lights which limit the\nshadows.\n\nThe under side of the leaf, although its colour may be in itself the\nsame as that of the upper side, shows a still finer colour--a colour\nthat is green verging on yellow--and this happens when the leaf is\nplaced between\n\n426.\n\nthe eye and the light which falls upon it from the opposite side.\n\nAnd its shadows are in the same positions as those were of the\nopposite side. Therefore, O Painter! when you do trees close at\nhand, remember that if the eye is almost under the tree you will see\nits leaves [some] on the upper and [some] on the under side, and the\nupper side will be bluer in proportion as they are seen more\nforeshortened, and the same leaf sometimes shows part of the right\nside and part of the under side, whence you must make it of two\ncolours.\n\nOf the transparency of leaves (427-429).\n\n427.\n\nThe shadows in transparent leaves seen from the under side are the\nsame shadows as there are on the right side of this leaf, they will\nshow through to the underside together with lights, but the lustre\n[reflected light] can never show through.\n\n428.\n\nWhen one green has another [green] behind it, the lustre on the\nleaves and their transparent [lights] show more strongly than in\nthose which are [seen] against the brightness of the atmosphere.\n\nAnd if the sun illuminates the leaves without their coming between\nit and the eye and without the eye facing the sun, then the\nreflected lights and the transparent lights are very strong.\n\nIt is very effective to show some branches which are low down and\ndark and so set off the illuminated greens which are at some\ndistance from the dark greens seen below. That part is darkest which\nis nearest to the eye or which is farthest from the luminous\natmosphere.\n\n429.\n\nNever paint leaves transparent to the sun, because they are\nconfused; and this is because on the transparency of one leaf will\nbe seen the shadow of another leaf which is above it. This shadow\nhas a distinct outline and a certain depth of shade and sometimes is\n[as much as] half or a third of the leaf which is shaded; and\nconsequently such an arrangement is very confused and the imitation\nof it should be avoided.\n\nThe light shines least through a leaf when it falls upon it at an\nacute angle.\n\nThe gradations of shade and colour in leaves (430-434).\n\n430.\n\nThe shadows of plants are never black, for where the atmosphere\npenetrates there can never be utter darkness.\n\n431.\n\nIf the light comes from _m_ and the eye is at _n_ the eye will see\nthe colour of the leaves _a b_ all affected by the colour of _m_\n--that is of the atmosphere; and _b c_ will be seen from the under\nside as transparent, with a beautiful green colour verging on\nyellow.\n\nIf _m_ is the luminous body lighting up the leaf _s_ all the eyes\nthat see the under side of this leaf will see it of a beautiful\nlight green, being transparent.\n\nIn very many cases the positions of the leaves will be without\nshadow [or in full light], and their under side will be transparent\nand the right side lustrous [reflecting light].\n\n432.\n\nThe willow and other similar trees, which have their boughs lopped\nevery 3 or 4 years, put forth very straight branches, and their\nshadow is about the middle where these boughs spring; and towards\nthe extreme ends they cast but little shade from having small leaves\nand few and slender branches. Hence the boughs which rise towards\nthe sky will have but little shade and little relief; and the\nbranches which are at an angle from the horizon, downwards, spring\nfrom the dark part of the shadow and grow thinner by degrees up to\ntheir ends, and these will be in strong relief, being in gradations\nof light against a background of shadow.\n\nThat tree will have the least shadow which has the fewest branches\nand few leaves.\n\n433.\n\nOF DARK LEAVES IN FRONT OF TRANSPARENT ONES.\n\nWhen the leaves are interposed between the light and the eye, then\nthat which is nearest to the eye will be the darkest, and the most\ndistant will be the lightest, not being seen against the atmosphere;\nand this is seen in the leaves which are away from the centre of the\ntree, that is towards the light.\n\n[Footnote: See Pl. XXVIII, No. 2, the lower sketch.]\n\n434.\n\nOF THE LIGHTS ON DARK LEAVES.\n\nThe lights on such leaves which are darkest, will be most near to\nthe colour of the atmosphere that is reflected in them. And the\ncause of this is that the light on the illuminated portion mingles\nwith the dark hue to compose a blue colour; and this light is\nproduced by the blueness of the atmosphere which is reflected in the\nsmooth surface of these leaves and adds to the blue hue which this\nlight usually produces when it falls on dark objects.\n\nOF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN.\n\nBut leaves of a green verging on yellow when they reflect the\natmosphere do not produce a reflection verging on blue, inasmuch as\nevery thing which appears in a mirror takes some colour from that\nmirror, hence the blue of the atmosphere being reflected in the\nyellow of the leaf appears green, because blue and yellow mixed\ntogether make a very fine green colour, therefore the lustre of\nlight leaves verging on yellow will be greenish yellow.\n\nA classification of trees according to their colours.\n\n435.\n\nThe trees in a landscape are of various kinds of green, inasmuch as\nsome verge towards blackness, as firs, pines, cypresses, laurels,\nbox and the like. Some tend to yellow such as walnuts, and pears,\nvines and verdure. Some are both yellowish and dark as chesnuts,\nholm-oak. Some turn red in autumn as the service-tree, pomegranate,\nvine, and cherry; and some are whitish as the willow, olive, reeds\nand the like. Trees are of various forms ...\n\nThe proportions of light and shade in trees (436-440).\n\n436.\n\nOF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES.\n\nThat part of the trees will be seen to lie in the least dark shadow\nwhich is farthest from the earth.\n\nTo prove it let _a p_ be the tree, _n b c_ the illuminated\nhemisphere [the sky], the under portion of the tree faces the earth\n_p c_, that is on the side _o_, and it faces a small part of the\nhemisphere at _c d_. But the highest part of the convexity a faces\nthe greatest part of the hemisphere, that is _b c_. For this\nreason--and because it does not face the darkness of the earth--it\nis in fuller light. But if the tree has dense foliage, as the\nlaurel, arbutus, box or holm oak, it will be different; because,\nalthough _a_ does not face the earth, it faces the dark [green] of\nthe leaves cut up by many shadows, and this darkness is reflected\nonto the under sides of the leaves immediately above. Thus these\ntrees have their darkest shadows nearest to the middle of the tree.\n\n437.\n\nOF THE SHADOWS OF VERDURE.\n\nThe shadows of verdure are always somewhat blue, and so is every\nshadow of every object; and they assume this hue more in proportion\nas they are remote from the eye, and less in proportion as they are\nnearer. The leaves which reflect the blue of the atmosphere always\npresent themselves to the eye edgewise.\n\nOF THE ILLUMINATED PART OF VERDURE AND OF MOUNTAINS.\n\nThe illuminated portion, at a great distance, will appear most\nnearly of its natural colour where the strongest light falls upon\nit.\n\n438.\n\nOF TREES THAT ARE LIGHTED BY THE SUN AND BY THE ATMOSPHERE.\n\nIn trees that are illuminated [both] by the sun and the atmosphere\nand that have leaves of a dark colour, one side will be illuminated\nby the atmosphere [only] and in consequence of this light will tend\nto blueness, while on the other side they will be illuminated by the\natmosphere and the sun; and the side which the eye sees illuminated\nby the sun will reflect light.\n\n439.\n\nOF DEPICTING A FOREST SCENE.\n\nThe trees and plants which are most thickly branched with slender\nbranches ought to have less dark shadow than those trees and plants\nwhich, having broader leaves, will cast more shadow.\n\n440.\n\nON PAINTING.\n\nIn the position of the eye which sees that portion of a tree\nilluminated which turns towards the light, one tree will never be\nseen to be illuminated equally with the other. To prove this, let\nthe eye be _c_ which sees the two trees _b d_ which are illuminated\nby the sun _a_; I say that this eye _c_ will not see the light in\nthe same proportion to the shade, in one tree as in the other.\nBecause, the tree which is nearest to the sun will display so much\nthe stronger shadow than the more distant one, in proportion as one\ntree is nearer to the rays of the sun that converge to the eye than\nthe other; &c.\n\nYou see that the eye _c_ sees nothing of the tree _d_ but shadow,\nwhile the same eye _c_ sees th\u00e8 tree _b_ half in light and half in\nshade.\n\nWhen a tree is seen from below, the eye sees the top of it as placed\nwithin the circle made by its boughs[23].\n\nRemember, O Painter! that the variety of depth of shade in any one\nparticular species of tree is in proportion to the rarity or density\nof their branches.\n\n[Footnote: The two lower sketches on the left of Pl XXVIII, No. 3,\nrefer to lines 21-23. The upper sketch has apparently been effaced\nby Leonardo himself.]\n\nThe distribution of light and shade with reference to the position\nof the spectator (441-443).\n\n441.\n\nThe shadows of trees placed in a landscape do not display themselves\nin the same position in the trees on the right hand and those on the\nleft; still more so if the sun is to the right or left. As is proved\nby the 4th which says: Opaque bodies placed between the light and\nthe eye display themselves entirely in shadow; and by the 5th: The\neye when placed between the opaque body and the light sees the\nopaque body entirely illuminated. And by the 6th: When the eye and\nthe opaque body are placed between darkness and light, it will be\nseen half in shadow and half in light.\n\n[Footnote: See the figure on the right hand side of Pl. XXVIII, No.\n3. The first five lines of the text are written below the diagram\nand above it are the last eight lines of the text, given as No.\n461.]\n\n442.\n\nOF THE HERBS OF THE FIELD.\n\nOf the plants which take a shadow from the plants which spring among\nthem, those which are on this side [in front] of the shadow have the\nstems lighted up on a background of shadow, and the plants on which\nthe shadows fall have their stems dark on a light background; that\nis on the background beyond the shadow.\n\nOF TREES WHICH ARE BETWEEN THE EYE AND THE LIGHT.\n\nOf the trees which are between the eye and the light the part in\nfront will be light; but this light will be broken by the\nramifications of transparent leaves--being seen from the under\nside--and lustrous leaves--being seen from the upper side; and the\nbackground below and behind will be dark green, being in shadow from\nthe front portion of the said tree. This occurs in trees placed\nabove the eye.\n\n443.\n\nFROM WHENCE TO DEPICT A LANDSCAPE\n\nLandscapes should be represented so that the trees may be half in\nlight and half in shadow; but it is better to do them when the sun\nis covered with clouds, for then the trees are lighted by the\ngeneral light of the sky, and the general darkness of the earth. And\nthen they are darkest in certain parts in proportion as those parts\nare nearest to the middle of the tree and to the earth.\n\nThe effects of morning light (444-448).\n\n444.\n\nOF TREES TO THE SOUTH.\n\nWhen the sun is in the east the trees to the South and to the North\nhave almost as much light as shadow. But a greater share of light in\nproportion as they lie to the West and a greater share of shadow in\nproportion as they lie to the East.\n\nOF MEADOWS.\n\nIf the sun is in the East the verdure of the meadows and of other\nsmall plants is of a most beautiful green from being transparent to\nthe sun; this does not occur in the meadows to the West, and in\nthose to the South and North the grass is of a moderately brilliant\ngreen.\n\n445.\n\nOF THE 4 POINTS OF THE COMPASS [IN LANDSCAPES].\n\nWhen the sun is in the East all the portions of plants lighted by it\nare of a most lively verdure, and this happens because the leaves\nlighted by the sun within the half of the horizon that is the\nEastern half, are transparent; and within the Western semicircle the\nverdure is of a dull hue and the moist air is turbid and of the\ncolour of grey ashes, not being transparent like that in the East,\nwhich is quite clear and all the more so in proportion as it is\nmoister.\n\nThe shadows of the trees to the East cover a large portion of them\nand are darker in proportion as the foliage of the trees is thicker.\n\n446.\n\nOF TREES IN THE EAST.\n\nWhen the sun is in the East the trees seen towards the East will\nhave the light which surrounds them all round their shadows,\nexcepting on the side towards the earth; unless the tree has been\npruned [below] in the past year. And the trees to the South and\nNorth will be half in shade and half in light, and more or less in\nshade or in light in proportion as they are more or less to the East\nor to the West.\n\nThe [position of] the eye above or below varies the shadows and\nlights in trees, inasmuch as the eye placed above sees the tree with\nthe little shadow, and the eye placed below with a great deal of\nshadow.\n\nThe colour of the green in plants varies as much as their species.\n\n447.\n\nOF THE SHADOWS IN TREES.\n\nThe sun being in the East [to the right], the trees to the West [or\nleft] of the eye will show in small relief and almost imperceptible\ngradations, because the atmosphere which lies between the eye and\nthose trees is very dense [Footnote 7: _per la 7a di questo_. This\npossibly referred to something written on the seventh page of this\nnote book marked _G_. Unfortunately it has been cut out and lost.],\nsee the 7th of this--and they have no shade; for though a shadow\nexists in every detail of the ramification, it results that the\nimages of the shade and light that reach the eye are confused and\nmingled together and cannot be perceived on account of their\nminuteness. And the principal lights are in the middle of the trees,\nand the shadows to wards the edges; and their separation is shown by\nthe shadows of the intervals between the trees; but when the forests\nare thick with trees the thin edges are but little seen.\n\n448.\n\nOF TREES TO THE EAST.\n\nWhen the sun is in the East the trees are darker towards the middle\nwhile their edges are light.\n\nThe effects of midday light.\n\n449.\n\nOBJECTS IN HIGH LIGHT SHOW BUT LITTLE, BUT BETWEEN LIGHT AND SHADOW\nTHEY STAND OUT WELL.\n\nTo represent a landscape choose that the sun shall be at noon and\nlook towards the West or East and then draw. And if you turn towards\nthe North, every object placed on that side will have no shadow,\nparticularly those which are nearest to the [direction of the]\nshadow of your head. And if you turn towards the South every object\non that side will be wholly in shadow. All the trees which are\ntowards the sun and have the atmosphere for their background are\ndark, and the other trees which lie against that darkness will be\nblack [very dark] in the middle and lighter towards the edges.\n\nThe appearance of trees in the distance (450. 451).\n\n450.\n\nOF THE SPACES [SHOWING THE SKY] IN TREES THEMSELVES.\n\nThe spaces between the parts in the mass of trees, and the spaces\nbetween the trees in the air, are, at great distances, invisible to\nthe eye; for, where it is an effort [even] to see the whole it is\nmost difficult to discern the parts.--But a confused mixture is the\nresult, partaking chiefly of the [hue] which predominates. The\nspaces between the leaves consist of particles of illuminated air\nwhich are very much smaller than the tree and are lost sight of\nsooner than the tree; but it does not therefore follow that they are\nnot there. Hence, necessarily, a compounded [effect] is produced of\nthe sky and of the shadows of the tree in shade, which both together\nstrike the eye which sees them.\n\nOF TREES WHICH CONCEAL THESE SPACES IN ONE ANOTHER.\n\nThat part of a tree will show the fewest spaces, behind which a\nlarge number of trees are standing between the tree and the air\n[sky]; thus in the tree _a_ the spaces are not concealed nor in _b_,\nas there is no tree behind. But in _c_ only half shows the spaces\nfilled up by the tree _d_, and part of the tree _d_ is filled up by\nthe tree _e_ and a little farther on all the spaces in the mass of\nthe trees are lost, and only that at the side remains.\n\n451.\n\nOF TREES.\n\nWhat outlines are seen in trees at a distance against the sky which\nserves as their background?\n\nThe outlines of the ramification of trees, where they lie against\nthe illuminated sky, display a form which more nearly approaches the\nspherical on proportion as they are remote, and the nearer they are\nthe less they appear in this spherical form; as in the first tree\n_a_ which, being near to the eye, displays the true form of its\nramification; but this shows less in _b_ and is altogether lost in\n_c_, where not merely the branches of the tree cannot be seen but\nthe whole tree is distinguished with difficulty. Every object in\nshadow, of whatever form it may be, at a great distance appears to\nbe spherical. And this occurs because, if it is a square body, at a\nvery short distance it loses its angles, and a little farther off it\nloses still more of its smaller sides which remain. And thus before\nthe whole is lost [to sight] the parts are lost, being smaller than\nthe whole; as a man, who in such a distant position loses his legs,\narms and head before [the mass of] his body, then the outlines of\nlength are lost before those of breadth, and where they have become\nequal it would be a square if the angles remained; but as they are\nlost it is round.\n\n[Footnote: The sketch No. 4, Pl. XXVIII, belongs to this passage.]\n\nThe cast shadow of trees (452. 453).\n\n452.\n\nThe image of the shadow of any object of uniform breadth can never\nbe [exactly] the same as that of the body which casts it.\n\n[Footnote: See Pl. XXVIII, No. 5.]\n\nLight and shade on groups of trees (453-457).\n\n453.\n\nAll trees seen against the sun are dark towards the middle and this\nshadow will be of the shape of the tree when apart from others.\n\nThe shadows cast by trees on which the sun shines are as dark as\nthose of the middle of the tree.\n\nThe shadow cast by a tree is never less than the mass of the tree\nbut becomes taller in proportion as the spot on which it falls,\nslopes towards the centre of the world.\n\nThe shadow will be densest in the middle of the tree when the tree\nhas the fewest branches.\n\n[Footnote: The three diagrams which accompany this text are placed,\nin the original, before lines 7-11. At the spots marked _B_ Leonardo\nwrote _Albero_ (tree). At _A_ is the word _Sole_ (sun), at _C Monte_\n(mountain) at _D piano_ (plain) and at _E cima_ (summit).]\n\nEvery branch participates of the central shadow of every other\nbranch and consequently [of that] of the whole tree.\n\nThe form of any shadow from a branch or tree is circumscribed by the\nlight which falls from the side whence the light comes; and this\nillumination gives the shape of the shadow, and this may be of the\ndistance of a mile from the side where the sun is.\n\nIf it happens that a cloud should anywhere overshadow some part of a\nhill the [shadow of the] trees there will change less than in the\nplains; for these trees on the hills have their branches thicker,\nbecause they grow less high each year than in the plains. Therefore\nas these branches are dark by nature and being so full of shade, the\nshadow of the clouds cannot darken them any more; but the open\nspaces between the trees, which have no strong shadow change very\nmuch in tone and particularly those which vary from green; that is\nploughed lands or fallen mountains or barren lands or rocks. Where\nthe trees are against the atmosphere they appear all the same\ncolour--if indeed they are not very close together or very thickly\ncovered with leaves like the fir and similar trees. When you see the\ntrees from the side from which the sun lights them, you will see\nthem almost all of the same tone, and the shadows in them will be\nhidden by the leaves in the light, which come between your eye and\nthose shadows.\n\nTREES AT A SHORT DISTANCE.\n\n[Footnote 29: The heading _alberi vicini_ (trees at a short\ndistance) is in the original manuscript written in the margin.] When\nthe trees are situated between the sun and the eye, beyond the\nshadow which spreads from their centre, the green of their leaves\nwill be seen transparent; but this transparency will be broken in\nmany places by the leaves and boughs in shadow which will come\nbetween you and them, or, in their upper portions, they will be\naccompanied by many lights reflected from the leaves.\n\n454.\n\nThe trees of the landscape stand out but little from each other;\nbecause their illuminated portions come against the illuminated\nportions of those beyond and differ little from them in light and\nshade.\n\n455.\n\nOf trees seen from below and against the light, one beyond the other\nand near together. The topmost part of the first will be in great\npart transparent and light, and will stand out against the dark\nportion of the second tree. And thus it will be with all in\nsuccession that are placed under the same conditions.\n\nLet _s_ be the light, and _r_ the eye, _c d n_ the first tree, _a b\nc_ the second. Then I say that _r_, the eye, will see the portion _c\nf_ in great part transparent and lighted by the light _s_ which\nfalls upon it from the opposite side, and it will see it, on a dark\nground _b c_ because that is the dark part and shadow of the tree _a\nb c_.\n\nBut if the eye is placed at _t_ it will see _o p_ dark on the light\nbackground _n g_.\n\nOf the transparent and shadowy parts of trees, that which is nearest\nto you is the darkest.\n\n456.\n\nThat part of a tree which has shadow for background, is all of one\ntone, and wherever the trees or branches are thickest they will be\ndarkest, because there are no little intervals of air. But where the\nboughs lie against a background of other boughs, the brighter parts\nare seen lightest and the leaves lustrous from the sunlight falling\non them.\n\n457.\n\nIn the composition of leafy trees be careful not to repeat too often\nthe same colour of one tree against the same colour of another\n[behind it]; but vary it with a lighter, or a darker, or a stronger\ngreen.\n\nOn the treatment of light for landscapes (458-464).\n\n458.\n\nThe landscape has a finer azure [tone] when, in fine weather the sun\nis at noon than at any other time of the day, because the air is\npurified of moisture; and looking at it under that aspect you will\nsee the trees of a beautiful green at the outside and the shadows\ndark towards the middle; and in the remoter distance the atmosphere\nwhich comes between you and them looks more beautiful when there is\nsomething dark beyond. And still the azure is most beautiful. The\nobjects seen from the side on which the sun shines will not show you\ntheir shadows. But, if you are lower than the sun, you can see what\nis not seen by the sun and that will be all in shade. The leaves of\nthe trees, which come between you and the sun are of two principal\ncolours which are a splendid lustre of green, and the reflection of\nthe atmosphere which lights up the objects which cannot be seen by\nthe sun, and the shaded portions which only face the earth, and the\ndarkest which are surrounded by something that is not dark. The\ntrees in the landscape which are between you and the sun are far\nmore beautiful than those you see when you are between the sun and\nthem; and this is so because those which face the sun show their\nleaves as transparent towards the ends of their branches, and those\nthat are not transparent--that is at the ends--reflect the light;\nand the shadows are dark because they are not concealed by any\nthing.\n\nThe trees, when you place yourself between them and the sun, will\nonly display to you their light and natural colour, which, in\nitself, is not very strong, and besides this some reflected lights\nwhich, being against a background which does not differ very much\nfrom themselves in tone, are not conspicuous; and if you are lower\ndown than they are situated, they may also show those portions on\nwhich the light of the sun does not fall and these will be dark.\n\nIn the Wind.\n\nBut, if you are on the side whence the wind blows, you will see the\ntrees look very much lighter than on the other sides, and this\nhappens because the wind turns up the under side of the leaves,\nwhich, in all trees, is much whiter than the upper sides; and, more\nespecially, will they be very light indeed if the wind blows from\nthe quarter where the sun is, and if you have your back turned to\nit.\n\n[Footnote: At _S_, in the original is the word _Sole_ (sun) and at\n_N parte di nuvolo_ (the side of the clouds).]\n\n459.\n\nWhen the sun is covered by clouds, objects are less conspicuous,\nbecause there is little difference between the light and shade of\nthe trees and of the buildings being illuminated by the brightness\nof the atmosphere which surrounds the objects in such a way that the\nshadows are few, and these few fade away so that their outline is\nlost in haze.\n\n460.\n\nOF TREES AND LIGHTS ON THEM.\n\nThe best method of practice in representing country scenes, or I\nshould say landscapes with their trees, is to choose them so that\nthe sun is covered with clouds so that the landscape receives an\nuniversal light and not the direct light of the sun, which makes the\nshadows sharp and too strongly different from the lights.\n\n461.\n\nOF PAINTING.\n\nIn landscapes which represent [a scene in] winter. The mountains\nshould not be shown blue, as we see in the mountains in the summer.\nAnd this is proved [Footnote 5. 6.: _Per la_ 4_a di questo_. It is\nimpossible to ascertain what this quotation refers to. _Questo_\ncertainly does not mean the MS. in hand, nor any other now known to\nus. The same remark applies to the phrase in line 15: _per la_ 2_a\ndi questo_.] in the 4th of this which says: Among mountains seen\nfrom a great distance those will look of the bluest colour which are\nin themselves the darkest; hence, when the trees are stripped of\ntheir leaves, they will show a bluer tinge which will be in itself\ndarker; therefore, when the trees have lost their leaves they will\nlook of a gray colour, while, with their leaves, they are green, and\nin proportion as the green is darker than the grey hue the green\nwill be of a bluer tinge than the gray. Also by the 2nd of this: The\nshadows of trees covered with leaves are darker than the shadows of\nthose trees which have lost their leaves in proportion as the trees\ncovered with leaves are denser than those without leaves--and thus\nmy meaning is proved.\n\nThe definition of the blue colour of the atmosphere explains why the\nlandscape is bluer in the summer than in the winter.\n\n462.\n\nOF PAINTING IN A LANDSCAPE.\n\nIf the slope of a hill comes between the eye and the horizon,\nsloping towards the eye, while the eye is opposite the middle of the\nheight of this slope, then that hill will increase in darkness\nthroughout its length. This is proved by the 7th of this which says\nthat a tree looks darkest when it is seen from below; the\nproposition is verified, since this hill will, on its upper half\nshow all its trees as much from the side which is lighted by the\nlight of the sky, as from that which is in shade from the darkness\nof the earth; whence it must result that these trees are of a medium\ndarkness. And from this [middle] spot towards the base of the hill,\nthese trees will be lighter by degrees by the converse of the 7th\nand by the said 7th: For trees so placed, the nearer they are to the\nsummit of the hill the darker they necessarily become. But this\ndarkness is not in proportion to the distance, by the 8th of this\nwhich says: That object shows darkest which is [seen] in the\nclearest atmosphere; and by the 10th: That shows darkest which\nstands out against a lighter background.\n\n[Footnote: The quotation in this passage again cannot be verified.]\n\n463.\n\nOF LANDSCAPES.\n\nThe colours of the shadows in mountains at a great distance take a\nmost lovely blue, much purer than their illuminated portions. And\nfrom this it follows that when the rock of a mountain is reddish the\nilluminated portions are violet (?) and the more they are lighted\nthe more they display their proper colour.\n\n464.\n\nA place is most luminous when it is most remote from mountains.\n\nOn the treatment of light for views of towns (465-469).\n\n465.\n\nOF LIGHT AND SHADOW IN A TOWN.\n\nWhen the sun is in the East and the eye is above the centre of a\ntown, the eye will see the Southern part of the town with its roofs\nhalf in shade and half in light, and the same towards the North; the\nEastern side will be all in shadow and the Western will be all in\nlight.\n\n466.\n\nOf the houses of a town, in which the divisions between the houses\nmay be distinguished by the light which fall on the mist at the\nbottom. If the eye is above the houses the light seen in the space\nthat is between one house and the next sinks by degrees into thicker\nmist; and yet, being less transparent, it appears whiter; and if the\nhouses are some higher than the others, since the true [colour] is\nalways more discernible through the thinner atmosphere, the houses\nwill look darker in proportion as they are higher up. Let _n o p q_\nrepresent the various density of the atmosphere thick with moisture,\n_a_ being the eye, the house _b c_ will look lightest at the bottom,\nbecause it is in a thicker atmosphere; the lines _c d f_ will appear\nequally light, for although _f_ is more distant than _c_, it is\nraised into a thinner atmosphere, if the houses _b e_ are of the\nsame height, because they cross a brightness which is varied by\nmist, but this is only because the line of the eye which starts from\nabove ends by piercing a lower and denser atmosphere at _d_ than at\n_b_. Thus the line a _f_ is lower at _f_ than at _c_; and the house\n_f_ will be seen darker at _e_ from the line _e k_ as far as _m_,\nthan the tops of the houses standing in front of it.\n\n467.\n\nOF TOWNS OR OTHER BUILDINGS SEEN IN THE EVENING OR THE MORNING\nTHROUGH THE MIST.\n\nOf buildings seen at a great distance in the evening or the morning,\nas in mist or dense atmosphere, only those portions are seen in\nbrightness which are lighted up by the sun which is near the\nhorizon; and those portions which are not lighted up by the sun\nremain almost of the same colour and medium tone as the mist.\n\nWHY OBJECTS WHICH ARE HIGH UP AND AT A DISTANCE ARE DARKER THAN THE\nLOWER ONES, EVEN IF THE MIST IS UNIFORMLY DENSE.\n\nOf objects standing in a mist or other dense atmosphere, whether\nfrom vapour or smoke or distance, those will be most visible which\nare the highest. And among objects of equal height that will be the\ndarkest [strongest] which has for background the deepest mist. Thus\nthe eye _h_ looking at _a b c_, towers of equal height, one with\nanother, sees _c_ the top of the first tower at _r_, at two degrees\nof depth in the mist; and sees the height of the middle tower _b_\nthrough one single degree of mist. Therefore the top of the tower\n_c_ appears stronger than the top of the tower _b_, &c.\n\n468.\n\nOF THE SMOKE OF A TOWN.\n\nSmoke is seen better and more distinctly on the Eastern side than on\nthe Western when the sun is in the East; and this arises from two\ncauses; the first is that the sun, with its rays, shines through the\nparticles of the smoke and lights them up and makes them visible.\nThe second is that the roofs of the houses seen in the East at this\ntime are in shadow, because their obliquity does not allow of their\nbeing illuminated by the sun. And the same thing occurs with dust;\nand both one and the other look the lighter in proportion as they\nare denser, and they are densest towards the middle.\n\n469.\n\nOF SMOKE AND DUST.\n\nIf the sun is in the East the smoke of cities will not be visible in\nthe West, because on that side it is not seen penetrated by the\nsolar rays, nor on a dark background; since the roofs of the houses\nturn the same side to the eye as they turn towards the sun, and on\nthis light background the smoke is not very visible.\n\nBut dust, under the same aspect, will look darker than smoke being\nof denser material than smoke which is moist.\n\nThe effect of wind on trees (470-473).\n\n470.\n\nOF REPRESENTING WIND.\n\nIn representing wind, besides the bending of the boughs and the\nreversing of their leaves towards the quarter whence the wind comes,\nyou should also represent them amid clouds of fine dust mingled with\nthe troubled air.\n\n471.\n\nDescribe landscapes with the wind, and the water, and the setting\nand rising of the sun.\n\nTHE WIND.\n\nAll the leaves which hung towards the earth by the bending of the\nshoots with their branches, are turned up side down by the gusts of\nwind, and here their perspective is reversed; for, if the tree is\nbetween you and the quarter of the wind, the leaves which are\ntowards you remain in their natural aspect, while those on the\nopposite side which ought to have their points in a contrary\ndirection have, by being turned over, their points turned towards\nyou.\n\n472.\n\nTrees struck by the force of the wind bend to the side towards which\nthe wind is blowing; and the wind being past they bend in the\ncontrary direction, that is in reverse motion.\n\n473.\n\nThat portion of a tree which is farthest from the force which\nstrikes it is the most injured by the blow because it bears most\nstrain; thus nature has foreseen this case by thickening them in\nthat part where they can be most hurt; and most in such trees as\ngrow to great heights, as pines and the like. [Footnote: Compare the\nsketch drawn with a pen and washed with Indian ink on Pl. XL, No. 1.\nIn the Vatican copy we find, under a section entitled '_del fumo_',\nthe following remark: _Era sotto di questo capitulo un rompimento di\nmontagna, per dentro delle quali roture scherzaua fiame di fuoco,\ndisegnate di penna et ombrate d'acquarella, da uedere cosa mirabile\net uiua (Ed. MANZI, p. 235. Ed. LUDWIG, Vol. I, 460). This appears\nto refer to the left hand portion of the drawing here given from the\nWindsor collection, and from this it must be inferred, that the leaf\nas it now exists in the library of the Queen of England, was already\nseparated from the original MS. at the time when the Vatican copy\nwas made.]\n\nLight and shade on clouds (474-477).\n\n474.\n\nDescribe how the clouds are formed and how they dissolve, and what\ncause raises vapour.\n\n475.\n\nThe shadows in clouds are lighter in proportion as they are nearer\nto the horizon.\n\n[Footnote: The drawing belonging to this was in black chalk and is\ntotally effaced.]\n\n476.\n\nWhen clouds come between the sun and the eye all the upper edges of\ntheir round forms are light, and towards the middle they are dark,\nand this happens because towards the top these edges have the sun\nabove them while you are below them; and the same thing happens with\nthe position of the branches of trees; and again the clouds, like\nthe trees, being somewhat transparent, are lighted up in part, and\nat the edges they show thinner.\n\nBut, when the eye is between the cloud and the sun, the cloud has\nthe contrary effect to the former, for the edges of its mass are\ndark and it is light towards the middle; and this happens because\nyou see the same side as faces the sun, and because the edges have\nsome transparency and reveal to the eye that portion which is hidden\nbeyond them, and which, as it does not catch the sunlight like that\nportion turned towards it, is necessarily somewhat darker. Again, it\nmay be that you see the details of these rounded masses from the\nlower side, while the sun shines on the upper side and as they are\nnot so situated as to reflect the light of the sun, as in the first\ninstance they remain dark.\n\nThe black clouds which are often seen higher up than those which are\nilluminated by the sun are shaded by other clouds, lying between\nthem and the sun.\n\nAgain, the rounded forms of the clouds that face the sun, show their\nedges dark because they lie against the light background; and to see\nthat this is true, you may look at the top of any cloud that is\nwholly light because it lies against the blue of the atmosphere,\nwhich is darker than the cloud.\n\n[Footnote: A drawing in red chalk from the Windsor collection (see\nPl. XXIX), representing a landscape with storm-clouds, may serve to\nillustrate this section as well as the following one.]\n\n477.\n\nOF CLOUDS, SMOKE AND DUST AND THE FLAMES OF A FURNACE OR OF A\nBURNING KILN.\n\nThe clouds do not show their rounded forms excepting on the sides\nwhich face the sun; on the others the roundness is imperceptible\nbecause they are in the shade. [Footnote: The text of this chapter\nis given in facsimile on Pls. XXXVI and XXXVII. The two halves of\nthe leaf form but one in the original. On the margin close to lines\n4 and 5 is the note: _rossore d'aria inverso l'orizonte_--(of the\nredness of the atmosphere near the horizon). The sketches on the\nlower portion of the page will be spoken of in No. 668.]\n\nIf the sun is in the East and the clouds in the West, the eye placed\nbetween the sun and the clouds sees the edges of the rounded forms\ncomposing these clouds as dark, and the portions which are\nsurrounded by this dark [edge] are light. And this occurs because\nthe edges of the rounded forms of these clouds are turned towards\nthe upper or lateral sky, which is reflected in them.\n\nBoth the cloud and the tree display no roundness at all on their\nshaded side.\n\nOn images reflected in water.\n\n478.\n\nPainters often deceive themselves, by representing water in which\nthey make the water reflect the objects seen by the man. But the\nwater reflects the object from one side and the man sees it from the\nother; and it often happens that the painter sees an object from\nbelow, and thus one and the same object is seen from hind part\nbefore and upside down, because the water shows the image of the\nobject in one way, and the eye sees it in another.\n\nOf rainbows and rain (479. 480).\n\n479.\n\nThe colours in the middle of the rainbow mingle together.\n\nThe bow in itself is not in the rain nor in the eye that sees it;\nthough it is generated by the rain, the sun, and the eye. The\nrainbow is always seen by the eye that is between the rain and the\nbody of the sun; hence if the sun is in the East and the rain is in\nthe West it will appear on the rain in the West.\n\n480.\n\nWhen the air is condensed into rain it would produce a vacuum if the\nrest of the air did not prevent this by filling its place, as it\ndoes with a violent rush; and this is the wind which rises in the\nsummer time, accompanied by heavy rain.\n\nOf flower seeds.\n\n481.\n\nAll the flowers which turn towards the sun perfect their seeds; but\nnot the others; that is to say those which get only the reflection\nof the sun.\n\nIX.\n\n_The Practice of Painting._\n\n_It is hardly necessary to offer any excuses for the division\ncarried out in the arrangement of the text into practical\nsuggestions and theoretical enquiries. It was evidently intended by\nLeonardo himself as we conclude from incidental remarks in the MSS.\n(for instance No_ 110_). The fact that this arrangement was never\ncarried out either in the old MS. copies or in any edition since, is\neasily accounted for by the general disorder which results from the\nprovisional distribution of the various chapters in the old copies.\nWe have every reason to believe that the earliest copyists, in\ndistributing the materials collected by them, did not in the least\nconsider the order in which the original MS.lay before them._\n\n_It is evident that almost all the chapters which refer to the\ncalling and life of the painter--and which are here brought together\nin the first section (Nos._ 482-508_)--may be referred to two\ndistinct periods in Leonardo's life; most of them can be dated as\nbelonging to the year_ 1492 _or to_ 1515. _At about this later time\nLeonardo may have formed the project of completing his Libro della\nPittura, after an interval of some years, as it would seem, during\nwhich his interest in the subject had fallen somewhat into the\nbackground._\n\n_In the second section, which treats first of the artist's studio,\nthe construction of a suitable window forms the object of careful\ninvestigations; the special importance attached to this by Leonardo\nis sufficiently obvious. His theory of the incidence of light which\nwas fully discussed in a former part of this work, was to him by no\nmeans of mere abstract value, but, being deduced, as he says, from\nexperience (or experiment) was required to prove its utility in\npractice. Connected with this we find suggestions for the choice of\na light with practical hints as to sketching a picture and some\nother precepts of a practical character which must come under\nconsideration in the course of completing the painting. In all this\nI have followed the same principle of arrangement in the text as was\ncarried out in the Theory of Painting, thus the suggestions for the\nPerspective of a picture, (Nos._ 536-569_), are followed by the\ntheory of light and shade for the practical method of optics (Nos._\n548--566_) and this by the practical precepts or the treatment of\naerial perspective (_567--570_)._\n\n_In the passage on Portrait and Figure Painting the principles of\npainting as applied to a bust and head are separated and placed\nfirst, since the advice to figure painters must have some connection\nwith the principles of the treatment of composition by which they\nare followed._\n\n_But this arrangement of the text made it seem advisable not to pick\nout the practical precepts as to the representation of trees and\nlandscape from the close connection in which they were originally\nplaced--unlike the rest of the practical precepts--with the theory\nof this branch of the subject. They must therefore be sought under\nthe section entitled Botany for Painters._\n\n_As a supplement to the_ Libro di Pittura _I have here added those\ntexts which treat of the Painter's materials,--as chalk, drawing\npaper, colours and their preparation, of the management of oils and\nvarnishes; in the appendix are some notes on chemical substances.\nPossibly some of these, if not all, may have stood in connection\nwith the preparation of colours. It is in the very nature of things\nthat Leonardo's incidental indications as to colours and the like\nshould be now-a-days extremely obscure and could only be explained\nby professional experts--by them even in but few instances. It might\ntherefore have seemed advisable to reproduce exactly the original\ntext without offering any translation. The rendering here given is\nmerely an attempt to suggest what Leonardo's meaning may have been._\n\n_LOMAZZO tells us in his_ Trattato dell'arte della Pittura, Scultura\ned Architettura (Milano 1584, libro II, Cap. XIV): \"Va discorrendo\ned argomentando Leonardo Vinci in un suo libro letto da me (?)\nquesti anni passati, ch'egli scrisse di mano stanca ai prieghi di\nLUDOVICO SFORZA duca di Milano, in determinazione di questa\nquestione, se e piu nobile la pittura o la scultura; dicendo che\nquanto piu un'arte porta seco fatica di corpo, e sudore, tanto piu e\nvile, e men pregiata\". _But the existence of any book specially\nwritten for Lodovico il Moro on the superiority of Painting over\nsculpture is perhaps mythical. The various passages in praise of\nPainting as compared not merely with Sculpture but with Poetry, are\nscattered among MSS. of very different dates._\n\n_Besides, the way, in which the subject is discussed appears not to\nsupport the supposition, that these texts were prepared at a special\nrequest of the Duke._\n\nI.\n\nMORAL PRECEPTS FOR THE STUDENT OF PAINTING.\n\nHow to ascertain the dispositions for an artistic career.\n\n482.\n\nA WARNING CONCERNING YOUTHS WISHING TO BE PAINTERS.\n\nMany are they who have a taste and love for drawing, but no talent;\nand this will be discernible in boys who are not diligent and never\nfinish their drawings with shading.\n\nThe course of instruction for an artist (483-485).\n\n483.\n\nThe youth should first learn perspective, then the proportions of\nobjects. Then he may copy from some good master, to accustom himself\nto fine forms. Then from nature, to confirm by practice the rules he\nhas learnt. Then see for a time the works of various masters. Then\nget the habit of putting his art into practice and work.\n\n[Footnote: The Vatican copy and numerous abridgements all place this\nchapter at the beginning of the _Trattato_, and in consequence\nDUFRESNE and all subsequent editors have done the same. In the\nVatican copy however all the general considerations on the relation\nof painting to the other arts are placed first, as introductory.]\n\n484.\n\nOF THE ORDER OF LEARNING TO DRAW.\n\nFirst draw from drawings by good masters done from works of art and\nfrom nature, and not from memory; then from plastic work, with the\nguidance of the drawing done from it; and then from good natural\nmodels and this you must put into practice.\n\n485.\n\nPRECEPTS FOR DRAWING.\n\nThe artist ought first to exercise his hand by copying drawings from\nthe hand of a good master. And having acquired that practice, under\nthe criticism of his master, he should next practise drawing objects\nin relief of a good style, following the rules which will presently\nbe given.\n\nThe study of the antique (486. 487).\n\n486.\n\nOF DRAWING.\n\nWhich is best, to draw from nature or from the antique? and which is\nmore difficult to do outlines or light and shade?\n\n487.\n\nIt is better to imitate [copy] the antique than modern work.\n\n[Footnote 486, 487: These are the only two passages in which\nLeonardo alludes to the importance of antique art in the training of\nan artist. The question asked in No. 486 remains unanswered by him\nand it seems to me very doubtful whether the opinion stated in No.\n487 is to be regarded as a reply to it. This opinion stands in the\nMS. in a connection--as will be explained later on--which seems to\nrequire us to limit its application to a single special case. At any\nrate we may suspect that when Leonardo put the question, he felt\nsome hesitation as to the answer. Among his very numerous drawings I\nhave not been able to find a single study from the antique, though a\ndrawing in black chalk, at Windsor, of a man on horseback (PI.\nLXXIII) may perhaps be a reminiscence of the statue of Marcus\nAurelius at Rome. It seems to me that the drapery in a pen and ink\ndrawing of a bust, also at Windsor, has been borrowed from an\nantique model (Pl. XXX). G. G. Rossi has, I believe, correctly\ninterpreted Leonardo's feeling towards the antique in the following\nnote on this passage in manzi's edition, p. 501: \"Sappiamo dalla\nstoria, che i valorosi artisti Toscani dell'et\u00e0 dell'oro dell'arte\nstudiarono sugli antichi marmi raccolti dal Magnifico LORENZO DE'\nMEDICI. Pare che il Vinci a tali monumenti non si accostasse. Quest'\nuomo sempre riconosce per maestra la natura, e questo principio lo\nstringeva alla sola imitazione d\u00ec essa\"--Compare No. 10, 26--28\nfootnote.]\n\nThe necessity of anatomical knowledge (488. 489).\n\n488.\n\nOF PAINTING.\n\nIt is indispensable to a Painter who would be thoroughly familiar\nwith the limbs in all the positions and actions of which they are\ncapable, in the nude, to know the anatomy of the sinews, bones,\nmuscles and tendons so that, in their various movements and\nexertions, he may know which nerve or muscle is the cause of each\nmovement and show those only as prominent and thickened, and not the\nothers all over [the limb], as many do who, to seem great\ndraughtsmen, draw their nude figures looking like wood, devoid of\ngrace; so that you would think you were looking at a sack of walnuts\nrather than the human form, or a bundle of radishes rather than the\nmuscles of figures.\n\n489.\n\nHOW IT IS NECESSARY TO A PAINTER THAT HE SHOULD KNOW THE INTRINSIC\nFORMS [STRUCTURE] OF MAN.\n\nThe painter who is familiar with the nature of the sinews, muscles,\nand tendons, will know very well, in giving movement to a limb, how\nmany and which sinews cause it; and which muscle, by swelling,\ncauses the contraction of that sinew; and which sinews, expanded\ninto the thinnest cartilage, surround and support the said muscle.\nThus he will variously and constantly demonstrate the different\nmuscles by means of the various attitudes of his figures, and will\nnot do, as many who, in a variety of movements, still display the\nvery same things [modelling] in the arms, back, breast and legs. And\nthese things are not to be regarded as minor faults.\n\nHow to acquire practice.\n\n490.\n\nOF STUDY AND THE ORDER OF STUDY.\n\nI say that first you ought to learn the limbs and their mechanism,\nand having this knowledge, their actions should come next, according\nto the circumstances in which they occur in man. And thirdly to\ncompose subjects, the studies for which should be taken from natural\nactions and made from time to time, as circumstances allow; and pay\nattention to them in the streets and _piazze_ and fields, and note\nthem down with a brief indication of the forms; [Footnote 5: Lines\n5-7 explained by the lower portion of the sketch No. 1 on Pl. XXXI.]\nthus for a head make an o, and for an arm a straight or a bent line,\nand the same for the legs and the body, [Footnote 7: Lines 5-7\nexplained by the lower portion of the sketch No. 1 on Pl. XXXI.] and\nwhen you return home work out these notes in a complete form. The\nAdversary says that to acquire practice and do a great deal of work\nit is better that the first period of study should be employed in\ndrawing various compositions done on paper or on walls by divers\nmasters, and that in this way practice is rapidly gained, and good\nmethods; to which I reply that the method will be good, if it is\nbased on works of good composition and by skilled masters. But since\nsuch masters are so rare that there are but few of them to be found,\nit is a surer way to go to natural objects, than to those which are\nimitated from nature with great deterioration, and so form bad\nmethods; for he who can go to the fountain does not go to the\nwater-jar.\n\n[Footnote: This passage has been published by Dr. M. JORDAN, _Das\nMalerbuck des L. da Vinci_, p. 89; his reading however varies\nslightly from mine.]\n\nIndustry and thoroughness the first conditions (491-493.)\n\n491.\n\nWHAT RULES SHOULD BE GIVEN TO BOYS LEARNING TO PAINT.\n\nWe know for certain that sight is one of the most rapid actions we\ncan perform. In an instant we see an infinite number of forms, still\nwe only take in thoroughly one object at a time. Supposing that you,\nReader, were to glance rapidly at the whole of this written page,\nyou would instantly perceive that it was covered with various\nletters; but you could not, in the time, recognise what the letters\nwere, nor what they were meant to tell. Hence you would need to see\nthem word by word, line by line to be able to understand the\nletters. Again, if you wish to go to the top of a building you must\ngo up step by step; otherwise it will be impossible that you should\nreach the top. Thus I say to you, whom nature prompts to pursue this\nart, if you wish to have a sound knowledge of the forms of objects\nbegin with the details of them, and do not go on to the second\n[step] till you have the first well fixed in memory and in practice.\nAnd if you do otherwise you will throw away your time, or certainly\ngreatly prolong your studies. And remember to acquire diligence\nrather than rapidity.\n\n492.\n\nHOW THAT DILIGENCE [ACCURACY] SHOULD FIRST BE LEARNT RATHER THAN\nRAPID EXECUTION.\n\nIf you, who draw, desire to study well and to good purpose, always\ngo slowly to work in your drawing; and discriminate in. the lights,\nwhich have the highest degree of brightness, and to what extent and\nlikewise in the shadows, which are those that are darker than the\nothers and in what way they intermingle; then their masses and the\nrelative proportions of one to the other. And note in their\noutlines, which way they tend; and which part of the lines is curved\nto one side or the other, and where they are more or less\nconspicuous and consequently broad or fine; and finally, that your\nlight and shade blend without strokes and borders [but] looking like\nsmoke. And when you have thus schooled your hand and your judgment\nby such diligence, you will acquire rapidity before you are aware.\n\nThe artist's private life and choice of company (493-494).\n\n493.\n\nOF THE LIFE OF THE PAINTER IN THE COUNTRY.\n\nA painter needs such mathematics as belong to painting. And the\nabsence of all companions who are alienated from his studies; his\nbrain must be easily impressed by the variety of objects, which\nsuccessively come before him, and also free from other cares\n[Footnote 6: Leonardo here seems to be speaking of his own method of\nwork as displayed in his MSS. and this passage explains, at least in\npart, the peculiarities in their arrangement.]. And if, when\nconsidering and defining one subject, a second subject\nintervenes--as happens when an object occupies the mind, then he\nmust decide which of these cases is the more difficult to work out,\nand follow that up until it becomes quite clear, and then work out\nthe explanation of the other [Footnote 11: Leonardo here seems to be\nspeaking of his own method of work as displayed in his MSS. and this\npassage explains, at least in part, the peculiarities in their\narrangement.]. And above all he must keep his mind as clear as the\nsurface of a mirror, which assumes colours as various as those of\nthe different objects. And his companions should be like him as to\ntheir studies, and if such cannot be found he should keep his\nspeculations to himself alone, so that at last he will find no more\nuseful company [than his own].\n\n[Footnote: In the title line Leonardo had originally written _del\npictore filosofo_ (the philosophical painter), but he himself struck\nout_filosofo_. Compare in No. 363 _pictora notomista_ (anatomical\npainter). The original text is partly reproduced on Pl. CI.]\n\n494.\n\nOF THE LIFE OF THE PAINTER IN HIS STUDIO.\n\nTo the end that well-being of the body may not injure that of the\nmind, the painter or draughtsman must remain solitary, and\nparticularly when intent on those studies and reflections which will\nconstantly rise up before his eye, giving materials to be well\nstored in the memory. While you are alone you are entirely your own\n[master] and if you have one companion you are but half your own,\nand the less so in proportion to the indiscretion of his behaviour.\nAnd if you have many companions you will fall deeper into the same\ntrouble. If you should say: \"I will go my own way and withdraw\napart, the better to study the forms of natural objects\", I tell\nyou, you will not be able to help often listening to their chatter.\nAnd so, since one cannot serve two masters, you will badly fill the\npart of a companion, and carry out your studies of art even worse.\nAnd if you say: \"I will withdraw so far that their words cannot\nreach me and they cannot disturb me\", I can tell you that you will\nbe thought mad. But, you see, you will at any rate be alone. And if\nyou must have companions ship find it in your studio. This may\nassist you to have the advantages which arise from various\nspeculations. All other company may be highly mischievous.\n\nThe distribution of time for studying (495-497).\n\n495.\n\nOF WHETHER IT IS BETTER TO DRAW WITH COMPANIONS OR NOT.\n\nI say and insist that drawing in company is much better than alone,\nfor many reasons. The first is that you would be ashamed to be seen\nbehindhand among the students, and such shame will lead you to\ncareful study. Secondly, a wholesome emulation will stimulate you to\nbe among those who are more praised than yourself, and this praise\nof others will spur you on. Another is that you can learn from the\ndrawings of others who do better than yourself; and if you are\nbetter than they, you can profit by your contempt for their defects,\nwhile the praise of others will incite you to farther merits.\n\n[Footnote: The contradiction by this passage of the foregoing\nchapter is only apparent. It is quite clear, from the nature of the\nreasoning which is here used to prove that it is more improving to\nwork with others than to work alone, that the studies of pupils only\nare under consideration here.]\n\n496.\n\nOF STUDYING, IN THE DARK, WHEN YOU WAKE, OR IN BED BEFORE YOU GO TO\nSLEEP.\n\nI myself have proved it to be of no small use, when in bed in the\ndark, to recall in fancy the external details of forms previously\nstudied, or other noteworthy things conceived by subtle speculation;\nand this is certainly an admirable exercise, and useful for\nimpressing things on the memory.\n\n497.\n\nOF THE TIME FOR STUDYING SELECTION OF SUBJECTS.\n\nWinter evenings ought to be employed by young students in looking\nover the things prepared during the summer; that is, all the\ndrawings from the nude done in the summer should be brought together\nand a choice made of the best [studies of] limbs and bodies among\nthem, to apply in practice and commit to memory.\n\nOF POSITIONS.\n\nAfter this in the following summer you should select some one who is\nwell grown and who has not been brought up in doublets, and so may\nnot be of stiff carriage, and make him go through a number of agile\nand graceful actions; and if his muscles do not show plainly within\nthe outlines of his limbs that does not matter at all. It is enough\nthat you can see good attitudes and you can correct [the drawing of]\nthe limbs by those you studied in the winter.\n\n[Footnote: An injunction to study in the evening occurs also in No.\n524.]\n\nOn the productive power of minor artists (498-501).\n\n498.\n\nHe is a poor disciple who does not excel his master.\n\n499.\n\nNor is the painter praiseworthy who does but one thing well, as the\nnude figure, heads, draperies, animals, landscapes or other such\ndetails, irrespective of other work; for there can be no mind so\ninept, that after devoting itself to one single thing and doing it\nconstantly, it should fail to do it well.\n\n[Footnote: In MANZI'S edition (p. 502) the painter G. G. Bossi\nindignantly remarks on this passage. \"_Parla il Vince in questo\nluogo come se tutti gli artisti avessero quella sublimita d'ingegno\ncapace di abbracciare tutte le cose, di cui era egli dotato\"_ And he\nthen mentions the case of CLAUDE LORRAIN. But he overlooks the fact\nthat in Leonardo's time landscape painting made no pretensions to\nindependence but was reckoned among the details (_particulari_,\nlines 3, 4).]\n\n500.\n\nTHAT A PAINTER IS NOT ADMIRABLE UNLESS HE IS UNIVERSAL.\n\nSome may distinctly assert that those persons are under a delusion\nwho call that painter a good master who can do nothing well but a\nhead or a figure. Certainly this is no great achievement; after\nstudying one single thing for a life-time who would not have\nattained some perfection in it? But, since we know that painting\nembraces and includes in itself every object produced by nature or\nresulting from the fortuitous actions of men, in short, all that the\neye can see, he seems to me but a poor master who can only do a\nfigure well. For do you not perceive how many and various actions\nare performed by men only; how many different animals there are, as\nwell as trees, plants, flowers, with many mountainous regions and\nplains, springs and rivers, cities with public and private\nbuildings, machines, too, fit for the purposes of men, divers\ncostumes, decorations and arts? And all these things ought to be\nregarded as of equal importance and value, by the man who can be\ntermed a good painter.\n\n501.\n\nOF THE MISERABLE PRETENCES MADE BY THOSE WHO FALSELY AND UNWORTHILY\nACQUIRE THE NAME OF PAINTERS.\n\nNow there is a certain race of painters who, having studied but\nlittle, must need take as their standard of beauty mere gold and\nazure, and these, with supreme conceit, declare that they will not\ngive good work for miserable payment, and that they could do as well\nas any other if they were well paid. But, ye foolish folks! cannot\nsuch artists keep some good work, and then say: this is a costly\nwork and this more moderate and this is average work and show that\nthey can work at all prices?\n\nA caution against one-sided study.\n\n502.\n\nHOW, IN IMPORTANT WORKS, A MAN SHOULD NOT TRUST ENTIRELY TO HIS\nMEMORY WITHOUT CONDESCENDING TO DRAW FROM NATURE.\n\nAny master who should venture to boast that he could remember all\nthe forms and effects of nature would certainly appear to me to be\ngraced with extreme ignorance, inasmuch as these effects are\ninfinite and our memory is not extensive enough to retain them.\nHence, O! painter, beware lest the lust of gain should supplant in\nyou the dignity of art; for the acquisition of glory is a much\ngreater thing than the glory of riches. Hence, for these and other\nreasons which might be given, first strive in drawing to represent\nyour intention to the eye by expressive forms, and the idea\noriginally formed in your imagination; then go on taking out or\nputting in, until you have satisfied yourself. Then have living men,\ndraped or nude, as you may have purposed in your work, and take care\nthat in dimensions and size, as determined by perspective, nothing\nis left in the work which is not in harmony with reason and the\neffects in nature. And this will be the way to win honour in your\nart.\n\nHow to acquire universality (503-506).\n\n503.\n\nOF VARIETY IN THE FIGURES.\n\nThe painter should aim at universality, because there is a great\nwant of self-respect in doing one thing well and another badly, as\nmany do who study only the [rules of] measure and proportion in the\nnude figure and do not seek after variety; for a man may be well\nproportioned, or he may be fat and short, or tall and thin, or\nmedium. And a painter who takes no account of these varieties always\nmakes his figures on one pattern so that they might all be taken for\nbrothers; and this is a defect that demands stern reprehension.\n\n504.\n\nHOW SOMETHING MAY BE LEARNT EVERYWHERE.\n\nNature has beneficently provided that throughout the world you may\nfind something to imitate.\n\n505.\n\nOF THE MEANS OF ACQUIRING UNIVERSALITY.\n\nIt is an easy matter to men to acquire universality, for all\nterrestrial animals resemble each other as to their limbs, that is\nin their muscles, sinews and bones; and they do not vary excepting\nin length or in thickness, as will be shown under Anatomy. But then\nthere are aquatic animals which are of great variety; I will not try\nto convince the painter that there is any rule for them for they are\nof infinite variety, and so is the insect tribe.\n\n506.\n\nPAINTING.\n\nThe mind of the painter must resemble a mirror, which always takes\nthe colour of the object it reflects and is completely occupied by\nthe images of as many objects as are in front of it. Therefore you\nmust know, Oh Painter! that you cannot be a good one if you are not\nthe universal master of representing by your art every kind of form\nproduced by nature. And this you will not know how to do if you do\nnot see them, and retain them in your mind. Hence as you go through\nthe fields, turn your attention to various objects, and, in turn\nlook now at this thing and now at that, collecting a store of divers\nfacts selected and chosen from those of less value. But do not do\nlike some painters who, when they are wearied with exercising their\nfancy dismiss their work from their thoughts and take exercise in\nwalking for relaxation, but still keep fatigue in their mind which,\nthough they see various objects [around them], does not apprehend\nthem; but, even when they meet friends or relations and are saluted\nby them, although they see and hear them, take no more cognisance of\nthem than if they had met so much empty air.\n\nUseful games and exercises (507. 508).\n\n507.\n\nOF GAMES TO BE PLAYED BY THOSE WHO DRAW.\n\nWhen, Oh draughtsmen, you desire to find relaxation in games you\nshould always practise such things as may be of use in your\nprofession, by giving your eye good practice in judging accurately\nof the breadth and length of objects. Thus, to accustom your mind to\nsuch things, let one of you draw a straight line at random on a\nwall, and each of you, taking a blade of grass or of straw in his\nhand, try to cut it to the length that the line drawn appears to him\nto be, standing at a distance of 10 braccia; then each one may go up\nto the line to measure the length he has judged it to be. And he who\nhas come nearest with his measure to the length of the pattern is\nthe best man, and the winner, and shall receive the prize you have\nsettled beforehand. Again you should take forshortened measures:\nthat is take a spear, or any other cane or reed, and fix on a point\nat a certain distance; and let each one estimate how many times he\njudges that its length will go into that distance. Again, who will\ndraw best a line one braccio long, which shall be tested by a\nthread. And such games give occasion to good practice for the eye,\nwhich is of the first importance in painting.\n\n508.\n\nA WAY OF DEVELOPING AND AROUSING THE MIND TO VARIOUS INVENTIONS.\n\nI cannot forbear to mention among these precepts a new device for\nstudy which, although it may seem but trivial and almost ludicrous,\nis nevertheless extremely useful in arousing the mind to various\ninventions. And this is, when you look at a wall spotted with\nstains, or with a mixture of stones, if you have to devise some\nscene, you may discover a resemblance to various landscapes,\nbeautified with mountains, rivers, rocks, trees, plains, wide\nvalleys and hills in varied arrangement; or again you may see\nbattles and figures in action; or strange faces and costumes, and an\nendless variety of objects, which you could reduce to complete and\nwell drawn forms. And these appear on such walls confusedly, like\nthe sound of bells in whose jangle you may find any name or word you\nchoose to imagine.\n\nII.\n\nTHE ARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF\nPERSPECTIVE.--ON JUDGING OF A PICTURE.\n\nOn the size of the studio.\n\n509.\n\nSmall rooms or dwellings discipline the mind, large ones weaken it.\n\nOn the construction of windows (510-512).\n\n510.\n\nThe larger the wall the less the light will be.\n\n511.\n\nThe different kinds of light afforded in cellars by various forms of\nwindows. The least useful and the coldest is the window at _a_. The\nmost useful, the lightest and warmest and most open to the sky is\nthe window at _b_. The window at _c_ is of medium utility.\n\n[Footnote: From a reference to the notes on the right light for\npainting it becomes evident that the observations made on\ncellar-windows have a direct bearing on the construction of the\nstudio-window. In the diagram _b_ as well as in that under No. 510\nthe window-opening is reduced to a minimum, but only, it would seem,\nin order to emphasize the advantage of walls constructed on the plan\nthere shown.]\n\n512.\n\nOF THE PAINTER'S WINDOW AND ITS ADVANTAGE.\n\nThe painter who works from nature should have a window, which he can\nraise and lower. The reason is that sometimes you will want to\nfinish a thing you are drawing, close to the light.\n\nLet _a b c d_ be the chest on which the work may be raised or\nlowered, so that the work moves up and down and not the painter. And\nevery evening you can let down the work and shut it up above so that\nin the evening it may be in the fashion of a chest which, when shut\nup, may serve the purpose of a bench.\n\n[Footnote: See Pl. XXXI, No. 2. In this plate the lines have\nunfortunately lost their sharpness, for the accidental loss of the\nnegative has necessitated a reproduction from a positive. But having\nformerly published this sketch by another process, in VON LUTZOW'S\n_Zeitschrift fur bildende Kunst_ (Vol. XVII, pg. 13) I have\nreproduced it here in the text. The sharpness of the outline in the\noriginal sketch is here preserved but it gives it from the reversed\nside.]\n\nOn the best light for painting (513-520).\n\n513.\n\nWhich light is best for drawing from nature; whether high or low, or\nlarge or small, or strong and broad, or strong and small, or broad\nand weak or small and weak?\n\n[Footnote: The question here put is unanswered in the original MS.]\n\n514.\n\nOF THE QUALITY OF THE LIGHT.\n\nA broad light high up and not too strong will render the details of\nobjects very agreeable.\n\n515.\n\nTHAT THE LIGHT FOR DRAWING FROM NATURE SHOULD BE HIGH UP.\n\nThe light for drawing from nature should come from the North in\norder that it may not vary. And if you have it from the South, keep\nthe window screened with cloth, so that with the sun shining the\nwhole day the light may not vary. The height of the light should be\nso arranged as that every object shall cast a shadow on the ground\nof the same length as itself.\n\n516.\n\nTHE KIND OF LIGHT REQUISITE FOR PAINTING LIGHT AND SHADE.\n\nAn object will display the greatest difference of light and shade\nwhen it is seen in the strongest light, as by sunlight, or, at\nnight, by the light of a fire. But this should not be much used in\npainting because the works remain crude and ungraceful.\n\nAn object seen in a moderate light displays little difference in the\nlight and shade; and this is the case towards evening or when the\nday is cloudy, and works then painted are tender and every kind of\nface becomes graceful. Thus, in every thing extremes are to be\navoided: Too much light gives crudeness; too little prevents our\nseeing. The medium is best.\n\nOF SMALL LIGHTS.\n\nAgain, lights cast from a small window give strong differences of\nlight and shade, all the more if the room lighted by it be large,\nand this is not good for painting.\n\n517.\n\nPAINTING.\n\nThe luminous air which enters by passing through orifices in walls\ninto dark rooms will render the place less dark in proportion as the\nopening cuts into the walls which surround and cover in the\npavement.\n\n518.\n\nOF THE QUALITY OF LIGHT.\n\nIn proportion to the number of times that _a b_ goes into _c d_ will\nit be more luminous than _c d_. And similarly, in proportion as the\npoint _e_ goes into _c d_ will it be more luminous than _c d;_ and\nthis light is useful for carvers of delicate work. [Footnote 5: For\nthe same reason a window thus constructed would be convenient for an\nilluminator or a miniature painter.]\n\n[Footnote: M. RAVAISSON in his edition of the Paris MS. A remarks on\nthis passage: _\"La figure porte les lettres_ f _et_ g, _auxquelles\nrien ne renvoie dans l'explication; par consequent, cette\nexplication est incomplete. La figure semblerait, d'ailleurs, se\nrapporter a l'effet de la reflexion par un miroir concave.\"_ So far\nas I can see the text is not imperfect, nor is the sense obscure. It\nis hardly necessary to observe that _c d_ here indicate the wall of\nthe room opposite to the window _e_ and the semicircle described by\n_f g_ stands for the arch of the sky; this occurs in various\ndiagrams, for example under 511. A similar semicircle, Pl III, No. 2\n(and compare No. 149) is expressly called '_orizonte_' in writing.]\n\n519.\n\nThat the light should fall upon a picture from one window only. This\nmay be seen in the case of objects in this form. If you want to\nrepresent a round ball at a certain height you must make it oval in\nthis shape, and stand so far off as that by foreshortening it\nappears round.\n\n520.\n\nOF SELECTING THE LIGHT WHICH GIVES MOST GRACE TO FACES.\n\nIf you should have a court yard that you can at pleasure cover with\na linen awning that light will be good. Or when you want to take a\nportrait do it in dull weather, or as evening falls, making the\nsitter stand with his back to one of the walls of the court yard.\nNote in the streets, as evening falls, the faces of the men and\nwomen, and when the weather is dull, what softness and delicacy you\nmay perceive in them. Hence, Oh Painter! have a court arranged with\nthe walls tinted black and a narrow roof projecting within the\nwalls. It should be 10 braccia wide and 20 braccia long and 10\nbraccia high and covered with a linen awning; or else paint a work\ntowards evening or when it is cloudy or misty, and this is a perfect\nlight.\n\nOn various helps in preparing a picture (521-530).\n\n521.\n\nTo draw a nude figure from nature, or any thing else, hold in your\nhand a plumb-line to enable you to judge of the relative position\nof objects.\n\n522.\n\nOF DRAWING AN OBJECT.\n\nWhen you draw take care to set up a principal line which you must\nobserve all throughout the object you are drawing; every thing\nshould bear relation to the direction of this principal line.\n\n523.\n\nOF A MODE OF DRAWING A PLACE ACCURATELY.\n\nHave a piece of glass as large as a half sheet of royal folio paper\nand set thus firmly in front of your eyes that is, between your eye\nand the thing you want to draw; then place yourself at a distance of\n2/3 of a braccia from the glass fixing your head with a machine in\nsuch a way that you cannot move it at all. Then shut or entirely\ncover one eye and with a brush or red chalk draw upon the glass that\nwhich you see beyond it; then trace it on paper from the glass,\nafterwards transfer it onto good paper, and paint it if you like,\ncarefully attending to the arial perspective.\n\nHOW TO LEARN TO PLACE YOUR FIGURES CORRECTLY.\n\nIf you want to acquire a practice of good and correct attitudes for\nyour figures, make a square frame or net, and square it out with\nthread; place this between your eye and the nude model you are\ndrawing, and draw these same squares on the paper on which you mean\nto draw the figure, but very delicately. Then place a pellet of wax\non a spot of the net which will serve as a fixed point, which,\nwhenever you look at your model, must cover the pit of the throat;\nor, if his back is turned, it may cover one of the vertebrae of the\nneck. Thus these threads will guide you as to each part of the body\nwhich, in any given attitude will be found below the pit of the\nthroat, or the angles of the shoulders, or the nipples, or hips and\nother parts of the body; and the transverse lines of the net will\nshow you how much the figure is higher over the leg on which it is\nposed than over the other, and the same with the hips, and the knees\nand the feet. But always fix the net perpendicularly so that all the\ndivisions that you see the model divided into by the net work\ncorrespond with your drawing of the model on the net work you have\nsketched. The squares you draw may be as much smaller than those of\nthe net as you wish that your figure should be smaller than nature.\nAfterwards remember when drawing figures, to use the rule of the\ncorresponding proportions of the limbs as you have learnt it from\nthe frame and net. This should be 3 braccia and a half high and 3\nbraccia wide; 7 braccia distant from you and 1 braccio from the\nmodel.\n\n[Footnote: Leonardo is commonly credited with the invention of the\narrangement of a plate of glass commonly known as the \"vertical\nplane.\" Professor E. VON BRUCKE in his _\"Bruchstucke aus der Theorie\nder bildenden Kunste,\"_ Leipzig 1877, pg. 3, writes on this\ncontrivance. _\"Unsere Glastafel ist die sogenannte Glastafel des\nLeonardo da Vinci, die in Gestalt einer Glastafel vorgestellte\nBildflache.\"_]\n\n524.\n\nA METHOD OF DRAWING AN OBJECT IN RELIEF AT NIGHT.\n\nPlace a sheet of not too transparent paper between the relievo and\nthe light and you can draw thus very well.\n\n[Footnote: Bodies thus illuminated will show on the surface of the\npaper how the copyist has to distribute light and shade.]\n\n525.\n\nIf you want to represent a figure on a wall, the wall being\nforeshortened, while the figure is to appear in its proper form, and\nas standing free from the wall, you must proceed thus: have a thin\nplate of iron and make a small hole in the centre; this hole must be\nround. Set a light close to it in such a position as that it shines\nthrough the central hole, then place any object or figure you please\nso close to the wall that it touches it and draw the outline of the\nshadow on the wall; then fill in the shade and add the lights; place\nthe person who is to see it so that he looks through that same hole\nwhere at first the light was; and you will never be able to persuade\nyourself that the image is not detached from the wall.\n\n[Footnote: _uno piccolo spiracelo nel mezzo_. M. RAVAISSON, in his\nedition of MS. A (Paris), p. 52, reads _nel muro_--evidently a\nmistake for _nel mezzo_ which is quite plainly written; and he\ntranslates it _\"fait lui une petite ouverture dans le mur,\"_ adding\nin a note: _\"les mots 'dans le mur' paraissent etre de trop.\nLeonardo a du les ecrire par distraction\"_ But _'nel mezzo'_ is\nclearly legible even on the photograph facsimile given by Ravaisson\nhimself, and the objection he raises disappears at once. It is not\nalways wise or safe to try to prove our author's absence of mind or\ninadvertence by apparent difficulties in the sense or connection of\nthe text.]\n\n526.\n\nTO DRAW A FIGURE ON A WALL 12 BRACCIA HIGH WHICH SHALL LOOK 24\nBRACCIA HIGH.\n\nIf you wish to draw a figure or any other object to look 24 braccia\nhigh you must do it in this way. First, on the surface _m r_ draw\nhalf the man you wish to represent; then the other half; then put on\nthe vault _m n_ [the rest of] the figure spoken of above; first set\nout the vertical plane on the floor of a room of the same shape as\nthe wall with the coved part on which you are to paint your figure.\nThen, behind it, draw a figure set out in profile of whatever size\nyou please, and draw lines from it to the point _f_ and, as these\nlines cut _m n_ on the vertical plane, so will the figure come on\nthe wall, of which the vertical plane gives a likeness, and you will\nhave all the [relative] heights and prominences of the figure. And\nthe breadth or thickness which are on the upright wall _m n_ are to\nbe drawn in their proper form, since, as the wall recedes the figure\nwill be foreshortened by itself; but [that part of] the figure which\ngoes into the cove you must foreshorten, as if it were standing\nupright; this diminution you must set out on a flat floor and there\nmust stand the figure which is to be transferred from the vertical\nplane _r n_[Footnote 17: _che leverai dalla pariete r n_. The\nletters refer to the larger sketch, No. 3 on Pl. XXXI.] in its real\nsize and reduce it once more on a vertical plane; and this will be a\ngood method [Footnote 18: Leonardo here says nothing as to how the\nimage foreshortened by perspective and thus produced on the vertical\nplane is to be transferred to the wall; but from what is said in\nNos. 525 and 523 we may conclude that he was familiar with the\nprocess of casting the enlarged shadow of a squaring net on the\nsurface of a wall to guide him in drawing the figure.\n\n_Pariete di rilieuo; \"sur une parai en relief\"_ (RAVAISSON). _\"Auf\neiner Schnittlinie zum Aufrichten\"_ (LUDWIG). The explanation of\nthis puzzling expression must be sought in No. 545, lines 15-17.].\n\n[Footnote: See Pl. XXXI. 3. The second sketch, which in the plate is\nincomplete, is here reproduced and completed from the original to\nillustrate the text. In the original the larger diagram is placed\nbetween lines 5 and 6.\n\n1. 2. C. A. 157a; 463a has the similar heading: '_del cressciere\ndella figura_', and the text begins: \"_Se voli fare 1a figura\ngrande_ b c\" but here it breaks off. The translation here given\nrenders the meaning of the passage as I think it must be understood.\nThe MS. is perfectly legible and the construction of the sentence is\nsimple and clear; difficulties can only arise from the very fullness\nof the meaning, particularly towards the end of the passage.]\n\n527.\n\nIf you would to draw a cube in an angle of a wall, first draw the\nobject in its own proper shape and raise it onto a vertical plane\nuntil it resembles the angle in which the said object is to be\nrepresented.\n\n528.\n\nWhy are paintings seen more correctly in a mirror than out of it?\n\n529.\n\nHOW THE MIRROR IS THE MASTER [AND GUIDE] OF PAINTERS.\n\nWhen you want to see if your picture corresponds throughout with the\nobjects you have drawn from nature, take a mirror and look in that\nat the reflection of the real things, and compare the reflected\nimage with your picture, and consider whether the subject of the two\nimages duly corresponds in both, particularly studying the mirror.\nYou should take the mirror for your guide--that is to say a flat\nmirror--because on its surface the objects appear in many respects\nas in a painting. Thus you see, in a painting done on a flat\nsurface, objects which appear in relief, and in the mirror--also a\nflat surface--they look the same. The picture has one plane surface\nand the same with the mirror. The picture is intangible, in so far\nas that which appears round and prominent cannot be grasped in the\nhands; and it is the same with the mirror. And since you can see\nthat the mirror, by means of outlines, shadows and lights, makes\nobjects appear in relief, you, who have in your colours far stronger\nlights and shades than those in the mirror, can certainly, if you\ncompose your picture well, make that also look like a natural scene\nreflected in a large mirror.\n\n[Footnote: I understand the concluding lines of this passage as\nfollows: If you draw the upper half a figure on a large sheet of\npaper laid out on the floor of a room (_sala be piana_) to the same\nscale (_con le sue vere grosseze_) as the lower half, already drawn\nupon the wall (lines 10, 11)you must then reduce them on a '_pariete\ndi rilievo_,' a curved vertical plane which serves as a model to\nreproduce the form of the vault.]\n\n530.\n\nOF JUDGING YOUR OWN PICTURES.\n\nWe know very well that errors are better recognised in the works of\nothers than in our own; and that often, while reproving little\nfaults in others, you may ignore great ones in yourself. To avoid\nsuch ignorance, in the first place make yourself a master of\nperspective, then acquire perfect knowledge of the proportions of\nmen and other animals, and also, study good architecture, that is so\nfar as concerns the forms of buildings and other objects which are\non the face of the earth; these forms are infinite, and the better\nyou know them the more admirable will your work be. And in cases\nwhere you lack experience do not shrink from drawing them from\nnature. But, to carry out my promise above [in the title]--I say\nthat when you paint you should have a flat mirror and often look at\nyour work as reflected in it, when you will see it reversed, and it\nwill appear to you like some other painter's work, so you will be\nbetter able to judge of its faults than in any other way. Again, it\nis well that you should often leave off work and take a little\nrelaxation, because, when you come back to it you are a better\njudge; for sitting too close at work may greatly deceive you. Again,\nit is good to retire to a distance because the work looks smaller\nand your eye takes in more of it at a glance and sees more easily\nthe discords or disproportion in the limbs and colours of the\nobjects.\n\nOn the management of works (531. 532).\n\n531.\n\nOF A METHOD OF LEARNING WELL BY HEART.\n\nWhen you want to know a thing you have studied in your memory\nproceed in this way: When you have drawn the same thing so many\ntimes that you think you know it by heart, test it by drawing it\nwithout the model; but have the model traced on flat thin glass and\nlay this on the drawing you have made without the model, and note\ncarefully where the tracing does not coincide with your drawing, and\nwhere you find you have gone wrong; and bear in mind not to repeat\nthe same mistakes. Then return to the model, and draw the part in\nwhich you were wrong again and again till you have it well in your\nmind. If you have no flat glass for tracing on, take some very thin\nkidts-kin parchment, well oiled and dried. And when you have used it\nfor one drawing you can wash it clean with a sponge and make a\nsecond.\n\n532.\n\nTHAT A PAINTER OUGHT TO BE CURIOUS TO HEAR THE OPINIONS OF EVERY ONE\nON HIS WORK.\n\nCertainly while a man is painting he ought not to shrink from\nhearing every opinion. For we know very well that a man, though he\nmay not be a painter, is familiar with the forms of other men and\nvery capable of judging whether they are hump backed, or have one\nshoulder higher or lower than the other, or too big a mouth or nose,\nand other defects; and, as we know that men are competent to judge\nof the works of nature, how much more ought we to admit that they\ncan judge of our errors; since you know how much a man may be\ndeceived in his own work. And if you are not conscious of this in\nyourself study it in others and profit by their faults. Therefore be\ncurious to hear with patience the opinions of others, consider and\nweigh well whether those who find fault have ground or not for\nblame, and, if so amend; but, if not make as though you had not\nheard, or if he should be a man you esteem show him by argument the\ncause of his mistake.\n\nOn the limitations of painting (533-535)\n\n533.\n\nHOW IN SMALL OBJECTS ERRORS ARE LESS EVIDENT THAN IN LARGE ONES.\n\nIn objects of minute size the extent of error is not so perceptible\nas in large ones; and the reason is that if this small object is a\nrepresentation of a man or of some other animal, from the immense\ndiminution the details cannot be worked out by the artist with the\nfinish that is requisite. Hence it is not actually complete; and,\nnot being complete, its faults cannot be determined. For instance:\nLook at a man at a distance of 300 braccia and judge attentively\nwhether he be handsome or ugly, or very remarkable or of ordinary\nappearance. You will find that with the utmost effort you cannot\npersuade yourself to decide. And the reason is that at such a\ndistance the man is so much diminished that the character of the\ndetails cannot be determined. And if you wish to see how much this\nman is diminished [by distance] hold one of your fingers at a span's\ndistance from your eye, and raise or lower it till the top joint\ntouches the feet of the figure you are looking at, and you will see\nan incredible reduction. For this reason we often doubt as to the\nperson of a friend at a distance.\n\n534.\n\nWHY A PAINTING CAN NEVER APPEAR DETACHED AS NATURAL OBJECTS DO.\n\nPainters often fall into despair of imitating nature when they see\ntheir pictures fail in that relief and vividness which objects have\nthat are seen in a mirror; while they allege that they have colours\nwhich for brightness or depth far exceed the strength of light and\nshade in the reflections in the mirror, thus displaying their own\nignorance rather than the real cause, because they do not know it.\nIt is impossible that painted objects should appear in such relief\nas to resemble those reflected in the mirror, although both are seen\non a flat surface, unless they are seen with only one eye; and the\nreason is that two eyes see one object behind another as _a_ and _b_\nsee _m_ and _n_. _m_ cannot exactly occupy [the space of] _n_\nbecause the base of the visual lines is so broad that the second\nbody is seen beyond the first. But if you close one eye, as at _s_\nthe body _f_ will conceal _r_, because the line of sight proceeds\nfrom a single point and makes its base in the first body, whence the\nsecond, of the same size, can never be seen.\n\n[Footnote: This passage contains the solution of the problem\nproposed in No. 29, lines 10-14. Leonardo was evidently familiar\nwith the law of optics on which the construction of the stereoscope\ndepends. Compare E. VON BRUCKE, _Bruchstucke aus der Theorie der\nbildenden Kunste_, pg. 69: \"_Schon Leonardo da Vinci wusste, dass\nein noch so gut gemaltes Bild nie den vollen Eindruck der\nKorperlichkeit geben kann, wie ihn die Natur selbst giebt. Er\nerklart dies auch in Kap. LIII und Kap. CCCXLI_ (ed. DU FRESNE)\n_des_ 'Trattato' _in sachgemasser Weise aus dem Sehen mit beiden\nAugen_.\"\n\nChap. 53 of DU FRESNE'S edition corresponds to No. 534 of this\nwork.]\n\n535.\n\nWHY OF TWO OBJECTS OF EQUAL SIZE A PAINTED ONE WILL LOOK LARGER THAN\nA SOLID ONE.\n\nThe reason of this is not so easy to demonstrate as many others.\nStill I will endeavour to accomplish it, if not wholly, at any rate\nin part. The perspective of diminution demonstrates by reason, that\nobjects diminish in proportion as they are farther from the eye, and\nthis reasoning is confirmed by experience. Hence, the lines of sight\nthat extend between the object and the eye, when they are directed\nto the surface of a painting are all intersected at uniform limits,\nwhile those lines which are directed towards a piece of sculpture\nare intersected at various limits and are of various lengths. The\nlines which are longest extend to a more remote limb than the others\nand therefore that limb looks smaller. As there are numerous lines\neach longer than the others--since there are numerous parts, each\nmore remote than the others and these, being farther off,\nnecessarily appear smaller, and by appearing smaller it follows that\ntheir diminution makes the whole mass of the object look smaller.\nBut this does not occur in painting; since the lines of sight all\nend at the same distance there can be no diminution, hence the parts\nnot being diminished the whole object is undiminished, and for this\nreason painting does not diminish, as a piece of sculpture does.\n\nOn the choice of a position (536-537)\n\n536.\n\nHOW HIGH THE POINT OF SIGHT SHOULD BE PLACED.\n\nThe point of sight must be at the level of the eye of an ordinary\nman, and the farthest limit of the plain where it touches the sky\nmust be placed at the level of that line where the earth and sky\nmeet; excepting mountains, which are independent of it.\n\n537.\n\nOF THE WAY TO DRAW FIGURES FOR HISTORICAL PICTURES.\n\nThe painter must always study on the wall on which he is to picture\na story the height of the position where he wishes to arrange his\nfigures; and when drawing his studies for them from nature he must\nplace himself with his eye as much below the object he is drawing\nas, in the picture, it will have to be above the eye of the\nspectator. Otherwise the work will look wrong.\n\nThe apparent size of figures in a picture (538-539)\n\n538.\n\nOF PLACING A FIGURE IN THE FOREGROUND OF A HISTORICAL PICTURE.\n\nYou must make the foremost figure in the picture less than the size\nof nature in proportion to the number of braccia at which you place\nit from the front line, and make the others in proportion by the\nabove rule.\n\n539.\n\nPERSPECTIVE.\n\nYou are asked, O Painter, why the figures you draw on a small scale\naccording to the laws of perspective do not appear--notwithstanding\nthe demonstration of distance--as large as real ones--their height\nbeing the same as in those painted on the wall.\n\nAnd why [painted] objects seen at a small distance appear larger\nthan the real ones?\n\nThe right position of the artist, when painting, and of the\nspectator (540-547)\n\n540.\n\nOF PAINTING.\n\nWhen you draw from nature stand at a distance of 3 times the height\nof the object you wish to draw.\n\n541.\n\nOF DRAWING FROM RELIEF.\n\nIn drawing from the round the draughtsman should so place himself\nthat the eye of the figure he is drawing is on a level with his own.\nThis should be done with any head he may have to represent from\nnature because, without exception, the figures or persons you meet\nin the streets have their eyes on the same level as your own; and if\nyou place them higher or lower you will see that your drawing will\nnot be true.\n\n542.\n\nWHY GROUPS OF FIGURES ONE ABOVE ANOTHER ARE TO BE AVOIDED.\n\nThe universal practice which painters adopt on the walls of chapels\nis greatly and reasonably to be condemned. Inasmuch as they\nrepresent one historical subject on one level with a landscape and\nbuildings, and then go up a step and paint another, varying the\npoint [of sight], and then a third and a fourth, in such a way as\nthat on one wall there are 4 points of sight, which is supreme folly\nin such painters. We know that the point of sight is opposite the\neye of the spectator of the scene; and if you would [have me] tell\nyou how to represent the life of a saint divided into several\npictures on one and the same wall, I answer that you must set out\nthe foreground with its point of sight on a level with the eye of\nthe spectator of the scene, and upon this plane represent the more\nimportant part of the story large and then, diminishing by degrees\nthe figures, and the buildings on various hills and open spaces, you\ncan represent all the events of the history. And on the remainder of\nthe wall up to the top put trees, large as compared with the\nfigures, or angels if they are appropriate to the story, or birds or\nclouds or similar objects; otherwise do not trouble yourself with it\nfor your whole work will be wrong.\n\n543.\n\nA PICTURE OF OBJECTS IN PERSPECTIVE WILL LOOK MORE LIFELIKE WHEN\nSEEN FROM THE POINT FROM WHICH THE OBJECTS WERE DRAWN.\n\nIf you want to represent an object near to you which is to have the\neffect of nature, it is impossible that your perspective should not\nlook wrong, with every false relation and disagreement of proportion\nthat can be imagined in a wretched work, unless the spectator, when\nhe looks at it, has his eye at the very distance and height and\ndirection where the eye or the point of sight was placed in doing\nthis perspective. Hence it would be necessary to make a window, or\nrather a hole, of the size of your face through which you can look\nat the work; and if you do this, beyond all doubt your work, if it\nis correct as to light and shade, will have the effect of nature;\nnay you will hardly persuade yourself that those objects are\npainted; otherwise do not trouble yourself about it, unless indeed\nyou make your view at least 20 times as far off as the greatest\nwidth or height of the objects represented, and this will satisfy\nany spectator placed anywhere opposite to the picture.\n\nIf you want the proof briefly shown, take a piece of wood in the\nform of a little column, eight times as high as it is thick, like a\ncolumn without any plinth or capital; then mark off on a flat wall\n40 equal spaces, equal to its width so that between them they make\n40 columns resembling your little column; you then must fix,\nopposite the centre space, and at 4 braccia from the wall, a thin\nstrip of iron with a small round hole in the middle about as large\nas a big pearl. Close to this hole place a light touching it. Then\nplace your column against each mark on the wall and draw the outline\nof its shadow; afterwards shade it and look through the hole in the\niron plate.\n\n[Footnote: In the original there is a wide space between lines 3 and\n4 in which we find two sketches not belonging to the text. It is\nunnecessary to give prominence to the points in which my reading\ndiffers from that of M. RAVAISSON or to justify myself, since they\nare all of secondary importance and can also be immediately verified\nfrom the photograph facsimile in his edition.]\n\n544.\n\nA diminished object should be seen from the same distance, height\nand direction as the point of sight of your eye, or else your\nknowledge will produce no good effect.\n\nAnd if you will not, or cannot, act on this principle--because as\nthe plane on which you paint is to be seen by several persons you\nwould need several points of sight which would make it look\ndiscordant and wrong--place yourself at a distance of at least 10\ntimes the size of the objects.\n\nThe lesser fault you can fall into then, will be that of\nrepresenting all the objects in the foreground of their proper size,\nand on whichever side you are standing the objects thus seen will\ndiminish themselves while the spaces between them will have no\ndefinite ratio. For, if you place yourself in the middle of a\nstraight row [of objects], and look at several columns arranged in a\nline you will see, beyond a few columns separated by intervals, that\nthe columns touch; and beyond where they touch they cover each\nother, till the last column projects but very little beyond the last\nbut one. Thus the spaces between the columns are by degrees entirely\nlost. So, if your method of perspective is good, it will produce the\nsame effect; this effect results from standing near the line in\nwhich the columns are placed. This method is not satisfactory unless\nthe objects seen are viewed from a small hole, in the middle of\nwhich is your point of sight; but if you proceed thus your work will\nbe perfect and will deceive the beholder, who will see the columns\nas they are here figured.\n\nHere the eye is in the middle, at the point _a_ and near to the\ncolumns.\n\n[Footnote: The diagram which stands above this chapter in the\noriginal with the note belonging to it: \"a b _e la ripruova_\" (_a b_\nis the proof) has obviously no connection with the text. The second\nsketch alone is reproduced and stands in the original between lines\n22 and 23.]\n\n545.\n\nIf you cannot arrange that those who look at your work should stand\nat one particular point, when constructing your work, stand back\nuntil your eye is at least 20 times as far off as the greatest\nheight and width of your work. This will make so little difference\nwhen the eye of the spectator moves, that it will be hardly\nappreciable, and it will look very good.\n\nIf the point of sight is at _t_ you would make the figures on the\ncircle _d b e_ all of one size, as each of them bears the same\nrelation to the point _t_. But consider the diagram given below and\nyou will see that this is wrong, and why I shall make _b_ smaller\nthan _d e_ [Footnote 8: The second diagram of this chapter stands in\nthe original between lines 8 and 9.].\n\nIt is easy to understand that if 2 objects equal to each other are\nplaced side by side the one at 3 braccia distance looks smaller than\nthat placed at 2 braccia. This however is rather theoretical than\nfor practice, because you stand close by [Footnote 11: Instead of\n'_se preso_' (=_sie presso_) M. RAVAISSON reads '_sempre se_' which\ngives rise to the unmeaning rendering: '_parceque toujours_ ...'].\n\nAll the objects in the foreground, whether large or small, are to be\ndrawn of their proper size, and if you see them from a distance they\nwill appear just as they ought, and if you see them close they will\ndiminish of themselves.\n\n[Footnote 15: Compare No. 526 line 18.] Take care that the vertical\nplan on which you work out the perspective of the objects seen is of\nthe same form as the wall on which the work is to be executed.\n\n546.\n\nOF PAINTING.\n\nThe size of the figures represented ought to show you the distance\nthey are seen from. If you see a figure as large as nature you know\nit appears to be close to the eye.\n\n547.\n\nWHERE A SPECTATOR SHOULD STAND TO LOOK AT A PICTURE.\n\nSupposing _a b_ to be the picture and _d_ to be the light, I say\nthat if you place yourself between _c_ and _e_ you will not\nunderstand the picture well and particularly if it is done in oils,\nor still more if it is varnished, because it will be lustrous and\nsomewhat of the nature of a mirror. And for this reason the nearer\nyou go towards the point _c_, the less you will see, because the\nrays of light falling from the window on the picture are reflected\nto that point. But if you place yourself between _e_ and _d_ you\nwill get a good view of it, and the more so as you approach the\npoint _d_, because that spot is least exposed to these reflected\nrays of light.\n\nIII.\n\nTHE PRACTICAL METHODS OF LIGHT AND SHADE AND AERIAL PERSPECTIVE.\n\nGradations of light and shade.\n\n548.\n\nOF PAINTING: OF THE DARKNESS OF THE SHADOWS, OR I MAY SAY, THE\nBRIGHTNESS OF THE LIGHTS.\n\nAlthough practical painters attribute to all shaded objects--trees,\nfields, hair, beards and skin--four degrees of darkness in each\ncolour they use: that is to say first a dark foundation, secondly a\nspot of colour somewhat resembling the form of the details, thirdly\na somewhat brighter and more defined portion, fourthly the lights\nwhich are more conspicuous than other parts of the figure; still to\nme it appears that these gradations are infinite upon a continuous\nsurface which is in itself infinitely divisible, and I prove it\nthus:--[Footnote 7: See Pl. XXXI, No. 1; the two upper sketches.]\nLet _a g_ be a continuous surface and let _d_ be the light which\nilluminates it; I say--by the 4th [proposition] which says that that\nside of an illuminated body is most highly lighted which is nearest\nto the source of light--that therefore _g_ must be darker than _c_\nin proportion as the line _d g_ is longer than the line _d c_, and\nconsequently that these gradations of light--or rather of shadow,\nare not 4 only, but may be conceived of as infinite, because _c d_\nis a continuous surface and every continuous surface is infinitely\ndivisible; hence the varieties in the length of lines extending\nbetween the light and the illuminated object are infinite, and the\nproportion of the light will be the same as that of the length of\nthe lines between them; extending from the centre of the luminous\nbody to the surface of the illuminated object.\n\nOn the choice of light for a picture (549-554).\n\n549.\n\nHOW THE PAINTER MUST PLACE HIMSELF WITH REFERENCE TO THE LIGHT, TO\nGIVE THE EFFECT OF RELIEF.\n\nLet _a b_ be the window, _m_ the point of light. I say that on\nwhichever side the painter places himself he will be well placed if\nonly his eye is between the shaded and the illuminated portions of\nthe object he is drawing; and this place you will find by putting\nyourself between the point _m_ and the division between the shadow\nand the light on the object to be drawn.\n\n550.\n\nTHAT SHADOWS CAST BY A PARTICULAR LIGHT SHOULD BE AVOIDED, BECAUSE\nTHEY ARE EQUALLY STRONG AT THE ENDS AND AT THE BEGINNING.\n\nThe shadows cast by the sun or any other particular light have not a\npleasing effect on the body to which they belong, because the parts\nremain confuse, being divided by distinct outlines of light and\nshade. And the shadows are of equal strength at the end and at the\nbeginning.\n\n551.\n\nHOW LIGHT SHOULD BE THROWN UPON FIGURES.\n\nThe light must be arranged in accordance with the natural conditions\nunder which you wish to represent your figures: that is, if you\nrepresent them in the sunshine make the shadows dark with large\nspaces of light, and mark their shadows and those of all the\nsurrounding objects strongly on the ground. And if you represent\nthem as in dull weather give little difference of light and shade,\nwithout any shadows at their feet. If you represent them as within\ndoors, make a strong difference between the lights and shadows, with\nshadows on the ground. If the window is screened and the walls\nwhite, there will be little difference of light. If it is lighted by\nfirelight make the high lights ruddy and strong, and the shadows\ndark, and those cast on the walls and on the floor will be clearly\ndefined and the farther they are from the body the broader and\nlonger will they be. If the light is partly from the fire and partly\nfrom the outer day, that of day will be the stronger and that of the\nfire almost as red as fire itself. Above all see that the figures\nyou paint are broadly lighted and from above, that is to say all\nliving persons that you paint; for you will see that all the people\nyou meet out in the street are lighted from above, and you must know\nthat if you saw your most intimate friend with a light [on his face]\nfrom below you would find it difficult to recognise him.\n\n552.\n\nOF HELPING THE APPARENT RELIEF OF A PICTURE BY GIVING IT ARTIFICIAL\nLIGHT AND SHADE.\n\nTo increase relief of a picture you may place, between your figure\nand the solid object on which its shadow falls, a line of bright\nlight, dividing the figure from the object in shadow. And on the\nsame object you shall represent two light parts which will surround\nthe shadow cast upon the wall by the figure placed opposite [6]; and\ndo this frequently with the limbs which you wish should stand out\nsomewhat from the body they belong to; particularly when the arms\ncross the front of the breast show, between the shadow cast by the\narms on the breast and the shadow on the arms themselves, a little\nlight seeming to fall through a space between the breast and the\narms; and the more you wish the arm to look detached from the breast\nthe broader you must make the light; always contrive also to arrange\nthe figures against the background in such a way as that the parts\nin shadow are against a light background and the illuminated\nportions against a dark background.\n\n[Footnote 6: Compare the two diagrams under No. 565.]\n\n553.\n\nOF SITUATION.\n\nRemember [to note] the situation of your figures; for the light and\nshade will be one thing if the object is in a dark place with a\nparticular light, and another thing if it is in a light place with\ndirect sunlight; one thing in a dark place with a diffused evening\nlight or a cloudy sky, and another in the diffused light of the\natmosphere lighted by the sun.\n\n554.\n\nOF THE JUDGMENT TO BE MADE OF A PAINTER'S WORK.\n\nFirst you must consider whether the figures have the relief required\nby their situation and the light which illuminates them; for the\nshadows should not be the same at the extreme ends of the\ncomposition as in the middle, because it is one thing when figures\nare surrounded by shadows and another when they have shadows only on\none side. Those which are in the middle of the picture are\nsurrounded by shadows, because they are shaded by the figures which\nstand between them and the light. And those are lighted on one side\nonly which stand between the principal group and the light, because\nwhere they do not look towards the light they face the group and the\ndarkness of the group is thrown on them: and where they do not face\nthe group they face the brilliant light and it is their own darkness\nshadowing them, which appears there.\n\nIn the second place observe the distribution or arrangement of\nfigures, and whether they are distributed appropriately to the\ncircumstances of the story. Thirdly, whether the figures are\nactively intent on their particular business.\n\n555.\n\nOF THE TREATMENT OF THE LIGHTS.\n\nFirst give a general shadow to the whole of that extended part which\nis away from the light. Then put in the half shadows and the strong\nshadows, comparing them with each other and, in the same way give\nthe extended light in half tint, afterwards adding the half lights\nand the high lights, likewise comparing them together.\n\nThe distribution of light and shade (556-559)\n\n556.\n\nOF SHADOWS ON BODIES.\n\nWhen you represent the dark shadows in bodies in light and shade,\nalways show the cause of the shadow, and the same with reflections;\nbecause the dark shadows are produced by dark objects and the\nreflections by objects only moderately lighted, that is with\ndiminished light. And there is the same proportion between the\nhighly lighted part of a body and the part lighted by a reflection\nas between the origin of the lights on the body and the origin of\nthe reflections.\n\n557.\n\nOF LIGHTS AND SHADOWS.\n\nI must remind you to take care that every portion of a body, and\nevery smallest detail which is ever so little in relief, must be\ngiven its proper importance as to light and shade.\n\n558.\n\nOF THE WAY TO MAKE THE SHADOW ON FIGURES CORRESPOND TO THE LIGHT AND\nTO [THE COLOUR] OF THE BODY.\n\nWhen you draw a figure and you wish to see whether the shadow is the\nproper complement to the light, and neither redder nor yellower than\nis the nature of the colour you wish to represent in shade, proceed\nthus. Cast a shadow with your finger on the illuminated portion, and\nif the accidental shadow that you have made is like the natural\nshadow cast by your finger on your work, well and good; and by\nputting your finger nearer or farther off, you can make darker or\nlighter shadows, which you must compare with your own.\n\n559.\n\nOF SURROUNDING BODIES BY VARIOUS FORMS OF SHADOW.\n\nTake care that the shadows cast upon the surface of the bodies by\ndifferent objects must undulate according to the various curves of\nthe limbs which cast the shadows, and of the objects on which they\nare cast.\n\nThe juxtaposition of light and shade (560, 561).\n\n560.\n\nON PAINTING.\n\nThe comparison of the various qualities of shadows and lights not\ninfrequently seems ambiguous and confused to the painter who desires\nto imitate and copy the objects he sees. The reason is this: If you\nsee a white drapery side by side with a black one, that part of the\nwhite drapery which lies against the black one will certainly look\nmuch whiter than the part which lies against something whiter than\nitself. [Footnote: It is evident from this that so early as in 1492\nLeonardo's writing in perspective was so far advanced that he could\nquote his own statements.--As bearing on this subject compare what\nis said in No. 280.] And the reason of this is shown in my [book on]\nperspective.\n\n561.\n\nOF SHADOWS.\n\nWhere a shadow ends in the light, note carefully where it is paler\nor deeper and where it is more or less indistinct towards the light;\nand, above all, in [painting] youthful figures I remind you not to\nmake the shadow end like a stone, because flesh has a certain\ntransparency, as may be seen by looking at a hand held between the\neye and the sun, which shines through it ruddy and bright. Place the\nmost highly coloured part between the light and shadow. And to see\nwhat shadow tint is needed on the flesh, cast a shadow on it with\nyour finger, and according as you wish to see it lighter or darker\nhold your finger nearer to or farther from your picture, and copy\nthat [shadow].\n\nOn the lighting of the background (562-565).\n\n562.\n\nOF THE BACKGROUNDS FOR PAINTED FIGURES.\n\nThe ground which surrounds the forms of any object you paint should\nbe darker than the high lights of those figures, and lighter than\ntheir shadowed part: &c.\n\n563.\n\nOF THE BACKGROUND THAT THE PAINTER SHOULD ADOPT IN HIS WORKS.\n\nSince experience shows us that all bodies are surrounded by light\nand shade it is necessary that you, O Painter, should so arrange\nthat the side which is in light shall terminate against a dark body\nand likewise that the shadow side shall terminate against a light\nbody. And by [following] this rule you will add greatly to the\nrelief of your figures.\n\n564.\n\nA most important part of painting consists in the backgrounds of the\nobjects represented; against these backgrounds the outlines of\nthose natural objects which are convex are always visible, and also\nthe forms of these bodies against the background, even though the\ncolours of the bodies should be the same as that of the background.\nThis is caused by the convex edges of the objects not being\nilluminated in the same way as, by the same light, the background is\nilluminated, since these edges will often be lighter or darker than\nthe background. But if the edge is of the same colour as the\nbackground, beyond a doubt it will in that part of the picture\ninterfere with your perception of the outline, and such a choice in\na picture ought to be rejected by the judgment of good painters,\ninasmuch as the purpose of the painter is to make his figures appear\ndetached from the background; while in the case here described the\ncontrary occurs, not only in the picture, but in the objects\nthemselves.\n\n565.\n\nThat you ought, when representing objects above the eye and on one\nside--if you wish them to look detached from the wall--to show,\nbetween the shadow on the object and the shadow it casts a middle\nlight, so that the body will appear to stand away from the wall.\n\nOn the lighting of white objects.\n\n566.\n\nHOW WHITE BODIES SHOULD BE REPRESENTED.\n\nIf you are representing a white body let it be surrounded by ample\nspace, because as white has no colour of its own, it is tinged and\naltered in some degree by the colour of the objects surrounding it.\nIf you see a woman dressed in white in the midst of a landscape,\nthat side which is towards the sun is bright in colour, so much so\nthat in some portions it will dazzle the eyes like the sun itself;\nand the side which is towards the atmosphere,--luminous through\nbeing interwoven with the sun's rays and penetrated by them--since\nthe atmosphere itself is blue, that side of the woman's figure will\nappear steeped in blue. If the surface of the ground about her be\nmeadows and if she be standing between a field lighted up by the sun\nand the sun itself, you will see every portion of those folds which\nare towards the meadow tinged by the reflected rays with the colour\nof that meadow. Thus the white is transmuted into the colours of the\nluminous and of the non-luminous objects near it.\n\nThe methods of aerial (567--570).\n\n567.\n\nWHY FACES [SEEN] AT A DISTANCE LOOK DARK.\n\nWe see quite plainly that all the images of visible objects that lie\nbefore us, whether large or small, reach our sense by the minute\naperture of the eye; and if, through so small a passage the image\ncan pass of the vast extent of sky and earth, the face of a\nman--being by comparison with such large images almost nothing by\nreason of the distance which diminishes it,--fills up so little of\nthe eye that it is indistinguishable. Having, also, to be\ntransmitted from the surface to the sense through a dark medium,\nthat is to say the crystalline lens which looks dark, this image,\nnot being strong in colour becomes affected by this darkness on its\npassage, and on reaching the sense it appears dark; no other reason\ncan in any way be assigned. If the point in the eye is black, it is\nbecause it is full of a transparent humour as clear as air and acts\nlike a perforation in a board; on looking into it it appears dark\nand the objects seen through the bright air and a dark one become\nconfused in this darkness.\n\nWHY A MAN SEEN AT A CERTAIN DISTANCE IS NOT RECOGNISABLE.\n\nThe perspective of diminution shows us that the farther away an\nobject is the smaller it looks. If you look at a man at a distance\nfrom you of an arrow's flight, and hold the eye of a small needle\nclose to your own eye, you can see through it several men whose\nimages are transmitted to the eye and will all be comprised within\nthe size of the needle's eye; hence, if the man who is at the\ndistance of an arrow's flight can send his whole image to your eye,\noccupying only a small space in the needle's eye how can you\n[expect] in so small a figure to distinguish or see the nose or\nmouth or any detail of his person? and, not seeing these you cannot\nrecognise the man, since these features, which he does not show, are\nwhat give men different aspects.\n\n568.\n\nTHE REASON WHY SMALL FIGURES SHOULD NOT BE MADE FINISHED.\n\nI say that the reason that objects appear diminished in size is\nbecause they are remote from the eye; this being the case it is\nevident that there must be a great extent of atmosphere between the\neye and the objects, and this air interferes with the distinctness\nof the forms of the object. Hence the minute details of these\nobjects will be indistinguishable and unrecognisable. Therefore, O\nPainter, make your smaller figures merely indicated and not highly\nfinished, otherwise you will produce effects the opposite to nature,\nyour supreme guide. The object is small by reason of the great\ndistance between it and the eye, this great distance is filled with\nair, that mass of air forms a dense body which intervenes and\nprevents the eye seeing the minute details of objects.\n\n569.\n\nWhenever a figure is placed at a considerable distance you lose\nfirst the distinctness of the smallest parts; while the larger parts\nare left to the last, losing all distinctness of detail and outline;\nand what remains is an oval or spherical figure with confused edges.\n\n570.\n\nOF PAINTING.\n\nThe density of a body of smoke looks white below the horizon while\nabove the horizon it is dark, even if the smoke is in itself of a\nuniform colour, this uniformity will vary according to the variety\nin the ground on which it is seen.\n\nIV.\n\nOF PORTRAIT AND FIGURE PAINTING.\n\nOf sketching figures and portraits (571-572).\n\n571.\n\nOF THE WAY TO LEARN TO COMPOSE FIGURES [IN GROUPS] IN HISTORICAL\nPICTURES.\n\nWhen you have well learnt perspective and have by heart the parts\nand forms of objects, you must go about, and constantly, as you go,\nobserve, note and consider the circumstances and behaviour of men in\ntalking, quarrelling or laughing or fighting together: the action of\nthe men themselves and the actions of the bystanders, who separate\nthem or who look on. And take a note of them with slight strokes\nthus, in a little book which you should always carry with you. And\nit should be of tinted paper, that it may not be rubbed out, but\nchange the old [when full] for a new one; since these things should\nnot be rubbed out but preserved with great care; for the forms, and\npositions of objects are so infinite that the memory is incapable of\nretaining them, wherefore keep these [sketches] as your guides and\nmasters.\n\n[Footnote: Among Leonardo's numerous note books of pocket size not\none has coloured paper, so no sketches answering to this description\ncan be pointed out. The fact that most of the notes are written in\nink, militates against the supposition that they were made in the\nopen air.]\n\n572.\n\nOF A METHOD OF KEEPING IN MIND THE FORM OF A FACE.\n\nIf you want to acquire facility for bearing in mind the expression\nof a face, first make yourself familiar with a variety of [forms of]\nseveral heads, eyes, noses, mouths, chins and cheeks and necks and\nshoulders: And to put a case: Noses are of 10 types: straight,\nbulbous, hollow, prominent above or below the middle, aquiline,\nregular, flat, round or pointed. These hold good as to profile. In\nfull face they are of 11 types; these are equal thick in the middle,\nthin in the middle, with the tip thick and the root narrow, or\nnarrow at the tip and wide at the root; with the nostrils wide or\nnarrow, high or low, and the openings wide or hidden by the point;\nand you will find an equal variety in the other details; which\nthings you must draw from nature and fix them in your mind. Or else,\nwhen you have to draw a face by heart, carry with you a little book\nin which you have noted such features; and when you have cast a\nglance at the face of the person you wish to draw, you can look, in\nprivate, which nose or mouth is most like, or there make a little\nmark to recognise it again at home. Of grotesque faces I need say\nnothing, because they are kept in mind without difficulty.\n\nThe position of the head.\n\n573.\n\nHOW YOU SHOULD SET TO WORK TO DRAW A HEAD OF WHICH ALL THE PARTS\nSHALL AGREE WITH THE POSITION GIVEN TO IT.\n\nTo draw a head in which the features shall agree with the turn and\nbend of the head, pursue this method. You know that the eyes,\neyebrows, nostrils, corners of the mouth, and sides of the chin, the\njaws, cheeks, ears and all the parts of a face are squarely and\nstraightly set upon the face.\n\n[Footnote: Compare the drawings and the text belonging to them on\nPl. IX. (No. 315), Pl. X (No. 316), Pl. XL (No. 318) and Pl. XII.\n(No. 319).]\n\nTherefore when you have sketched the face draw lines passing from\none corner of the eye to the other; and so for the placing of each\nfeature; and after having drawn the ends of the lines beyond the two\nsides of the face, look if the spaces inside the same parallel lines\non the right and on the left are equal [12]. But be sure to remember\nto make these lines tend to the point of sight.\n\n[Footnote: See Pl. XXXI, No. 4, the slight sketch on the left hand\nside. The text of this passage is written by the side of it. In this\nsketch the lines seem intentionally incorrect and converging to the\nright (compare I. 12) instead of parallel. Compare too with this\ntext the drawing in red chalk from Windsor Castle which is\nreproduced on Pl. XL, No. 2.]\n\nOf the light on the face (574-576).\n\n574.\n\nHOW TO KNOW WHICH SIDE OF AN OBJECT IS TO BE MORE OR LESS LUMINOUS\nTHAN THE OTHER.\n\nLet _f_ be the light, the head will be the object illuminated by it\nand that side of the head on which the rays fall most directly will\nbe the most highly lighted, and those parts on which the rays fall\nmost aslant will be less lighted. The light falls as a blow might,\nsince a blow which falls perpendicularly falls with the greatest\nforce, and when it falls obliquely it is less forcible than the\nformer in proportion to the width of the angle. _Exempli gratia_ if\nyou throw a ball at a wall of which the extremities are equally far\nfrom you the blow will fall straight, and if you throw the ball at\nthe wall when standing at one end of it the ball will hit it\nobliquely and the blow will not tell.\n\n[Footnote: See Pl. XXXI. No. 4; the sketch on the right hand side.]\n\n575.\n\nTHE PROOF AND REASON WHY AMONG THE ILLUMINATED PARTS CERTAIN\nPORTIONS ARE IN HIGHER LIGHT THAN OTHERS.\n\nSince it is proved that every definite light is, or seems to be,\nderived from one single point the side illuminated by it will have\nits highest light on the portion where the line of radiance falls\nperpendicularly; as is shown above in the lines _a g_, and also in\n_a h_ and in _l a_; and that portion of the illuminated side will be\nleast luminous, where the line of incidence strikes it between two\nmore dissimilar angles, as is seen at _b c d_. And by this means you\nmay also know which parts are deprived of light as is seen at _m k_.\n\nWhere the angles made by the lines of incidence are most equal there\nwill be the highest light, and where they are most unequal it will\nbe darkest.\n\nI will make further mention of the reason of reflections.\n\n[Footnote: See Pl. XXXII. The text, here given complete, is on the\nright hand side. The small circles above the beginning of lines 5\nand 11 as well as the circle above the text on Pl. XXXI, are in a\npaler ink and evidently added by a later hand in order to\ndistinguish the text as belonging to the _Libro di Pittura_ (see\nProlegomena. No. 12, p. 3). The text on the left hand side of this\npage is given as Nos. 577 and 137.]\n\n576.\n\nWhere the shadow should be on the face.\n\nGeneral suggestions for historical pictures (577-581).\n\n577.\n\nWhen you compose a historical picture take two points, one the point\nof sight, and the other the source of light; and make this as\ndistant as possible.\n\n578.\n\nHistorical pictures ought not to be crowded and confused with too\nmany figures.\n\n579.\n\nPRECEPTS IN PAINTING.\n\nLet you sketches of historical pictures be swift and the working out\nof the limbs not be carried too far, but limited to the position of\nthe limbs, which you can afterwards finish as you please and at your\nleisure.\n\n[Footnote: See Pl. XXXVIII, No. 2. The pen and ink drawing given\nthere as No. 3 may also be compared with this passage. It is in the\nWindsor collection where it is numbered 101.]\n\n580.\n\nThe sorest misfortune is when your views are in advance of your\nwork.\n\n581.\n\nOf composing historical pictures. Of not considering the limbs in\nthe figures in historical pictures; as many do who, in the wish to\nrepresent the whole of a figure, spoil their compositions. And when\nyou place one figure behind another take care to draw the whole of\nit so that the limbs which come in front of the nearer figures may\nstand out in their natural size and place.\n\nHow to represent the differences of age and sex (582-583).\n\n582.\n\nHow the ages of man should be depicted: that is, Infancy, Childhood,\nYouth, Manhood, Old age, Decrepitude.\n\n[Footnote: No answer is here given to this question, in the original\nMS.]\n\n583.\n\nOld men ought to be represented with slow and heavy movements, their\nlegs bent at the knees, when they stand still, and their feet placed\nparallel and apart; bending low with the head leaning forward, and\ntheir arms but little extended.\n\nWomen must be represented in modest attitudes, their legs close\ntogether, their arms closely folded, their heads inclined and\nsomewhat on one side.\n\nOld women should be represented with eager, swift and furious\ngestures, like infernal furies; but the action should be more\nviolent in their arms and head than in their legs.\n\nLittle children, with lively and contorted movements when sitting,\nand, when standing still, in shy and timid attitudes.\n\n[Footnote: _bracci raccolte_. Compare Pl. XXXIII. This drawing, in\nsilver point on yellowish tinted paper, the lights heightened with\nwhite, represents two female hands laid together in a lap. Above is\na third finished study of a right hand, apparently holding a veil\nfrom the head across the bosom. This drawing evidently dates from\nbefore 1500 and was very probably done at Florence, perhaps as a\npreparatory study for some picture. The type of hand with its\nslender thin forms is more like the style of the _Vierge aux\nRochers_ in the Louvre than any later works--as the Mona Lisa for\ninstance.]\n\nOf representing the emotions.\n\n584.\n\nTHAT A FIGURE IS NOT ADMIRABLE UNLESS IT EXPRESSES BY ITS ACTION THE\nPASSION OF ITS SENTIMENT.\n\nThat figure is most admirable which by its actions best expresses\nthe passion that animates it.\n\nHOW AN ANGRY MAN IS TO BE FIGURED.\n\nYou must make an angry person holding someone by the hair, wrenching\nhis head against the ground, and with one knee on his ribs; his\nright arm and fist raised on high. His hair must be thrown up, his\nbrow downcast and knit, his teeth clenched and the two corners of\nhis mouth grimly set; his neck swelled and bent forward as he leans\nover his foe, and full of furrows.\n\nHOW TO REPRESENT A MAN IN DESPAIR.\n\nYou must show a man in despair with a knife, having already torn\nopen his garments, and with one hand tearing open the wound. And\nmake him standing on his feet and his legs somewhat bent and his\nwhole person leaning towards the earth; his hair flying in disorder.\n\nOf representing imaginary animals.\n\n585.\n\nHOW YOU SHOULD MAKE AN IMAGINARY ANIMAL LOOK NATURAL.\n\nYou know that you cannot invent animals without limbs, each of\nwhich, in itself, must resemble those of some other animal. Hence if\nyou wish to make an animal, imagined by you, appear natural--let us\nsay a Dragon, take for its head that of a mastiff or hound, with the\neyes of a cat, the ears of a porcupine, the nose of a greyhound, the\nbrow of a lion, the temples of an old cock, the neck of a water\ntortoise.\n\n[Footnote: The sketch here inserted of two men on horseback fighting\na dragon is the facsimile of a pen and ink drawing belonging to\nBARON EDMOND DE ROTHSCHILD of Paris.]\n\nThe selection of forms.\n\n586.\n\nOF THE DELUSIONS WHICH ARISE IN JUDGING OF THE LIMBS.\n\nA painter who has clumsy hands will paint similar hands in his\nworks, and the same will occur with any limb, unless long study has\ntaught him to avoid it. Therefore, O Painter, look carefully what\npart is most ill-favoured in your own person and take particular\npains to correct it in your studies. For if you are coarse, your\nfigures will seem the same and devoid of charm; and it is the same\nwith any part that may be good or poor in yourself; it will be shown\nin some degree in your figures.\n\n587.\n\nOF THE SELECTION OF BEAUTIFUL FACES.\n\nIt seems to me to be no small charm in a painter when he gives his\nfigures a pleasing air, and this grace, if he have it not by nature,\nhe may acquire by incidental study in this way: Look about you and\ntake the best parts of many beautiful faces, of which the beauty is\nconfirmed rather by public fame than by your own judgment; for you\nmight be mistaken and choose faces which have some resemblance to\nyour own. For it would seem that such resemblances often please us;\nand if you should be ugly, you would select faces that were not\nbeautiful and you would then make ugly faces, as many painters do.\nFor often a master's work resembles himself. So select beauties as I\ntell you, and fix them in your mind.\n\n588.\n\nOf the limbs, which ought to be carefully selected, and of all the\nother parts with regard to painting.\n\n589.\n\nWhen selecting figures you should choose slender ones rather than\nlean and wooden ones.\n\n590.\n\nOF THE MUSCLES OF ANIMALS.\n\nThe hollow spaces interposed between the muscles must not be of such\na character as that the skin should seem to cover two sticks laid\nside by side like _c_, nor should they seem like two sticks somewhat\nremote from such contact so that the skin hangs in an empty loose\ncurve as at _f_; but it should be like _i_, laid over the spongy fat\nthat lies in the angles as the angle _n m o_; which angle is formed\nby the contact of the ends of the muscles and as the skin cannot\nfold down into such an angle, nature has filled up such angles with\na small quantity of spongy and, as I may say, vesicular fat, with\nminute bladders [in it] full of air, which is condensed or rarefied\nin them according to the increase or the diminution of the substance\nof the muscles; in which latter case the concavity _i_ always has a\nlarger curve than the muscle.\n\n591.\n\nOF UNDULATING MOVEMENTS AND EQUIPOISE IN FIGURES AND OTHER ANIMALS.\n\nWhen representing a human figure or some graceful animal, be careful\nto avoid a wooden stiffness; that is to say make them move with\nequipoise and balance so as not to look like a piece of wood; but\nthose you want to represent as strong you must not make so,\nexcepting in the turn of the head.\n\nHow to pose figures.\n\n592.\n\nOF GRACE IN THE LIMBS.\n\nThe limbs should be adapted to the body with grace and with\nreference to the effect that you wish the figure to produce. And if\nyou wish to produce a figure that shall of itself look light and\ngraceful you must make the limbs elegant and extended, and without\ntoo much display of the muscles; and those few that are needed for\nyour purpose you must indicate softly, that is, not very prominent\nand without strong shadows; the limbs, and particularly the arms\neasy; that is, none of the limbs should be in a straight line with\nthe adjoining parts. And if the hips, which are the pole of a man,\nare by reason of his position, placed so, that the right is higher\nthan the left, make the point of the higher shoulder in a\nperpendicular line above the highest prominence of the hip, and let\nthis right shoulder be lower than the left. Let the pit of the\nthroat always be over the centre of the joint of the foot on which\nthe man is leaning. The leg which is free should have the knee lower\nthan the other, and near the other leg. The positions of the head\nand arms are endless and I shall therefore not enlarge on any rules\nfor them. Still, let them be easy and pleasing, with various turns\nand twists, and the joints gracefully bent, that they may not look\nlike pieces of wood.\n\nOf appropriate gestures (593-600).\n\n593.\n\nA picture or representation of human figures, ought to be done in\nsuch a way as that the spectator may easily recognise, by means of\ntheir attitudes, the purpose in their minds. Thus, if you have to\nrepresent a man of noble character in the act of speaking, let his\ngestures be such as naturally accompany good words; and, in the same\nway, if you wish to depict a man of a brutal nature, give him fierce\nmovements; as with his arms flung out towards the listener, and his\nhead and breast thrust forward beyond his feet, as if following the\nspeaker's hands. Thus it is with a deaf and dumb person who, when he\nsees two men in conversation--although he is deprived of\nhearing--can nevertheless understand, from the attitudes and\ngestures of the speakers, the nature of their discussion. I once saw\nin Florence a man who had become deaf who, when you spoke very loud\ndid not understand you, but if you spoke gently and without making\nany sound, understood merely from the movement of the lips. Now\nperhaps you will say that the lips of a man who speaks loudly do not\nmove like those of one speaking softly, and that if they were to\nmove them alike they would be alike understood. As to this argument,\nI leave the decision to experiment; make a man speak to you gently\nand note [the motion of] his lips.\n\n[Footnote: The first ten lines of this text have already been\npublished, but with a slightly different reading by Dr. M. JORDAN:\n_Das Malerbuch Leonardo da Vinci's_ p. 86.]\n\n594.\n\nOF REPRESENTING A MAN SPEAKING TO A MULTITUDE.\n\nWhen you wish to represent a man speaking to a number of people,\nconsider the matter of which he has to treat and adapt his action to\nthe subject. Thus, if he speaks persuasively, let his action be\nappropriate to it. If the matter in hand be to set forth an\nargument, let the speaker, with the fingers of the right hand hold\none finger of the left hand, having the two smaller ones closed; and\nhis face alert, and turned towards the people with mouth a little\nopen, to look as though he spoke; and if he is sitting let him\nappear as though about to rise, with his head forward. If you\nrepresent him standing make him leaning slightly forward with body\nand head towards the people. These you must represent as silent and\nattentive, all looking at the orator's face with gestures of\nadmiration; and make some old men in astonishment at the things they\nhear, with the corners of their mouths pulled down and drawn in,\ntheir cheeks full of furrows, and their eyebrows raised, and\nwrinkling the forehead where they meet. Again, some sitting with\ntheir fingers clasped holding their weary knees. Again, some bent\nold man, with one knee crossed over the other; on which let him hold\nhis hand with his other elbow resting in it and the hand supporting\nhis bearded chin.\n\n[Footnote: The sketches introduced here are a facsimile of a pen and\nink drawing in the Louvre which Herr CARL BRUN considers as studies\nfor the Last Supper in the church of _Santa Maria delle Grazie_ (see\nLeonardo da Vinci, LXI, pp. 21, 27 and 28 in DOHME'S _Kunst und\nKunstler_, Leipzig, Seemann). I shall not here enter into any\ndiscussion of this suggestion; but as a justification for\nintroducing the drawing in this place, I may point out that some of\nthe figures illustrate this passage as perfectly as though they had\nbeen drawn for that express purpose. I have discussed the\nprobability of a connection between this sketch and the picture of\nthe Last Supper on p. 335. The original drawing is 27 3/4\ncentimetres wide by 21 high.--The drawing in silver point on reddish\npaper given on Pl. LII. No. 1--the original at Windsor Castle--may\nalso serve to illustrate the subject of appropriate gestures,\ntreated in Nos. 593 and 594.]\n\n595.\n\nOF THE DISPOSITION OF LIMBS.\n\nAs regards the disposition of limbs in movement you will have to\nconsider that when you wish to represent a man who, by some chance,\nhas to turn backwards or to one side, you must not make him move his\nfeet and all his limbs towards the side to which he turns his head.\nRather must you make the action proceed by degrees and through the\ndifferent joints; that is, those of the foot, the knee and the hip\nand the neck. And if you set him on the right leg, you must make the\nleft knee bend inwards, and let his foot be slightly raised on the\noutside, and the left shoulder be somewhat lower than the right,\nwhile the nape of the neck is in a line directly over the outer\nancle of the left foot. And the left shoulder will be in a\nperpendicular line above the toes of the right foot. And always set\nyour figures so that the side to which the head turns is not the\nside to which the breast faces, since nature for our convenience has\nmade us with a neck which bends with ease in many directions, the\neye wishing to turn to various points, the different joints. And if\nat any time you make a man sitting with his arms at work on\nsomething which is sideways to him, make the upper part of his body\nturn upon the hips.\n\n[Footnote: Compare Pl. VII, No. 5. The original drawing at Windsor\nCastle is numbered 104.]\n\n596.\n\nWhen you draw the nude always sketch the whole figure and then\nfinish those limbs which seem to you the best, but make them act\nwith the other limbs; otherwise you will get a habit of never\nputting the limbs well together on the body.\n\nNever make the head turn the same way as the torso, nor the arm and\nleg move together on the same side. And if the face is turned to the\nright shoulder, make all the parts lower on the left side than on\nthe right; and when you turn the body with the breast outwards, if\nthe head turns to the left side make the parts on the right side\nhigher than those on the left.\n\n[Footnote: In the original MS. a much defaced sketch is to be seen\nby the side of the second part of this chapter; its faded condition\nhas rendered reproduction impossible. In M. RAVAISSON'S facsimile\nthe outlines of the head have probably been touched up. This passage\nhowever is fitly illustrated by the drawings on Pl. XXI.]\n\n597.\n\nOF PAINTING.\n\nOf the nature of movements in man. Do not repeat the same gestures\nin the limbs of men unless you are compelled by the necessity of\ntheir action, as is shown in _a b_.\n\n[Footnote: See Pl. V, where part of the text is also reproduced. The\neffaced figure to the extreme left has evidently been cancelled by\nLeonardo himself as unsatisfactory.]\n\n598.\n\nThe motions of men must be such as suggest their dignity or their\nbaseness.\n\n599.\n\nOF PAINTING.\n\nMake your work carry out your purpose and meaning. That is when you\ndraw a figure consider well who it is and what you wish it to be\ndoing.\n\nOF PAINTING.\n\nWith regard to any action which you give in a picture to an old man\nor to a young one, you must make it more energetic in the young man\nin proportion as he is stronger than the old one; and in the same\nway with a young man and an infant.\n\n600.\n\nOF SETTING ON THE LIMBS.\n\nThe limbs which are used for labour must be muscular and those which\nare not much used you must make without muscles and softly rounded.\n\nOF THE ACTION OF THE FIGURES.\n\nRepresent your figures in such action as may be fitted to express\nwhat purpose is in the mind of each; otherwise your art will not be\nadmirable.\n\nV.\n\nSUGGESTIONS FOR COMPOSITIONS.\n\nOf painting battle pieces (601-603).\n\n601.\n\nOF THE WAY OF REPRESENTING A BATTLE.\n\nFirst you must represent the smoke of artillery mingling in the air\nwith the dust and tossed up by the movement of horses and the\ncombatants. And this mixture you must express thus: The dust, being\na thing of earth, has weight; and although from its fineness it is\neasily tossed up and mingles with the air, it nevertheless readily\nfalls again. It is the finest part that rises highest; hence that\npart will be least seen and will look almost of the same colour as\nthe air. The higher the smoke mixed with the dust-laden air rises\ntowards a certain level, the more it will look like a dark cloud;\nand it will be seen that at the top, where the smoke is more\nseparate from the dust, the smoke will assume a bluish tinge and the\ndust will tend to its colour. This mixture of air, smoke and dust\nwill look much lighter on the side whence the light comes than on\nthe opposite side. The more the combatants are in this turmoil the\nless will they be seen, and the less contrast will there be in their\nlights and shadows. Their faces and figures and their appearance,\nand the musketeers as well as those near them you must make of a\nglowing red. And this glow will diminish in proportion as it is\nremote from its cause.\n\nThe figures which are between you and the light, if they be at a\ndistance, will appear dark on a light background, and the lower part\nof their legs near the ground will be least visible, because there\nthe dust is coarsest and densest [19]. And if you introduce horses\ngalloping outside the crowd, make the little clouds of dust distant\nfrom each other in proportion to the strides made by the horses; and\nthe clouds which are furthest removed from the horses, should be\nleast visible; make them high and spreading and thin, and the nearer\nones will be more conspicuous and smaller and denser [23]. The air\nmust be full of arrows in every direction, some shooting upwards,\nsome falling, some flying level. The balls from the guns must have a\ntrain of smoke following their flight. The figures in the foreground\nyou must make with dust on the hair and eyebrows and on other flat\nplaces likely to retain it. The conquerors you will make rushing\nonwards with their hair and other light things flying on the wind,\nwith their brows bent down,\n\n[Footnote: 19--23. Compare 608. 57--75.]\n\n602.\n\nand with the opposite limbs thrust forward; that is where a man puts\nforward the right foot the left arm must be advanced. And if you\nmake any one fallen, you must show the place where he has slipped\nand been dragged along the dust into blood stained mire; and in the\nhalf-liquid earth arround show the print of the tramping of men and\nhorses who have passed that way. Make also a horse dragging the dead\nbody of his master, and leaving behind him, in the dust and mud, the\ntrack where the body was dragged along. You must make the conquered\nand beaten pale, their brows raised and knit, and the skin above\ntheir brows furrowed with pain, the sides of the nose with wrinkles\ngoing in an arch from the nostrils to the eyes, and make the\nnostrils drawn up--which is the cause of the lines of which I\nspeak--, and the lips arched upwards and discovering the upper\nteeth; and the teeth apart as with crying out and lamentation. And\nmake some one shielding his terrified eyes with one hand, the palm\ntowards the enemy, while the other rests on the ground to support\nhis half raised body. Others represent shouting with their mouths\nopen, and running away. You must scatter arms of all sorts among the\nfeet of the combatants, as broken shields, lances, broken swords and\nother such objects. And you must make the dead partly or entirely\ncovered with dust, which is changed into crimson mire where it has\nmingled with the flowing blood whose colour shows it issuing in a\nsinuous stream from the corpse. Others must be represented in the\nagonies of death grinding their teeth, rolling their eyes, with\ntheir fists clenched against their bodies and their legs contorted.\nSome might be shown disarmed and beaten down by the enemy, turning\nupon the foe, with teeth and nails, to take an inhuman and bitter\nrevenge. You might see some riderless horse rushing among the enemy,\nwith his mane flying in the wind, and doing no little mischief with\nhis heels. Some maimed warrior may be seen fallen to the earth,\ncovering himself with his shield, while the enemy, bending over him,\ntries to deal him a deathstroke. There again might be seen a number\nof men fallen in a heap over a dead horse. You would see some of the\nvictors leaving the fight and issuing from the crowd, rubbing their\neyes and cheeks with both hands to clean them of the dirt made by\ntheir watering eyes smarting from the dust and smoke. The reserves\nmay be seen standing, hopeful but cautious; with watchful eyes,\nshading them with their hands and gazing through the dense and murky\nconfusion, attentive to the commands of their captain. The captain\nhimself, his staff raised, hurries towards these auxiliaries,\npointing to the spot where they are most needed. And there may be a\nriver into which horses are galloping, churning up the water all\nround them into turbulent waves of foam and water, tossed into the\nair and among the legs and bodies of the horses. And there must not\nbe a level spot that is not trampled with gore.\n\n603.\n\nOF LIGHTING THE LOWER PARTS OF BODIES CLOSE TOGETHER, AS OF MEN IN\nBATTLE.\n\nAs to men and horses represented in battle, their different parts\nwill be dark in proportion as they are nearer to the ground on which\nthey stand. And this is proved by the sides of wells which grow\ndarker in proportion to their depth, the reason of which is that the\ndeepest part of the well sees and receives a smaller amount of the\nluminous atmosphere than any other part.\n\nAnd the pavement, if it be of the same colour as the legs of these\nsaid men and horses, will always be more lighted and at a more\ndirect angle than the said legs &c.\n\n604.\n\nOF THE WAY TO REPRESENT A NIGHT [SCENE].\n\nThat which is entirely bereft of light is all darkness; given a\nnight under these conditions and that you want to represent a night\nscene,--arrange that there shall be a great fire, then the objects\nwhich are nearest to this fire will be most tinged with its colour;\nfor those objects which are nearest to a coloured light participate\nmost in its nature; as therefore you give the fire a red colour, you\nmust make all the objects illuminated by it ruddy; while those which\nare farther from the fire are more tinted by the black hue of night.\nThe figures which are seen against the fire look dark in the glare\nof the firelight because that side of the objects which you see is\ntinged by the darkness of the night and not by the fire; and those\nwho stand at the side are half dark and half red; while those who\nare visible beyond the edges of the flame will be fully lighted by\nthe ruddy glow against a black background. As to their gestures,\nmake those which are near it screen themselves with their hands and\ncloaks as a defence against the intense heat, and with their faces\nturned away as if about to retire. Of those farther off represent\nseveral as raising their hands to screen their eyes, hurt by the\nintolerable glare.\n\nOf depicting a tempest (605. 606).\n\n605.\n\nDescribe a wind on land and at sea. Describe a storm of rain.\n\n606.\n\nHOW TO REPRESENT A TEMPEST.\n\nIf you wish to represent a tempest consider and arrange well its\neffects as seen, when the wind, blowing over the face of the sea and\nearth, removes and carries with it such things as are not fixed to\nthe general mass. And to represent the storm accurately you must\nfirst show the clouds scattered and torn, and flying with the wind,\naccompanied by clouds of sand blown up from the sea shore, and\nboughs and leaves swept along by the strength and fury of the blast\nand scattered with other light objects through the air. Trees and\nplants must be bent to the ground, almost as if they would follow\nthe course of the gale, with their branches twisted out of their\nnatural growth and their leaves tossed and turned about [Footnote\n11: See Pl. XL, No. 2.]. Of the men who are there some must have\nfallen to the ground and be entangled in their garments, and hardly\nto be recognized for the dust, while those who remain standing may\nbe behind some tree, with their arms round it that the wind may not\ntear them away; others with their hands over their eyes for the\ndust, bending to the ground with their clothes and hair streaming in\nthe wind. [Footnote 15: See Pl. XXXIV, the right hand lower sketch.]\nLet the sea be rough and tempestuous and full of foam whirled among\nthe lofty waves, while the wind flings the lighter spray through the\nstormy air, till it resembles a dense and swathing mist. Of the\nships that are therein some should be shown with rent sails and the\ntatters fluttering through the air, with ropes broken and masts\nsplit and fallen. And the ship itself lying in the trough of the sea\nand wrecked by the fury of the waves with the men shrieking and\nclinging to the fragments of the vessel. Make the clouds driven by\nthe impetuosity of the wind and flung against the lofty mountain\ntops, and wreathed and torn like waves beating upon rocks; the air\nitself terrible from the deep darkness caused by the dust and fog\nand heavy clouds.\n\nOf representing the deluge (607-609).\n\n607.\n\nTO REPRESENT THE DELUGE.\n\nThe air was darkened by the heavy rain whose oblique descent driven\naslant by the rush of the winds, flew in drifts through the air not\notherwise than as we see dust, varied only by the straight lines of\nthe heavy drops of falling water. But it was tinged with the colour\nof the fire kindled by the thunder-bolts by which the clouds were\nrent and shattered; and whose flashes revealed the broad waters of\nthe inundated valleys, above which was seen the verdure of the\nbending tree tops. Neptune will be seen in the midst of the water\nwith his trident, and [15] let AEolus with his winds be shown\nentangling the trees floating uprooted, and whirling in the huge\nwaves. The horizon and the whole hemisphere were obscure, but lurid\nfrom the flashes of the incessant lightning. Men and birds might be\nseen crowded on the tall trees which remained uncovered by the\nswelling waters, originators of the mountains which surround the\ngreat abysses [Footnote 23: Compare Vol. II. No. 979.].\n\n608.\n\nOF THE DELUGE AND HOW TO REPRESENT IT IN A PICTURE.\n\nLet the dark and gloomy air be seen buffeted by the rush of contrary\nwinds and dense from the continued rain mingled with hail and\nbearing hither and thither an infinite number of branches torn from\nthe trees and mixed with numberless leaves. All round may be seen\nvenerable trees, uprooted and stripped by the fury of the winds; and\nfragments of mountains, already scoured bare by the torrents,\nfalling into those torrents and choking their valleys till the\nswollen rivers overflow and submerge the wide lowlands and their\ninhabitants. Again, you might have seen on many of the hill-tops\nterrified animals of different kinds, collected together and subdued\nto tameness, in company with men and women who had fled there with\ntheir children. The waters which covered the fields, with their\nwaves were in great part strewn with tables, bedsteads, boats and\nvarious other contrivances made from necessity and the fear of\ndeath, on which were men and women with their children amid sounds\nof lamentation and weeping, terrified by the fury of the winds which\nwith their tempestuous violence rolled the waters under and over and\nabout the bodies of the drowned. Nor was there any object lighter\nthan the water which was not covered with a variety of animals\nwhich, having come to a truce, stood together in a frightened\ncrowd--among them wolves, foxes, snakes and others--fleing from\ndeath. And all the waters dashing on their shores seemed to be\nbattling them with the blows of drowned bodies, blows which killed\nthose in whom any life remained [19]. You might have seen\nassemblages of men who, with weapons in their hands, defended the\nsmall spots that remained to them against lions, wolves and beasts\nof prey who sought safety there. Ah! what dreadful noises were heard\nin the air rent by the fury of the thunder and the lightnings it\nflashed forth, which darted from the clouds dealing ruin and\nstriking all that opposed its course. Ah! how many you might have\nseen closing their ears with their hands to shut out the tremendous\nsounds made in the darkened air by the raging of the winds mingling\nwith the rain, the thunders of heaven and the fury of the\nthunder-bolts. Others were not content with shutting their eyes, but\nlaid their hands one over the other to cover them the closer that\nthey might not see the cruel slaughter of the human race by the\nwrath of God. Ah! how many laments! and how many in their terror\nflung themselves from the rocks! Huge branches of great oaks loaded\nwith men were seen borne through the air by the impetuous fury of\nthe winds. How many were the boats upset, some entire, and some\nbroken in pieces, on the top of people labouring to escape with\ngestures and actions of grief foretelling a fearful death. Others,\nwith desperate act, took their own lives, hopeless of being able to\nendure such suffering; and of these, some flung themselves from\nlofty rocks, others strangled themselves with their own hands, other\nseized their own children and violently slew them at a blow; some\nwounded and killed themselves with their own weapons; others,\nfalling on their knees recommended themselves to God. Ah! how many\nmothers wept over their drowned sons, holding them upon their knees,\nwith arms raised spread out towards heaven and with words and\nvarious threatening gestures, upbraiding the wrath of the gods.\nOthers with clasped hands and fingers clenched gnawed them and\ndevoured them till they bled, crouching with their breast down on\ntheir knees in their intense and unbearable anguish. Herds of\nanimals were to be seen, such as horses, oxen, goats and swine\nalready environed by the waters and left isolated on the high peaks\nof the mountains, huddled together, those in the middle climbing to\nthe top and treading on the others, and fighting fiercely\nthemselves; and many would die for lack of food. Already had the\nbirds begun to settle on men and on other animals, finding no land\nuncovered which was not occupied by living beings, and already had\nfamine, the minister of death, taken the lives of the greater number\nof the animals, when the dead bodies, now fermented, where leaving\nthe depth of the waters and were rising to the top. Among the\nbuffeting waves, where they were beating one against the other, and,\nlike as balls full of air, rebounded from the point of concussion,\nthese found a resting place on the bodies of the dead. And above\nthese judgements, the air was seen covered with dark clouds, riven\nby the forked flashes of the raging bolts of heaven, lighting up on\nall sides the depth of the gloom.\n\nThe motion of the air is seen by the motion of the dust thrown up by\nthe horse's running and this motion is as swift in again filling up\nthe vacuum left in the air which enclosed the horse, as he is rapid\nin passing away from the air.\n\nPerhaps it will seem to you that you may reproach me with having\nrepresented the currents made through the air by the motion of the\nwind notwithstanding that the wind itself is not visible in the air.\nTo this I must answer that it is not the motion of the wind but only\nthe motion of the things carried along by it which is seen in the\nair.\n\nTHE DIVISIONS. [Footnote 76: These observations, added at the bottom\nof the page containing the full description of the doluge seem to\nindicate that it was Leonardo's intention to elaborate the subject\nstill farther in a separate treatise.]\n\nDarkness, wind, tempest at sea, floods of water, forests on fire,\nrain, bolts from heaven, earthquakes and ruins of mountains,\noverthrow of cities [Footnote 81: _Spianamenti di citta_ (overthrow\nof cities). A considerable number of drawings in black chalk, at\nWindsor, illustrate this catastrophe. Most of them are much rubbed;\none of the least injured is reproduced at Pl. XXXIX. Compare also\nthe pen and ink sketch Pl. XXXVI.].\n\nWhirlwinds which carry water [spouts] branches of trees, and men\nthrough the air.\n\nBoughs stripped off by the winds, mingling by the meeting of the\nwinds, with people upon them.\n\nBroken trees loaded with people.\n\nShips broken to pieces, beaten on rocks.\n\nFlocks of sheep. Hail stones, thunderbolts, whirlwinds.\n\nPeople on trees which are unable to to support them; trees and\nrocks, towers and hills covered with people, boats, tables, troughs,\nand other means of floating. Hills covered with men, women and\nanimals; and lightning from the clouds illuminating every thing.\n\n[Footnote: This chapter, which, with the next one, is written on a\nloose sheet, seems to be the passage to which one of the compilers\nof the Vatican copy alluded when he wrote on the margin of fol. 36:\n\"_Qua mi ricordo della mirabile discritione del Diluuio dello\nautore._\" It is scarcely necessary to point out that these chapters\nare among those which have never before been published. The\ndescription in No. 607 may be regarded as a preliminary sketch for\nthis one. As the MS. G. (in which it is to be found) must be\nattributed to the period of about 1515 we may deduce from it the\napproximate date of the drawings on Pl. XXXIV, XXXV, Nos. 2 and 3,\nXXXVI and XXXVII, since they obviously belong to this text. The\ndrawings No. 2 on Pl. XXXV are, in the original, side by side with\nthe text of No. 608; lines 57 to 76 are shown in the facsimile. In\nthe drawing in Indian ink given on Pl. XXXIV we see Wind-gods in the\nsky, corresponding to the allusion to Aeolus in No. 607 1.\n15.-Plates XXXVI and XXXVII form one sheet in the original. The\ntexts reproduced on these Plates have however no connection with the\nsketches, excepting the sketches of clouds on the right hand side.\nThese texts are given as No. 477. The group of small figures on Pl.\nXXXVII, to the left, seems to be intended for a '_congregatione\nd'uomini._' See No. 608, 1. 19.]\n\n609.\n\nDESCRIPTION OF THE DELUGE.\n\nLet there be first represented the summit of a rugged mountain with\nvalleys surrounding its base, and on its sides let the surface of\nthe soil be seen to slide, together with the small roots of the\nbushes, denuding great portions of the surrounding rocks. And\ndescending ruinous from these precipices in its boisterous course,\nlet it dash along and lay bare the twisted and gnarled roots of\nlarge trees overthrowing their roots upwards; and let the mountains,\nas they are scoured bare, discover the profound fissures made in\nthem by ancient earthquakes. The base of the mountains may be in\ngreat part clothed and covered with ruins of shrubs, hurled down\nfrom the sides of their lofty peaks, which will be mixed with mud,\nroots, boughs of trees, with all sorts of leaves thrust in with the\nmud and earth and stones. And into the depth of some valley may have\nfallen the fragments of a mountain forming a shore to the swollen\nwaters of its river; which, having already burst its banks, will\nrush on in monstrous waves; and the greatest will strike upon and\ndestroy the walls of the cities and farmhouses in the valley [14].\nThen the ruins of the high buildings in these cities will throw up a\ngreat dust, rising up in shape like smoke or wreathed clouds against\nthe falling rain; But the swollen waters will sweep round the pool\nwhich contains them striking in eddying whirlpools against the\ndifferent obstacles, and leaping into the air in muddy foam; then,\nfalling back, the beaten water will again be dashed into the air.\nAnd the whirling waves which fly from the place of concussion, and\nwhose impetus moves them across other eddies going in a contrary\ndirection, after their recoil will be tossed up into the air but\nwithout dashing off from the surface. Where the water issues from\nthe pool the spent waves will be seen spreading out towards the\noutlet; and there falling or pouring through the air and gaining\nweight and impetus they will strike on the water below piercing it\nand rushing furiously to reach its depth; from which being thrown\nback it returns to the surface of the lake, carrying up the air that\nwas submerged with it; and this remains at the outlet in foam\nmingled with logs of wood and other matters lighter than water.\nRound these again are formed the beginnings of waves which increase\nthe more in circumference as they acquire more movement; and this\nmovement rises less high in proportion as they acquire a broader\nbase and thus they are less conspicuous as they die away. But if\nthese waves rebound from various objects they then return in direct\nopposition to the others following them, observing the same law of\nincrease in their curve as they have already acquired in the\nmovement they started with. The rain, as it falls from the clouds is\nof the same colour as those clouds, that is in its shaded side;\nunless indeed the sun's rays should break through them; in that case\nthe rain will appear less dark than the clouds. And if the heavy\nmasses of ruin of large mountains or of other grand buildings fall\ninto the vast pools of water, a great quantity will be flung into\nthe air and its movement will be in a contrary direction to that of\nthe object which struck the water; that is to say: The angle of\nreflection will be equal to the angle of incidence. Of the objects\ncarried down by the current, those which are heaviest or rather\nlargest in mass will keep farthest from the two opposite shores. The\nwater in the eddies revolves more swiftly in proportion as it is\nnearer to their centre. The crests of the waves of the sea tumble to\ntheir bases falling with friction on the bubbles of their sides; and\nthis friction grinds the falling water into minute particles and\nthis being converted into a dense mist, mingles with the gale in the\nmanner of curling smoke and wreathing clouds, and at last it, rises\ninto the air and is converted into clouds. But the rain which falls\nthrough the atmosphere being driven and tossed by the winds becomes\nrarer or denser according to the rarity or density of the winds that\nbuffet it, and thus there is generated in the atmosphere a moisture\nformed of the transparent particles of the rain which is near to the\neye of the spectator. The waves of the sea which break on the slope\nof the mountains which bound it, will foam from the velocity with\nwhich they fall against these hills; in rushing back they will meet\nthe next wave as it comes and and after a loud noise return in a\ngreat flood to the sea whence they came. Let great numbers of\ninhabitants--men and animals of all kinds--be seen driven [54] by\nthe rising of the deluge to the peaks of the mountains in the midst\nof the waters aforesaid.\n\nThe wave of the sea at Piombino is all foaming water. [Footnote 55.\n56: These two lines are written below the bottom sketch on Pl. XXXV,\n3. The MS. Leic. being written about the year 1510 or later, it does\nnot seem to me to follow that the sketches must have been made at\nPiombino, where Leonardo was in the year 1502 and possibly returned\nthere subsequently (see Vol. II. Topographical notes).]\n\nOf the water which leaps up from the spot where great masses fall on\nits surface. Of the winds of Piombino at Piombino. Eddies of wind\nand rain with boughs and shrubs mixed in the air. Emptying the boats\nof the rain water.\n\n[Footnote: The sketches on Pl. XXXV 3 stand by the side of lines 14\nto 54.]\n\nOf depicting natural phenomena (610. 611).\n\n610.\n\nThe tremendous fury of the wind driven by the falling in of the\nhills on the caves within--by the falling of the hills which served\nas roofs to these caverns.\n\nA stone flung through the air leaves on the eye which sees it the\nimpression of its motion, and the same effect is produced by the\ndrops of water which fall from the clouds when it [16] rains.\n\n[17] A mountain falling on a town, will fling up dust in the form of\nclouds; but the colour of this dust will differ from that of the\nclouds. Where the rain is thickest let the colour of the dust be\nless conspicuous and where the dust is thickest let the rain be less\nconspicuous. And where the rain is mingled with the wind and with\nthe dust the clouds created by the rain must be more transparent\nthan those of dust [alone]. And when flames of fire are mingled with\nclouds of smoke and water very opaque and dark clouds will be formed\n[Footnote 26-28: Compare Pl. XL, 1--the drawing in Indian ink on the\nleft hand side, which seems to be a reminiscence of his observations\nof an eruption (see his remarks on Mount Etna in Vol II).]. And the\nrest of this subject will be treated in detail in the book on\npainting.\n\n[Footnote: See the sketches and text on Pl. XXXVIII, No. 1. Lines\n1-16 are there given on the left hand side, 17-30 on the right. The\nfour lines at the bottom on the right are given as No. 472. Above\nthese texts, which are written backwards, there are in the original\nsixteen lines in a larger writing from left to right, but only half\nof this is here visible. They treat of the physical laws of motion\nof air and water. It does not seem to me that there is any reason\nfor concluding that this writing from left to right is spurious.\nCompare with it the facsimile of the rough copy of Leonardo's letter\nto Ludovico il Moro in Vol. II.]\n\n611.\n\nPeople were to be seen eagerly embarking victuals on various kinds\nof hastily made barks. But little of the waves were visible in those\nplaces where the dark clouds and rain were reflected.\n\nBut where the flashes caused by the bolts of heaven were reflected,\nthere were seen as many bright spots, caused by the image of the\nflashes, as there were waves to reflect them to the eye of the\nspectator.\n\nThe number of the images produced by the flash of lightning on the\nwaves of the water were multiplied in proportion to the distance of\nthe spectator's eye.\n\nSo also the number of the images was diminished in proportion as\nthey were nearer the eye which saw them [Footnote 22. 23: _Com'e\nprovato_. See Vol. II, Nos. 874-878 and 892-901], as it has been\nproved in the definition of the luminosity of the moon, and of our\nmarine horizon when the sun's rays are reflected in it and the eye\nwhich receives the reflection is remote from the sea.\n\nVI.\n\nTHE ARTIST'S MATERIALS.\n\nOf chalk and paper (612--617).\n\n612.\n\nTo make points [crayons] for colouring dry. Temper with a little wax\nand do not dry it; which wax you must dissolve with water: so that\nwhen the white lead is thus tempered, the water being distilled, may\ngo off in vapour and the wax may remain; you will thus make good\ncrayons; but you must know that the colours must be ground with a\nhot stone.\n\n613.\n\nChalk dissolves in wine and in vinegar or in aqua fortis and can be\nrecombined with gum.\n\n614.\n\nPAPER FOR DRAWING UPON IN BLACK BY THE AID OF YOUR SPITTLE.\n\nTake powdered gall nuts and vitriol, powder them and spread them on\npaper like a varnish, then write on it with a pen wetted with\nspittle and it will turn as black as ink.\n\n615.\n\nIf you want to make foreshortened letters stretch the paper in a\ndrawing frame and then draw your letters and cut them out, and make\nthe sunbeams pass through the holes on to another stretched paper,\nand then fill up the angles that are wanting.\n\n616.\n\nThis paper should be painted over with candle soot tempered with\nthin glue, then smear the leaf thinly with white lead in oil as is\ndone to the letters in printing, and then print in the ordinary way.\nThus the leaf will appear shaded in the hollows and lighted on the\nparts in relief; which however comes out here just the contrary.\n\n[Footnote: This text, which accompanies a facsimile impression of a\nleaf of sage, has already been published in the _Saggio delle Opere\ndi L. da Vinci_, Milano 1872, p. 11. G. GOVI observes on this\npassage: \"_Forse aveva egli pensato ancora a farsi un erbario, od\nalmeno a riprodurre facilmente su carta le forme e i particolari\ndelle foglie di diverse piante; poiche (modificando un metodo che\nprobabilmente gli eia stato insegnato da altri, e che piu tardi si\nlegge ripetuto in molti ricettarii e libri di segreti), accanto a\nuna foglia di Salvia impressa in nero su carta bianca, lascio\nscritto: Questa carta ...\n\nErano i primi tentativi di quella riproduzione immediata delle parti\nvegetali, che poi sotto il nome d'Impressione Naturale, fu condotta\na tanta perfezione in questi ultimi tempi dal signor de Hauer e da\naltri_.\"]\n\n617.\n\nVery excellent will be a stiff white paper, made of the usual\nmixture and filtered milk of an herb called calves foot; and when\nthis paper is prepared and damped and folded and wrapped up it may\nbe mixed with the mixture and thus left to dry; but if you break it\nbefore it is moistened it becomes somewhat like the thin paste\ncalled _lasagne_ and you may then damp it and wrap it up and put it\nin the mixture and leave it to dry; or again this paper may be\ncovered with stiff transparent white and _sardonio_ and then damped\nso that it may not form angles and then covered up with strong\ntransparent size and as soon as it is firm cut it two fingers, and\nleave it to dry; again you may make stiff cardboard of _sardonio_\nand dry it and then place it between two sheets of papyrus and break\nit inside with a wooden mallet with a handle and then open it with\ncare holding the lower sheet of paper flat and firm so that the\nbroken pieces be not separated; then have a sheet of paper covered\nwith hot glue and apply it on the top of all these pieces and let\nthem stick fast; then turn it upside down and apply transparent size\nseveral times in the spaces between the pieces, each time pouring in\nfirst some black and then some stiff white and each time leaving it\nto dry; then smooth it and polish it.\n\nOn the preparation and use of colours (618-627).\n\n618.\n\nTo make a fine green take green and mix it with bitumen and you will\nmake the shadows darker. Then, for lighter [shades] green with\nyellow ochre, and for still lighter green with yellow, and for the\nhigh lights pure yellow; then mix green and turmeric together and\nglaze every thing with it. To make a fine red take cinnabar or red\nchalk or burnt ochre for the dark shadows and for the lighter ones\nred chalk and vermilion and for the lights pure vermilion and then\nglaze with fine lake. To make good oil for painting. One part of\noil, one of the first refining and one of the second.\n\n619.\n\nUse black in the shadow, and in the lights white, yellow, green,\nvermilion and lake. Medium shadows; take the shadow as above and mix\nit with the flesh tints just alluded to, adding to it a little\nyellow and a little green and occasionally some lake; for the\nshadows take green and lake for the middle shades.\n\n[Footnote 618 and 619: If we may judge from the flourishes with\nwhich the writing is ornamented these passages must have been\nwritten in Leonardo's youth.]\n\n620.\n\nYou can make a fine ochre by the same method as you use to make\nwhite.\n\n621.\n\nA FINE YELLOW.\n\nDissolve realgar with one part of orpiment, with aqua fortis.\n\nWHITE.\n\nPut the white into an earthen pot, and lay it no thicker than a\nstring, and let it stand in the sun undisturbed for 2 days; and in\nthe morning when the sun has dried off the night dews.\n\n622.\n\nTo make reddish black for flesh tints take red rock crystals from\nRocca Nova or garnets and mix them a little; again armenian bole is\ngood in part.\n\n623.\n\nThe shadow will be burnt ,terra-verte'.\n\n624.\n\nTHE PROPORTIONS OF COLOURS.\n\nIf one ounce of black mixed with one ounce of white gives a certain\nshade of darkness, what shade of darkness will be produced by 2\nounces of black to 1 ounce of white?\n\n625.\n\nRemix black, greenish yellow and at the end blue.\n\n626.\n\nVerdigris with aloes, or gall or turmeric makes a fine green and so\nit does with saffron or burnt orpiment; but I doubt whether in a\nshort time they will not turn black. Ultramarine blue and glass\nyellow mixed together make a beautiful green for fresco, that is\nwall-painting. Lac and verdigris make a good shadow for blue in oil\npainting.\n\n627.\n\nGrind verdigris many times coloured with lemon juice and keep it\naway from yellow (?).\n\nOf preparing the panel.\n\n628.\n\nTO PREPARE A PANEL FOR PAINTING ON.\n\nThe panel should be cypress or pear or service-tree or walnut. You\nmust coat it over with mastic and turpentine twice distilled and\nwhite or, if you like, lime, and put it in a frame so that it may\nexpand and shrink according to its moisture and dryness. Then give\nit [a coat] of aqua vitae in which you have dissolved arsenic or\n[corrosive] sublimate, 2 or 3 times. Then apply boiled linseed oil\nin such a way as that it may penetrate every part, and before it is\ncold rub it well with a cloth to dry it. Over this apply liquid\nvarnish and white with a stick, then wash it with urine when it is\ndry, and dry it again. Then pounce and outline your drawing finely\nand over it lay a priming of 30 parts of verdigris with one of\nverdigris with two of yellow.\n\n[Footnote: M. RAVAISSON'S reading varies from mine in the following\npassages:\n\n1._opero allor [?] bo [alloro?]_ = \"_ou bien de [laurier]_.\"\n\n6. _fregalo bene con un panno_. He reads _pane_ for _panno_ and\nrenders it. \"_Frotte le bien avec un pain de facon [jusqu'a ce]\nqu'il_\" etc.\n\n7. _colla stecca po laua_. He reads \"_polacca_\" = \"_avec le couteau\nde bois [?] polonais [?]_.\"]\n\nThe preparation of oils (629--634).\n\n629.\n\nOIL.\n\nMake some oil of mustard seed; and if you wish to make it with\ngreater ease mix the ground seeds with linseed oil and put it all\nunder the press.\n\n630.\n\nTO REMOVE THE SMELL OF OIL.\n\nTake the rank oil and put ten pints into a jar and make a mark on\nthe jar at the height of the oil; then add to it a pint of vinegar\nand make it boil till the oil has sunk to the level of the mark and\nthus you will be certain that the oil is returned to its original\nquantity and the vinegar will have gone off in vapour, carrying with\nit the evil smell; and I believe you may do the same with nut oil or\nany other oil that smells badly.\n\n631.\n\nSince walnuts are enveloped in a thin rind, which partakes of the\nnature of ..., if you do not remove it when you make the oil from\nthem, this skin tinges the oil, and when you work with it this skin\nseparates from the oil and rises to the surface of the painting, and\nthis is what makes it change.\n\n632.\n\nTO RESTORE OIL COLOURS THAT HAVE BECOME DRY.\n\nIf you want to restore oil colours that have become dry keep them\nsoaking in soft soap for a night and, with your finger, mix them up\nwith the soft soap; then pour them into a cup and wash them with\nwater, and in this way you can restore colours that have got dry.\nBut take care that each colour has its own vessel to itself adding\nthe colour by degrees as you restore it and mind that they are\nthoroughly softened, and when you wish to use them for tempera wash\nthem five and six times with spring water, and leave them to settle;\nif the soft soap should be thick with any of the colours pass it\nthrough a filter. [Footnote: The same remark applies to these\nsections as to No. 618 and 619.]\n\n633.\n\nOIL.\n\nMustard seed pounded with linseed oil.\n\n634.\n\n... outside the bowl 2 fingers lower than the level of the oil, and\npass it into the neck of a bottle and let it stand and thus all the\noil will separate from this milky liquid; it will enter the bottle\nand be as clear as crystal; and grind your colours with this, and\nevery coarse or viscid part will remain in the liquid. You must know\nthat all the oils that have been created in seads or fruits are\nquite clear by nature, and the yellow colour you see in them only\ncomes of your not knowing how to draw it out. Fire or heat by its\nnature has the power to make them acquire colour. See for example\nthe exudation or gums of trees which partake of the nature of rosin;\nin a short time they harden because there is more heat in them than\nin oil; and after some time they acquire a certain yellow hue\ntending to black. But oil, not having so much heat does not do so;\nalthough it hardens to some extent into sediment it becomes finer.\nThe change in oil which occurs in painting proceeds from a certain\nfungus of the nature of a husk which exists in the skin which covers\nthe nut, and this being crushed along with the nuts and being of a\nnature much resembling oil mixes with it; it is of so subtle a\nnature that it combines with all colours and then comes to the\nsurface, and this it is which makes them change. And if you want the\noil to be good and not to thicken, put into it a little camphor\nmelted over a slow fire and mix it well with the oil and it will\nnever harden.\n\n[Footnote: The same remark applies to these sections as to No. 618\nand 619.]\n\nOn varnishes [or powders] (635-637).\n\n635.\n\nVARNISH [OR POWDER].\n\nTake cypress [oil] and distil it and have a large pitcher, and put\nin the extract with so much water as may make it appear like amber,\nand cover it tightly so that none may evaporate. And when it is\ndissolved you may add in your pitcher as much of the said solution,\nas shall make it liquid to your taste. And you must know that amber\nis the gum of the cypress-tree.\n\nVARNISH [OR POWDER].\n\nAnd since varnish [powder] is the resin of juniper, if you distil\njuniper you can dissolve the said varnish [powder] in the essence,\nas explained above.\n\n636.\n\nVARNISH [OR POWDER].\n\nNotch a juniper tree and give it water at the roots, mix the liquor\nwhich exudes with nut-oil and you will have a perfect varnish\n[powder], made like amber varnish [powder], fine and of the best\nquality make it in May or April.\n\n637.\n\nVARNISH [OR POWDER].\n\nMercury with Jupiter and Venus,--a paste made of these must be\ncorrected by the mould (?) continuously, until Mercury separates\nitself entirely from Jupiter and Venus. [Footnote: Here, and in No.\n641 _Mercurio_ seems to mean quicksilver, _Giove_ stands for iron,\n_Venere_ for copper and _Saturno_ for lead.]\n\nOn chemical materials (638-650).\n\n638.\n\nNote how aqua vitae absorbs into itself all the colours and smells\nof flowers. If you want to make blue put iris flowers into it and\nfor red solanum berries (?)\n\n639.\n\nSalt may be made from human excrement burnt and calcined and made\ninto lees, and dried by a slow fire, and all dung in like manner\nyields salt, and these salts when distilled are very pungent.\n\n640.\n\nSea water filtered through mud or clay, leaves all its saltness in\nit. Woollen stuffs placed on board ship absorb fresh water. If sea\nwater is distilled under a retort it becomes of the first excellence\nand any one who has a little stove in his kitchen can, with the same\nwood as he cooks with, distil a great quantity of water if the\nretort is a large one.\n\n641.\n\nMOULD(?).\n\nThe mould (?) may be of Venus, or of Jupiter and Saturn and placed\nfrequently in the fire. And it should be worked with fine emery and\nthe mould (?) should be of Venus and Jupiter impasted over (?)\nVenus. But first you will test Venus and Mercury mixed with Jove,\nand take means to cause Mercury to disperse; and then fold them well\ntogether so that Venus or Jupiter be connected as thinly as\npossible.\n\n[Footnote: See the note to 637.]\n\n642.\n\nNitre, vitriol, cinnabar, alum, salt ammoniac, sublimated mercury,\nrock salt, alcali salt, common salt, rock alum, alum schist (?),\narsenic, sublimate, realgar, tartar, orpiment, verdegris.\n\n643.\n\nPitch four ounces virgin wax, four ounces incense, two ounces oil of\nroses one ounce.\n\n644.\n\nFour ounces virgin wax, four ounces Greek pitch, two ounces incense,\none ounce oil of roses, first melt the wax and oil then the Greek\npitch then the other things in powder.\n\n645.\n\nVery thin glass may be cut with scissors and when placed over inlaid\nwork of bone, gilt, or stained of other colours you can saw it\nthrough together with the bone and then put it together and it will\nretain a lustre that will not be scratched nor worn away by rubbing\nwith the hand.\n\n646.\n\nTO DILUTE WHITE WINE AND MAKE IT PURPLE.\n\nPowder gall nuts and let this stand 8 days in the white wine; and in\nthe same way dissolve vitriol in water, and let the water stand and\nsettle very clear, and the wine likewise, each by itself, and strain\nthem well; and when you dilute the white wine with the water the\nwine will become red.\n\n647.\n\nPut marcasite into aqua fortis and if it turns green, know that it\nhas copper in it. Take it out with saltpetre and soft soap.\n\n648.\n\nA white horse may have the spots removed with the Spanish haematite\nor with aqua fortis or with ... Removes the black hair on a white\nhorse with the singeing iron. Force him to the ground.\n\n649.\n\nFIRE.\n\nIf you want to make a fire which will set a hall in a blaze without\ninjury do this: first perfume the hall with a dense smoke of incense\nor some other odoriferous substance: It is a good trick to play. Or\nboil ten pounds of brandy to evaporate, but see that the hall is\ncompletely closed and throw up some powdered varnish among the fumes\nand this powder will be supported by the smoke; then go into the\nroom suddenly with a lighted torch and at once it will be in a\nblaze.\n\n650.\n\nFIRE.\n\nTake away that yellow surface which covers oranges and distill them\nin an alembic, until the distillation may be said to be perfect.\n\nFIRE.\n\nClose a room tightly and have a brasier of brass or iron with fire\nin it and sprinkle on it two pints of aqua vitae, a little at a\ntime, so that it may be converted into smoke. Then make some one\ncome in with a light and suddenly you will see the room in a blaze\nlike a flash of lightning, and it will do no harm to any one.\n\nVII.\n\nPHILOSOPHY AND HISTORY OF THE ART OF PAINTING.\n\nThe relation of art and nature (651. 652).\n\n651.\n\nWhat is fair in men, passes away, but not so in art.\n\n652.\n\nHE WHO DESPISES PAINTING LOVES NEITHER PHILOSOPHY NOR NATURE.\n\nIf you condemn painting, which is the only imitator of all visible\nworks of nature, you will certainly despise a subtle invention which\nbrings philosophy and subtle speculation to the consideration of the\nnature of all forms--seas and plains, trees, animals, plants and\nflowers--which are surrounded by shade and light. And this is true\nknowledge and the legitimate issue of nature; for painting is born\nof nature--or, to speak more correctly, we will say it is the\ngrandchild of nature; for all visible things are produced by nature,\nand these her children have given birth to painting. Hence we may\njustly call it the grandchild of nature and related to God.\n\nPainting is superior to poetry (653. 654).\n\n653.\n\nTHAT PAINTING SURPASSES ALL HUMAN WORKS BY THE SUBTLE CONSIDERATIONS\nBELONGING TO IT.\n\nThe eye, which is called the window of the soul, is the principal\nmeans by which the central sense can most completely and abundantly\nappreciate the infinite works of nature; and the ear is the second,\nwhich acquires dignity by hearing of the things the eye has seen. If\nyou, historians, or poets, or mathematicians had not seen things\nwith your eyes you could not report of them in writing. And if you,\n0 poet, tell a story with your pen, the painter with his brush can\ntell it more easily, with simpler completeness and less tedious to\nbe understood. And if you call painting dumb poetry, the painter may\ncall poetry blind painting. Now which is the worse defect? to be\nblind or dumb? Though the poet is as free as the painter in the\ninvention of his fictions they are not so satisfactory to men as\npaintings; for, though poetry is able to describe forms, actions and\nplaces in words, the painter deals with the actual similitude of the\nforms, in order to represent them. Now tell me which is the nearer\nto the actual man: the name of man or the image of the man. The name\nof man differs in different countries, but his form is never changed\nbut by death.\n\n654.\n\nAnd if the poet gratifies the sense by means of the ear, the painter\ndoes so by the eye--the worthier sense; but I will say no more of\nthis but that, if a good painter represents the fury of a battle,\nand if a poet describes one, and they are both together put before\nthe public, you will see where most of the spectators will stop, to\nwhich they will pay most attention, on which they will bestow most\npraise, and which will satisfy them best. Undoubtedly painting being\nby a long way the more intelligible and beautiful, will please most.\nWrite up the name of God [Christ] in some spot and setup His image\nopposite and you will see which will be most reverenced. Painting\ncomprehends in itself all the forms of nature, while you have\nnothing but words, which are not universal as form is, and if you\nhave the effects of the representation, we have the representation\nof the effects. Take a poet who describes the beauty of a lady to\nher lover and a painter who represents her and you will see to which\nnature guides the enamoured critic. Certainly the proof should be\nallowed to rest on the verdict of experience. You have ranked\npainting among the mechanical arts but, in truth, if painters were\nas apt at praising their own works in writing as you are, it would\nnot lie under the stigma of so base a name. If you call it\nmechanical because it is, in the first place, manual, and that it is\nthe hand which produces what is to be found in the imagination, you\ntoo writers, who set down manually with the pen what is devised in\nyour mind. And if you say it is mechanical because it is done for\nmoney, who falls into this error--if error it can be called--more\nthan you? If you lecture in the schools do you not go to whoever\npays you most? Do you do any work without pay? Still, I do not say\nthis as blaming such views, for every form of labour looks for its\nreward. And if a poet should say: \"I will invent a fiction with a\ngreat purpose,\" the painter can do the same, as Apelles painted\nCalumny. If you were to say that poetry is more eternal, I say the\nworks of a coppersmith are more eternal still, for time preserves\nthem longer than your works or ours; nevertheless they have not much\nimagination [29]. And a picture, if painted on copper with enamel\ncolours may be yet more permanent. We, by our arts may be called the\ngrandsons of God. If poetry deals with moral philosophy, painting\ndeals with natural philosophy. Poetry describes the action of the\nmind, painting considers what the mind may effect by the motions [of\nthe body]. If poetry can terrify people by hideous fictions,\npainting can do as much by depicting the same things in action.\nSupposing that a poet applies himself to represent beauty, ferocity,\nor a base, a foul or a monstrous thing, as against a painter, he may\nin his ways bring forth a variety of forms; but will the painter not\nsatisfy more? are there not pictures to be seen, so like the actual\nthings, that they deceive men and animals?\n\nPainting is superior to sculpture (655. 656).\n\n655.\n\nTHAT SCULPTURE IS LESS INTELLECTUAL THAN PAINTING, AND LACKS MANY\nCHARACTERISTICS OF NATURE.\n\nI myself, having exercised myself no less in sculpture than in\npainting and doing both one and the other in the same degree, it\nseems to me that I can, without invidiousness, pronounce an opinion\nas to which of the two is of the greatest merit and difficulty and\nperfection. In the first place sculpture requires a certain light,\nthat is from above, a picture carries everywhere with it its own\nlight and shade. Thus sculpture owes its importance to light and\nshade, and the sculptor is aided in this by the nature, of the\nrelief which is inherent in it, while the painter whose art\nexpresses the accidental aspects of nature, places his effects in\nthe spots where nature must necessarily produce them. The sculptor\ncannot diversify his work by the various natural colours of objects;\npainting is not defective in any particular. The sculptor when he\nuses perspective cannot make it in any way appear true; that of the\npainter can appear like a hundred miles beyond the picture itself.\nTheir works have no aerial perspective whatever, they cannot\nrepresent transparent bodies, they cannot represent luminous bodies,\nnor reflected lights, nor lustrous bodies--as mirrors and the like\npolished surfaces, nor mists, nor dark skies, nor an infinite number\nof things which need not be told for fear of tedium. As regards the\npower of resisting time, though they have this resistance [Footnote\n19: From what is here said as to painting on copper it is very\nevident that Leonardo was not acquainted with the method of painting\nin oil on thin copper plates, introduced by the Flemish painters of\nthe XVIIth century. J. LERMOLIEFF has already pointed out that in\nthe various collections containing pictures by the great masters of\nthe Italian Renaissance, those painted on copper (for instance the\nfamous reading Magdalen in the Dresden Gallery) are the works of a\nmuch later date (see _Zeitschrift fur bildende Kunst_. Vol. X pg.\n333, and: _Werke italienischer Master in den Galerien von Munchen,\nDresden und Berlin_. Leipzig 1880, pg. 158 and 159.)--Compare No.\n654, 29.], a picture painted on thick copper covered with white\nenamel on which it is painted with enamel colours and then put into\nthe fire again and baked, far exceeds sculpture in permanence. It\nmay be said that if a mistake is made it is not easy to remedy it;\nit is but a poor argument to try to prove that a work be the nobler\nbecause oversights are irremediable; I should rather say that it\nwill be more difficult to improve the mind of the master who makes\nsuch mistakes than to repair the work he has spoilt.\n\n656.\n\nWe know very well that a really experienced and good painter will\nnot make such mistakes; on the contrary, with sound rules he will\nremove so little at a time that he will bring his work to a good\nissue. Again the sculptor if working in clay or wax, can add or\nreduce, and when his model is finished it can easily be cast in\nbronze, and this is the last operation and is the most permanent\nform of sculpture. Inasmuch as that which is merely of marble is\nliable to ruin, but not bronze. Hence a painting done on copper\nwhich as I said of painting may be added to or altered, resembles\nsculpture in bronze, which, having first been made in wax could then\nbe altered or added to; and if sculpture in bronze is durable, this\nwork in copper and enamel is absolutely imperishable. Bronze is but\ndark and rough after all, but this latter is covered with various\nand lovely colours in infinite variety, as has been said above; or\nif you will have me only speak of painting on panel, I am content to\npronounce between it and sculpture; saying that painting is the more\nbeautiful and the more imaginative and the more copious, while\nsculpture is the more durable but it has nothing else. Sculpture\nshows with little labour what in painting appears a miraculous thing\nto do; to make what is impalpable appear palpable, flat objects\nappear in relief, distant objects seem close. In fact painting is\nadorned with infinite possibilities which sculpture cannot command.\n\nAphorisms (657-659).\n\n657.\n\nOF PAINTING.\n\nMen and words are ready made, and you, O Painter, if you do not know\nhow to make your figures move, are like an orator who knows not how\nto use his words.\n\n658.\n\nAs soon as the poet ceases to represent in words what exists in\nnature, he in fact ceases to resemble the painter; for if the poet,\nleaving such representation, proceeds to describe the flowery and\nflattering speech of the figure, which he wishes to make the\nspeaker, he then is an orator and no longer a poet nor a painter.\nAnd if he speaks of the heavens he becomes an astrologer, and\nphilosopher; and a theologian, if he discourses of nature or God.\nBut, if he restricts himself to the description of objects, he would\nenter the lists against the painter, if with words he could satisfy\nthe eye as the painter does.\n\n659.\n\nThough you may be able to tell or write the exact description of\nforms, the painter can so depict them that they will appear alive,\nwith the shadow and light which show the expression of a face; which\nyou cannot accomplish with the pen though it can be achieved by the\nbrush.\n\nOn the history of painting (660. 661).\n\n660.\n\nTHAT PAINTING DECLINES AND DETERIORATES FROM AGE TO AGE, WHEN\nPAINTERS HAVE NO OTHER STANDARD THAN PAINTING ALREADY DONE.\n\nHence the painter will produce pictures of small merit if he takes\nfor his standard the pictures of others. But if he will study from\nnatural objects he will bear good fruit; as was seen in the painters\nafter the Romans who always imitated each other and so their art\nconstantly declined from age to age. After these came Giotto the\nFlorentine who--not content with imitating the works of Cimabue his\nmaster--being born in the mountains and in a solitude inhabited only\nby goats and such beasts, and being guided by nature to his art,\nbegan by drawing on the rocks the movements of the goats of which he\nwas keeper. And thus he began to draw all the animals which were to\nbe found in the country, and in such wise that after much study he\nexcelled not only all the masters of his time but all those of many\nbygone ages. Afterwards this art declined again, because everyone\nimitated the pictures that were already done; thus it went on from\ncentury to century until Tomaso, of Florence, nicknamed Masaccio,\nshowed by his perfect works how those who take for their standard\nany one but nature--the mistress of all masters--weary themselves in\nvain. And, I would say about these mathematical studies that those\nwho only study the authorities and not the works of nature are\ndescendants but not sons of nature the mistress of all good authors.\nOh! how great is the folly of those who blame those who learn from\nnature [Footnote 22: _lasciando stare li autori_. In this\nobservation we may detect an indirect evidence that Leonardo\nregarded his knowledge of natural history as derived from his own\ninvestigations, as well as his theories of perspective and optics.\nCompare what he says in praise of experience (Vol II; _XIX_).],\nsetting aside those authorities who themselves were the disciples of\nnature.\n\n661.\n\nThat the first drawing was a simple line drawn round the shadow of a\nman cast by the sun on a wall.\n\nThe painter's scope.\n\n662.\n\nThe painter strives and competes with nature.\n\n_X.\n\nStudies and Sketches for Pictures and Decorations.\n\nAn artist's manuscript notes can hardly be expected to contain any\nthing more than incidental references to those masterpieces of his\nwork of which the fame, sounded in the writings of his\ncontemporaries, has left a glorious echo to posterity. We need not\ntherefore be surprised to find that the texts here reproduced do not\nafford us such comprehensive information as we could wish. On the\nother hand, the sketches and studies prepared by Leonardo for the\ntwo grandest compositions he ever executed: The Fresco of the Last\nSupper in the Refectory of Santa Maria delle Grazie at Milan, and\nthe Cartoon of the Battle of Anghiari, for the Palazzo della\nSignoria at Florence--have been preserved; and, though far from\ncomplete, are so much more numerous than the manuscript notes, that\nwe are justified in asserting that in value and interest they amply\ncompensate for the meagerness of the written suggestions.\n\nThe notes for the composition of the Last Supper, which are given\nunder nos._ 665 _and_ 666 _occur in a MS. at South Kensington, II2,\nwritten in the years_ 1494-1495. _This MS. sketch was noted down not\nmore than three or four years before the painting was executed,\nwhich justifies the inference that at the time when it was written\nthe painter had not made up his mind definitely even as to the\ngeneral scheme of the work; and from this we may also conclude that\nthe drawings of apostles' heads at Windsor, in red chalk, must be\nascribed to a later date. They are studies for the head of St.\nMatthew, the fourth figure on Christ's left hand--see Pl. XL VII,\nthe sketch (in black chalk) for the head of St. Philip, the third\nfigure on the left hand--see Pl. XL VIII, for St. Peter's right\narm--see Pl. XLIX, and for the expressive head of Judas which has\nunfortunately somewhat suffered by subsequent restoration of\noutlines,--see Pl. L. According to a tradition, as unfounded as it\nis improbable, Leonardo made use of the head of Padre Bandelli, the\nprior of the convent, as the prototype of his Judas; this however\nhas already been contradicted by Amoretti \"Memorie storiche\" cap.\nXIV. The study of the head of a criminal on Pl. LI has, it seems to\nme, a better claim to be regarded as one of the preparatory sketches\nfor the head of Judas. The Windsor collection contains two old\ncopies of the head of St. Simon, the figure to the extreme left of\nChrist, both of about equal merit (they are marked as Nos._ 21 _and_\n36_)--the second was reproduced on Pl. VIII of the Grosvenor\nGallery Publication in_ 1878. _There is also at Windsor a drawing in\nblack chalk of folded hands (marked with the old No._ 212; _No. LXI\nof the Grosvenor Gallery Publication) which I believe to be a copy\nof the hands of St. John, by some unknown pupil. A reproduction of\nthe excellent drawings of heads of Apostles in the possession of H.\nR. H. the Grand Duchess of Weimar would have been out of my province\nin this work, and, with regard to them, I must confine myself to\npointing out that the difference in style does not allow of our\nplacing the Weimar drawings in the same category as those here\nreproduced. The mode of grouping in the Weimar drawings is of itself\nsufficient to indicate that they were not executed before the\npicture was painted, but, on the contrary, afterwards, and it is, on\nthe face of it, incredible that so great a master should thus have\ncopied from his own work.\n\nThe drawing of Christ's head, in the Brera palace at Milan was\nperhaps originally the work of Leonardo's hand; it has unfortunately\nbeen entirely retouched and re-drawn, so that no decisive opinion\ncan be formed as to its genuineness.\n\nThe red chalk drawing reproduced on Pl. XLVI is in the Accademia at\nVenice; it was probably made before the text, Nos._ 664 _and_ 665,\n_was written.\n\nThe two pen and ink sketches on Pl. XLV seem to belong to an even\nearlier date; the more finished drawing of the two, on the right\nhand, represents Christ with only St. John and Judas and a third\ndisciple whose action is precisely that described in No._ 666,\n_Pl._ 4. _It is hardly necessary to observe that the other sketches\non this page and the lines of text below the circle (containing the\nsolution of a geometrical problem) have no reference to the picture\nof the Last Supper. With this figure of Christ may be compared a\nsimilar pen and ink drawing reproduced on page_ 297 _below on the\nleft hand; the original is in the Louvre. On this page again the\nrest of the sketches have no direct bearing on the composition of\nthe Last Supper, not even, as it seems to me, the group of four men\nat the bottom to the right hand--who are listening to a fifth, in\ntheir midst addressing them. Moreover the writing on this page (an\nexplanation of a disk shaped instrument) is certainly not in the\nsame style as we find constantly used by Leonardo after the year_\n1489.\n\n_It may be incidentally remarked that no sketches are known for the\nportrait of \"Mona Lisa\", nor do the MS. notes ever allude to it,\nthough according to Vasari the master had it in hand for fully four\nyears.\n\nLeonardo's cartoon for the picture of the battle of Anghiari has\nshared the fate of the rival work, Michaelangelo's \"Bathers summoned\nto Battle\". Both have been lost in some wholly inexplicable manner.\nI cannot here enter into the remarkable history of this work; I can\nonly give an account of what has been preserved to us of Leonardo's\nscheme and preparations for executing it. The extent of the material\nin studies and drawings was till now quite unknown. Their\npublication here may give some adequate idea of the grandeur of this\nfamous work. The text given as No._ 669 _contains a description of\nthe particulars of the battle, but for the reasons given in the note\nto this text, I must abandon the idea of taking this passage as the\nbasis of my attempt to reconstruct the picture as the artist\nconceived and executed it.\n\nI may here remind the reader that Leonardo prepared the cartoon in\nthe Sala del Papa of Santa Maria Novella at Florence and worked\nthere from the end of October 1503 till February 1504, and then was\nbusied with the painting in the Sala del Consiglio in the Palazzo\ndella Signoria, till the work was interrupted at the end of May\n1506. (See Milanesi's note to Vasari pp. 43--45 Vol. IV ed. 1880.)\nVasari, as is well known, describes only one scene or episode of the\ncartoon--the Battle for the Standard in the foreground of the\ncomposition, as it would seem; and this only was ever finished as a\nmural decoration in the Sala del Consiglio. This portion of the\ncomposition is familiar to all from the disfigured copy engraved by\nEdelinck. Mariette had already very acutely observed that Edelinck\nmust surely have worked from a Flemish copy of the picture. There is\nin the Louvre a drawing by Rubens (No. 565) which also represents\nfour horsemen fighting round a standard and which agrees with\nEdelinck's engraving, but the engraving reverses the drawing. An\nearlier Flemish drawing, such as may have served as the model for\nboth Rubens and Edelinck, is in the Uffizi collection (see\nPhilpots's Photograph, No. 732). It seems to be a work of the second\nhalf of the XVIth century, a time when both the picture and the\ncartoon had already been destroyed. It is apparently the production\nof a not very skilled hand. Raphael Trichet du Fresne, 1651,\nmentions that a small picture by Leonardo himself of the Battle of\nthe Standard was then extant in the Tuileries; by this he probably\nmeans the painting on panel which is now in the possession of Madame\nTimbal in Paris, and which has lately been engraved by Haussoullier\nas a work by Leonardo. The picture, which is very carefully painted,\nseems to me however to be the work of some unknown Florentine\npainter, and probably executed within the first ten years of the\nXVIth century. At the same time, it would seem to be a copy not from\nLeonardo's cartoon, but from his picture in the Palazzo della\nSignoria; at any rate this little picture, and the small Flemish\ndrawing in Florence are the oldest finished copies of this episode\nin the great composition of the Battle of Anghiari.\n\nIn his Life of Raphael, Vasari tells us that Raphael copied certain\nworks of Leonardo's during his stay in Florence. Raphael's first\nvisit to Florence lasted from the middle of October 1504 till July\n1505, and he revisited it in the summer of 1506. The hasty sketch,\nnow in the possession of the University of Oxford and reproduced on\npage 337 also represents the Battle of the Standard and seems to\nhave been made during his first stay, and therefore not from the\nfresco but from the cartoon; for, on the same sheet we also find,\nbesides an old man's head drawn in Leonardo's style, some studies\nfor the figure of St. John the Martyr which Raphael used in 1505 in\nhis great fresco in the Church of San Severo at Perugia.\n\nOf Leonardo's studies for the Battle of Anghiari I must in the first\nplace point to five, on three of which--Pl. LII 2, Pl. LIII, Pl.\nLVI--we find studies for the episode of the Standard. The standard\nbearer, who, in the above named copies is seen stooping, holding on\nto the staff across his shoulder, is immediately recognisable as the\nleft-hand figure in Raphael's sketch, and we find it in a similar\nattitude in Leonardo's pen and ink drawing in the British\nMuseum--Pl. LII, 2--the lower figure to the right. It is not\ndifficult to identify the same figure in two more complicated groups\nin the pen and ink drawings, now in the Accademia at Venice--Pl.\nLIII, and Pl. LIV--where we also find some studies of foot soldiers\nfighting. On the sheet in the British Museum--Pl. LII, 2--we find,\namong others, one group of three horses galloping forwards: one\nhorseman is thrown and protects himself with his buckler against the\nlance thrusts of two others on horseback, who try to pierce him as\nthey ride past. The same action is repeated, with some variation, in\ntwo sketches in pen and ink on a third sheet, in the Accademia at\nVenice, Pl. LV; a coincidence which suggests the probability of such\nan incident having actually been represented on the cartoon. We are\nnot, it is true, in a position to declare with any certainty which\nof these three dissimilar sketches may have been the nearest to the\ngroup finally adopted in executing the cartoon.\n\nWith regard, however, to one of the groups of horsemen it is\npossible to determine with perfect certainty not only which\narrangement was preferred, but the position it occupied in the\ncomposition. The group of horsemen on Pl. LVII is a drawing in black\nchalk at Windsor, which is there attributed to Leonardo, but which\nappears to me to be the work of Cesare da Sesto, and the\nCommendatore Giov. Morelli supports me in this view. It can hardly\nbe doubted that da Sesto, as a pupil of Leonardo's, made this\ndrawing from his master's cartoon, if we compare it with the copy\nmade by Raphael--here reproduced, for just above the fighting\nhorseman in Raphael's copy it is possible to detect a horse which is\nseen from behind, going at a slower pace, with his tail flying out\nto the right and the same horse may be seen in the very same\nattitude carrying a dimly sketched rider, in the foreground of\nCesare da Sesto's drawing._\n\n_If a very much rubbed drawing in black chalk at Windsor--Pl.\nLVI--is, as it appears to be, the reversed impression of an original\ndrawing, it is not difficult to supplement from it the portions\ndrawn by Cesare da Sesto. Nay, it may prove possible to reconstruct\nthe whole of the lost cartoon from the mass of materials we now have\nat hand which we may regard as the nucleus of the composition. A\nlarge pen and ink drawing by Raphael in the Dresden collection,\nrepresenting three horsemen fighting, and another, by Cesare da\nSesto, in the Uffizi, of light horsemen fighting are a further\ncontribution which will help us to reconstruct it._\n\n_The sketch reproduced on Pl. LV gives a suggestive example of the\nway in which foot-soldiers may have been introduced into the cartoon\nas fighting among the groups of horsemen; and I may here take the\nopportunity of mentioning that, for reasons which it would be out of\nplace to enlarge upon here, I believe the two genuine drawings by\nRaphael's hand in his \"Venetian sketch-book\" as it is called--one of\na standard bearer marching towards the left, and one of two\nfoot-soldiers armed with spears and fighting with a horseman--to be\nundoubtedly copies from the cartoon of the Battle of Anghiari._\n\n_Leonardo's two drawings, preserved in the museum at Buda-Pesth and\nreproduced on pages 338 and 339 are preliminary studies for the\nheads of fighting warriors. The two heads drawn in black chalk (pg.\n338) and the one seen in profile, turned to the left, drawn in red\nchalk (pg. 339), correspond exactly with those of two horsemen in\nthe scene of the fight round the standard as we see them in Madame\nTimbal's picture and in the other finished copies. An old copy of\nthe last named drawing by a pupil of Leonardo is in MS. C. A. 187b;\n561b (See Saggio, Tav. XXII). Leonardo used to make such finished\nstudies of heads as those, drawn on detached sheets, before\nbeginning his pictures from his drawings--compare the preparatory\nstudies for the fresco of the Last Supper, given on Pl. XLVII and\nPl. L. Other drawings of heads, all characterised by the expression\nof vehement excitement that is appropriate to men fighting, are to\nbe seen at Windsor (No. 44) and at the Accademia at Venice (IV, 13);\nat the back of one of the drawings at Buda-Pesth there is the bust\nof a warrior carrying a spear on his left shoulder, holding up the\nleft arm (See Csatakepek a XVI--lk Szazadbol osszeallitotta Pvlszky\nKaroly). These drawings may have been made for other portions of the\ncartoon, of which no copies exist, and thus we are unable to\nidentify these preparatory drawings. Finally I may add that a sketch\nof fighting horse and foot soldiers, formerly in the possession of\nM. Thiers and published by Charles Blanc in his \"Vies des Peintres\"\ncan hardly be accepted as genuine. It is not to be found, as I am\ninformed, among the late President's property, and no one appears to\nknow where it now is._\n\n_An attempted reconstruction of the Cartoon, which is not only\nunsuccessful but perfectly unfounded, is to be seen in the\nlithograph by Bergeret, published in Charles Blanc's \"Vies des\npeintres\" and reprinted in \"The great Artists. L. da Vinci\", p. 80.\nThis misleading pasticcio may now be rejected without hesitation._\n\n_There are yet a few original drawings by Leonardo which might be\nmentioned here as possibly belonging to the cartoon of the Battle;\nsuch as the pen and ink sketches on Pl. XXI and on Pl. XXXVIII, No.\n3, but we should risk too wide a departure from the domain of\nascertained fact._\n\n_With regard to the colours and other materials used by Leonardo the\nreader may be referred to the quotations from the accounts for the\npicture in question given by Milanesi in his edition of Vasari (Vol.\nIV, p. 44, note) where we find entries of a similar character to\nthose in Leonardo's note books for the year 1505; S. K. M. 12 (see\nNo. 636)._\n\n_That Leonardo was employed in designing decorations and other\npreparations for high festivals, particularly for the court of\nMilan, we learn not only from the writings of his contemporaries but\nfrom his own incidental allusions; for instance in MS. C. l5b (1),\nl. 9. In the arrangement of the texts referring to this I have\nplaced those first, in which historical personages are named--Nos.\n670-674. Among the descriptions of Allegorical subjects two texts\nlately found at Oxford have been included, Nos. 676 and 677. They\nare particularly interesting because they are accompanied by large\nsketches which render the meaning of the texts perfectly clear. It\nis very intelligible that in other cases, where there are no\nillustrative sketches, the notes must necessarily remain obscure or\nadmit of various interpretations. The literature of the time affords\nample evidence of the use of such allegorical representations,\nparticularly during the Carnival and in Leonardo's notes we find the\nCarnival expressly mentioned--Nos. 685 and 704. Vasari in his Life\nof Pontormo, particularly describes that artist's various\nundertakings for Carnival festivities. These very graphic\ndescriptions appear to me to throw great light in more ways than one\non the meaning of Leonardo's various notes as to allegorical\nrepresentations and also on mottoes and emblems--Nos. 681-702. In\npassing judgment on the allegorical sketches and emblems it must not\nbe overlooked that even as pictures they were always accompanied by\nexplanations in words. Several finished drawings of allegorical\ncompositions or figures have been preserved, but as they have no\ncorresponding explanation in the MSS. they had no claim to be\nreproduced here. The female figure on Pl. XXVI may perhaps be\nregarded as a study for such an allegorical painting, of which the\npurport would have been explained by an inscription._\n\nOn Madonna pictures.\n\n663.\n\n[In the autumn of] 1478 I began the two Madonna [pictures].\n\n[Footnote: Photographs of this page have been published by BRAUN,\nNo. 439, and PHILPOT, No. 718.\n\n1. _Incominciai_. We have no other information as to the two\npictures of the Madonna here spoken of. As Leonardo here tells us\nthat he had begun two Madonnas at the same time, the word\n'_incominciai_' may be understood to mean that he had begun at the\nsame time preparatory studies for two pictures to be painted later.\nIf this is so, the non-existence of the pictures may be explained by\nsupposing that they were only planned and never executed. I may here\nmention a few studies for pictures of the Madonna which probably\nbelong to this early time; particularly a drawing in silver-point on\nbluish tinted paper at Windsor--see Pl. XL, No. 3--, a drawing of\nwhich the details have almost disappeared in the original but have\nbeen rendered quite distinct in the reproduction; secondly a slight\npen and ink sketch in, the Codex VALLARDI, in the Louvre, fol. 64,\nNo. 2316; again a silver point drawing of a Virgin and child drawn\nover again with the pen in the His de la Salle collection also in\nthe Louvre, No. 101. (See Vicomte BOTH DE TAUZIA, _Notice des\ndessins de la collection His de la Salle, exposes au Louvre_. Paris\n1881, pp. 80, 81.) This drawing is, it is true, traditionally\nascribed to Raphael, but the author of the catalogue very justly\npoints out its great resemblance with the sketches for Madonnas in\nthe British Museum which are indisputably Leonardo's. Some of these\nhave been published by Mr. HENRY WALLIS in the Art Journal, New Ser.\nNo. 14, Feb. 1882. If the non-existence of the two pictures here\nalluded to justifies my hypothesis that only studies for such\npictures are meant by the text, it may also be supposed that the\ndrawings were made for some comrade in VERROCCHIO'S atelier. (See\nVASARI, Sansoni's ed. Florence 1880. Vol. IV, p. 564): \"_E perche a\nLerenzo piaceva fuor di modo la maniera di Lionardo, la seppe cosi\nbene imitare, che niuno fu che nella pulitezza e nel finir l'opere\ncon diligenza l'imitasse pi\u00f9 di lui_.\" Leonardo's notes give me no\nopportunity of discussing the pictures executed by him in Florence,\nbefore he moved to Milan. So the studies for the unfinished picture\nof the Adoration of the Magi--in the Uffizi, Florence--cannot be\ndescribed here, nor would any discussion about the picture in the\nLouvre \"_La Vierge aux Rochers_\" be appropriate in the absence of\nall allusion to it in the MSS. Therefore, when I presently add a few\nremarks on this painting in explanation of the Master's drawings for\nit, it will be not merely with a view to facilitate critical\nresearches about the picture now in the National Gallery, London,\nwhich by some critics has been pronounced to be a replica of the\nLouvre picture, but also because I take this opportunity of\npublishing several finished studies of the Master's which, even if\nthey were not made in Florence but later in Milan, must have been\nprior to the painting of the Last Supper. The original picture in\nParis is at present so disfigured by dust and varnish that the\ncurrent reproductions in photography actually give evidence more of\nthe injuries to which the picture has been exposed than of the\noriginal work itself. The wood-cut given on p. 344, is only intended\nto give a general notion of the composition. It must be understood\nthat the outline and expression of the heads, which in the picture\nis obscured but not destroyed, is here altogether missed. The\nfacsimiles which follow are from drawings which appear to me to be\nstudies for \"_La Vierge aux Rochers_.\"\n\n1. A drawing in silver point on brown toned paper of a woman's head\nlooking to the left. In the Royal Library at Turin, apparently a\nstudy from nature for the Angel's head (Pl. XLII).\n\n2. A study of drapery for the left leg of the same figure, done with\nthe brush, Indian ink on greenish paper, the lights heightened with\nwhite.\n\nThe original is at Windsor, No. 223. The reproduction Pl. XLIII is\ndefective in the shadow on the upper part of the thigh, which is not\nso deep as in the original; it should also be observed that the\nfolds of the drapery near the hips are somewhat altered in the\nfinished work in the Louvre, while the London copy shows a greater\nresemblance to this study in that particular.\n\n3. A study in red chalk for the bust of the Infant Christ--No. 3 in\nthe Windsor collection (Pl. XLIV). The well-known silver-point\ndrawing on pale green paper, in the Louvre, of a boy's head (No. 363\nin REISET, _Notice des dessins, Ecoles d'Italie_) seems to me to be\na slightly altered copy, either from the original picture or from\nthis red chalk study.\n\n4. A silver-point study on greenish paper, for the head of John the\nBaptist, reproduced on p. 342. This was formerly in the Codex\nVallardi and is now exhibited among the drawings in the Louvre. The\nlights are, in the original, heightened with white; the outlines,\nparticularly round the head and ear, are visibly restored.\n\nThere is a study of an outstretched hand--No. 288 in the Windsor\ncollection--which was published in the Grosvenor Gallery\nPublication, 1878, simply under the title of: \"No. 72 Study of a\nhand, pointing\" which, on the other hand, I regard as a copy by a\npupil. The action occurs in the kneeling angel of the Paris picture\nand not in the London copy.\n\nThese four genuine studies form, I believe, a valuable substitute in\nthe absence of any MS. notes referring to the celebrated Paris\npicture.]\n\nBernardo di Bandino's Portrait.\n\n664.\n\nA tan-coloured small cap, A doublet of black serge, A black jerkin\nlined A blue coat lined, with fur of foxes' breasts, and the collar\nof the jerkin covered with black and white stippled velvet Bernardo\ndi Bandino Baroncelli; black hose.\n\n[Footnote: These eleven lines of text are by the side of the pen and\nink drawing of a man hanged--Pl. LXII, No. 1. This drawing was\nexhibited in 1879 at the _Ecole des Beaux-Arts_ in Paris and the\ncompilers of the catalogue amused themselves by giving the victim's\nname as follows: \"_Un pendu, vetu d'une longue robe, les mains li\u00e9es\nsur le dos ... Bernardo di Bendino Barontigni, marchand de\npantalons_\" (see _Catalogue descriptif des Dessins de Mailres\nanciens exposes a l'Ecole des Beaux Arts_, Paris 1879; No. 83, pp.\n9-10). Now, the criminal represented here, is none other than\nBernardino di Bandino Baroncelli the murderer of Giuliano de'Medici,\nwhose name as a coadjutor in the conspiracy of the Pazzi has gained\na melancholy notoriety by the tragedy of the 26th April 1478.\nBernardo was descended from an ancient family and the son of the man\nwho, under King Ferrante, was President of the High Court of Justice\nin Naples. His ruined fortunes, it would seem, induced him to join\nthe Pazzi; he and Francesco Pazzi were entrusted with the task of\nmurdering Giuliano de'Medici on the fixed day. Their victim not\nappearing in the cathedral at the hour when they expected him, the\ntwo conspirators ran to the palace of the Medici and induced him to\naccompany them. Giuliano then took his place in the chancel of the\nCathedral, and as the officiating priest raised the Host--the sign\nagreed upon--Bernardo stabbed the unsuspecting Giuliano in the\nbreast with a short sword; Giuliano stepped backwards and fell dead.\nThe attempt on Lorenzo's life however, by the other conspirators at\nthe same moment, failed of success. Bernardo no sooner saw that\nLorenzo tried to make his escape towards the sacristy, than he\nrushed upon him, and struck down Francesco Nori who endeavoured to\nprotect Lorenzo. How Lorenzo then took refuge behind the brazen\ndoors of the sacristy, and how, as soon as Giuliano's death was made\nknown, the further plans of the conspirators were defeated, while a\nterrible vengeance overtook all the perpetrators and accomplices,\nthis is no place to tell. Bernardo Bandini alone seemed to be\nfavoured by fortune; he hid first in the tower of the Cathedral, and\nthen escaped undiscovered from Florence. Poliziano, who was with\nLorenzo in the Cathedral, says in his 'Conjurationis Pactianae\nCommentarium': \"_Bandinus fugitans in Tiphernatem incidit, a quo in\naciem receptus Senas pervenit_.\" And Gino Capponi in summing up the\nreports of the numerous contemporary narrators of the event, says:\n\"_Bernardo Bandini ricoverato in Costantinopoli, fu per ordine del\nSultano preso e consegnato a un Antonio di Bernardino dei Medici,\nche Lorenzo aveva mandato apposta in Turchia: cos\u00ec era grande la\npotenza di quest' uomo e grande la voglia di farne mostra e che non\nrestasse in vita chi aveagli ucciso il fratello, fu egli applicato\nappena giunto_\" (_Storia della Republica di Firenze II_, 377, 378).\nDetails about the dates may be found in the _Chronichetta di\nBelfredello Strinati Alfieri_: \"_Bernardo di Bandino Bandini\nsopradetto ne venne preso da Gostantinopoti a d\u00ec 14. Dicembre 1479 e\ndisaminato, che fu al Bargello, fu impiccato alle finestre di detto\nBargello allato alla Doana a d\u00ec 29. Dicembre MCCCCLXXIX che pochi d\u00ec\nstette_.\" It may however be mentioned with reference to the mode of\nwriting the name of the assassin that, though most of his\ncontemporaries wrote Bernardo Bandini, in the _Breve Chronicon\nCaroli Petri de Joanninis_ he is called Bernardo di Bandini\nBaroncelli; and, in the _Sententiae Domini Matthaei de Toscana_,\nBernardus Joannis Bandini de Baroncellis, as is written on\nLeonardo's drawing of him when hanged. Now VASARI, in the life of\n_Andrea del Castagno_ (Vol. II, 680; ed. Milanesi 1878), tells us\nthat in 1478 this painter was commissioned by order of the Signoria\nto represent the members of the Pazzi conspiracy as traitors, on the\nfacade of the Palazzo del Podest\u00e0--the Bargello. This statement is\nobviously founded on a mistake, for Andrea del Castagno was already\ndead in 1457. He had however been commissioned to paint Rinaldo\ndegli Albizzi, when declared a rebel and exiled in 1434, and his\nadherents, as hanging head downwards; and in consequence he had\nacquired the nickname of Andrea degl' Impiccati. On the 21st July\n1478 the Council of Eight came to the following resolution: \"_item\nservatis etc. deliberaverunt et santiaverunt Sandro Botticelli pro\nejus labore in pingendo proditores flor. quadraginta largos_\" (see\nG. MILANESI, _Arch. star. VI_ (1862) p. 5 note.)\n\nAs has been told, Giuliano de' Medici was murdered on the 26th April\n1478, and we see by this that only three months later Botticelli was\npaid for his painting of the \"_proditores_\". We can however hardly\nsuppose that all the members of the conspiracy were depicted by him\nin fresco on the facade of the palace, since no fewer than eighty\nhad been condemned to death. We have no means of knowing whether,\nbesides Botticelli, any other painters, perhaps Leonardo, was\ncommissioned, when the criminals had been hanged in person out of\nthe windows of the Palazzo del Podest\u00e0 to represent them there\nafterwards in effigy in memory of their disgrace. Nor do we know\nwhether the assassin who had escaped may at first not have been\nprovisionally represented as hanged in effigy. Now, when we try to\nconnect the historical facts with this drawing by Leonardo\nreproduced on Pl. LXII, No. I, and the full description of the\nconspirator's dress and its colour on the same sheet, there seems to\nbe no reasonable doubt that Bernardo Bandini is here represented as\nhe was actually hanged on December 29th, 1479, after his capture at\nConstantinople. The dress is certainly not that in which he\ncommitted the murder. A long furred coat might very well be worn at\nConstantinople or at Florence in December, but hardly in April. The\ndoubt remains whether Leonardo described Bernardo's dress so fully\nbecause it struck him as remarkable, or whether we may not rather\nsuppose that this sketch was actually made from nature with the\nintention of using it as a study for a wall painting to be executed.\nIt cannot be denied that the drawing has all the appearance of\nhaving been made for this purpose. Be this as it may, the sketch\nunder discussion proves, at any rate, that Leonardo was in Florence\nin December 1479, and the note that accompanies it is valuable as\nadding one more characteristic specimen to the very small number of\nhis MSS. that can be proved to have been written between 1470 and\n1480.]\n\nNotes on the Last Supper (665-668).\n\n665.\n\nOne who was drinking and has left the glass in its position and\nturned his head towards the speaker.\n\nAnother, twisting the fingers of his hands together turns with stern\nbrows to his companion [6]. Another with his hands spread open shows\nthe palms, and shrugs his shoulders up his ears making a mouth of\nastonishment [8].\n\n[9] Another speaks into his neighbour's ear and he, as he listens to\nhim, turns towards him to lend an ear [10], while he holds a knife\nin one hand, and in the other the loaf half cut through by the\nknife. [13] Another who has turned, holding a knife in his hand,\nupsets with his hand a glass on the table [14].\n\n[Footnote 665, 666: In the original MS. there is no sketch to\naccompany these passages, and if we compare them with those drawings\nmade by Leonardo in preparation for the composition of the\npicture--Pl. XLV, XLVI--, (compare also Pl. LII, 1 and the drawings\non p. 297) it is impossible to recognise in them a faithful\ninterpretation of the whole of this text; but, if we compare these\npassages with the finished picture (see p. 334) we shall see that in\nmany places they coincide. For instance, compare No. 665, 1. 6--8,\nwith the fourth figure on the right hand of Christ. The various\nactions described in lines 9--10, 13--14 are to be seen in the group\nof Peter, John and Judas; in the finished picture however it is not\na glass but a salt cellar that Judas is upsetting.]\n\n666.\n\nAnother lays his hand on the table and is looking. Another blows his\nmouthful. [3] Another leans forward to see the speaker shading his\neyes with his hand. [5] Another draws back behind the one who leans\nforward, and sees the speaker between the wall and the man who is\nleaning [Footnote: 6. _chinato_. I have to express my regret for\nhaving misread this word, written _cinato_ in the original, and\nhaving altered it to _\"ciclo\"_ when I first published this text, in\n'The Academy' for Nov. 8, 1879 immediately after I had discovered\nit, and subsequently in the small biography of Leonardo da Vinci\n(Great Artists) p. 29.].\n\n[Footnote: In No. 666. Line I must refer to the furthest figure on\nthe left; 3, 5 and 6 describe actions which are given to the group\nof disciples on the left hand of Christ.]\n\n667.\n\nCHRIST.\n\nCount Giovanni, the one with the Cardinal of Mortaro.\n\n[Footnote: As this note is in the same small Manuscript as the\npassage here immediately preceding it, I may be justified in\nassuming that Leonardo meant to use the features of the person here\nnamed as a suitable model for the figure of Christ. The celebrated\ndrawing of the head of Christ, now hanging in the Brera Gallery at\nMilan, has obviously been so much restored that it is now impossible\nto say, whether it was ever genuine. We have only to compare it with\nthe undoubtedly genuine drawings of heads of the disciples in PI.\nXLVII, XLVIII and L, to admit that not a single line of the Milan\ndrawing in its present state can be by the same hand.]\n\n668.\n\nPhilip, Simon, Matthew, Thomas, James the Greater, Peter, Philip,\nAndrew, Bartholomew.\n\n[Footnote: See PI. XLVI. The names of the disciples are given in the\norder in which they are written in the original, from right to left,\nabove each head. The original drawing is here slightly reduced in\nscale; it measures 39 centimetres in length by 26 in breadth.]\n\n669.\n\n  On the battle of Anghiari.\n  Florentine\n  Neri di Gino Capponi\n  Bernardetto de' Medici\n  Micheletto,\n  Niccolo da Pisa\n  Conte Francesco\n                         Pietro Gian Paolo\n                         Guelfo Orsino,\n                         Messer  Rinaldo   degli\n                                      Albizzi\n\nBegin with the address of Niccolo Piccinino to the soldiers and the\nbanished Florentines among whom are Messer Rinaldo degli Albizzi and\nother Florentines. Then let it be shown how he first mounted on\nhorseback in armour; and the whole army came after him--40 squadrons\nof cavalry, and 2000 foot soldiers went with him. Very early in the\nmorning the Patriarch went up a hill to reconnoitre the country,\nthat is the hills, fields and the valley watered by a river; and\nfrom thence he beheld Niccolo Picinino coming from Borgo San\nSepolcro with his people, and with a great dust; and perceiving them\nhe returned to the camp of his own people and addressed them. Having\nspoken he prayed to God with clasped hands, when there appeared a\ncloud in which Saint Peter appeared and spoke to the Patriarch.--500\ncavalry were sent forward by the Patriarch to hinder or check the\nrush of the enemy. In the foremost troop Francesco the son of\nNiccolo Piccinino [24] was the first to attack the bridge which was\nheld by the Patriarch and the Florentines. Beyond the bridge to his\nleft he sent forward some infantry to engage ours, who drove them\nback, among whom was their captain Micheletto [29] whose lot it was\nto be that day at the head of the army. Here, at this bridge there\nis a severe struggle; our men conquer and the enemy is repulsed.\nHere Guido and Astorre, his brother, the Lord of Faenza with a great\nnumber of men, re-formed and renewed the fight, and rushed upon the\nFlorentines with such force that they recovered the bridge and\npushed forward as far as the tents. But Simonetto advanced with 600\nhorse, and fell upon the enemy and drove them back once more from\nthe place, and recaptured the bridge; and behind him came more men\nwith 2000 horse soldiers. And thus for a long time they fought with\nvarying fortune. But then the Patriarch, in order to divert the\nenemy, sent forward Niccolo da Pisa [44] and Napoleone Orsino, a\nbeardless lad, followed by a great multitude of men, and then was\ndone another great feat of arms. At the same time Niccolo Piccinino\nurged forward the remnant of his men, who once more made ours give\nway; and if it had not been that the Patriarch set himself at their\nhead and, by his words and deeds controlled the captains, our\nsoldiers would have taken to flight. The Patriarch had some\nartillery placed on the hill and with these he dispersed the enemy's\ninfantry; and the disorder was so complete that Niccolo began to\ncall back his son and all his men, and they took to flight towards\nBorgo. And then began a great slaughter of men; none escaped but the\nforemost of those who had fled or who hid themselves. The battle\ncontinued until sunset, when the Patriarch gave his mind to\nrecalling his men and burying the dead, and afterwards a trophy was\nerected.\n\n[Footnote: 669. This passage does not seem to me to be in Leonardo's\nhand, though it has hitherto been generally accepted as genuine. Not\nonly is the writing unlike his, but the spelling also is quite\ndifferent. I would suggest that this passage is a description of the\nevents of the battle drawn up for the Painter by order of the\nSignoria, perhaps by some historian commissioned by them, to serve\nas a scheme or programme of the work. The whole tenor of the style\nseems to me to argue in favour of this theory; and besides, it would\nbe in no way surprising that such a document should have been\npreserved among Leonardo's autographs.]\n\nAllegorical representations referring to the duke of Milan\n(670-673).\n\n670.\n\nErmine with blood Galeazzo, between calm weather and a\nrepresentation of a tempest.\n\n[Footnote: 670. Only the beginning of this text is legible; the\nwriting is much effaced and the sense is consequently obscure. It\nseems to refer like the following passage to an allegorical\npicture.]\n\n671.\n\nIl Moro with spectacles, and Envy depicted with False Report and\nJustice black for il Moro.\n\nLabour as having a branch of vine [_or_ a screw] in her hand.\n\n672.\n\nIl Moro as representing Good Fortune, with hair, and robes, and his\nhands in front, and Messer Gualtieri taking him by the robes with a\nrespectful air from below, having come in from the front [5].\n\nAgain, Poverty in a hideous form running behind a youth. Il Moro\ncovers him with the skirt of his robe, and with his gilt sceptre he\nthreatens the monster.\n\nA plant with its roots in the air to represent one who is at his\nlast;--a robe and Favour.\n\nOf tricks [_or_ of magpies] and of burlesque poems [_or_ of\nstarlings].\n\nThose who trust themselves to live near him, and who will be a large\ncrowd, these shall all die cruel deaths; and fathers and mothers\ntogether with their families will be devoured and killed by cruel\ncreatures.\n\n[Footnote: 1--10 have already been published by _Amoretti_ in\n_Memorie Storiche_ cap. XII. He adds this note with regard to\nGualtieri: \"_A questo M. Gualtieri come ad uomo generoso e benefico\nscrive il Bellincioni un Sonetto (pag, 174) per chiedergli un\npiacere; e 'l Tantio rendendo ragione a Lodovico il Moro, perche\npubblicasse le Rime del Bellincioni; ci\u00f2 hammi imposto, gli dice:\nl'humano fidele, prudente e sollicito executore delli tuoi\ncomandamenti Gualtero, che fa in tutte le cose ove tu possi far\nutile, ogni studio vi metti._\" A somewhat mysterious and evidently\nallegorical composition--a pen and ink drawing--at Windsor, see PL\nLVIII, contains a group of figures in which perhaps the idea is\nworked out which is spoken of in the text, lines 1-5.]\n\n673.\n\nHe was blacker than a hornet, his eyes were as red as a burning fire\nand he rode on a tall horse six spans across and more than 20 long\nwith six giants tied up to his saddle-bow and one in his hand which\nhe gnawed with his teeth. And behind him came boars with tusks\nsticking out of their mouths, perhaps ten spans.\n\nAllegorical representations (674--678).\n\n674.\n\nAbove the helmet place a half globe, which is to signify our\nhemisphere, in the form of a world; on which let there be a peacock,\nrichly decorated, and with his tail spread over the group; and every\nornament belonging to the horse should be of peacock's feathers on a\ngold ground, to signify the beauty which comes of the grace bestowed\non him who is a good servant.\n\nOn the shield a large mirror to signify that he who truly desires\nfavour must be mirrored in his virtues.\n\nOn the opposite side will be represented Fortitude, in like manner\nin her place with her pillar in her hand, robed in white, to signify\n... And all crowned; and Prudence with 3 eyes. The housing of the\nhorse should be of plain cloth of gold closely sprinkled with\npeacock's eyes, and this holds good for all the housings of the\nhorse, and the man's dress. And the man's crest and his neck-chain\nare of peacock's feathers on golden ground.\n\nOn the left side will be a wheel, the centre of which should be\nattached to the centre of the horse's hinder thigh piece, and in the\ncentre Prudence is seen robed in red, Charity sitting in a fiery\nchariot and with a branch of laurel in her hand, to signify the hope\nwhich comes of good service.\n\n[21] Messer Antonio Grimani of Venice companion of Antonio Maria\n[23].\n\n[Footnote: _Messer Antonio Gri_. His name thus abbreviated is, there\ncan be no doubt, Grimani. Antonio Grimani was the famous Doge who in\n1499 commanded the Venetian fleet in battle against the Turks. But\nafter the abortive conclusion of the expedition--Ludovico being the\nally of the Turks who took possession of Friuli--, Grimani was driven\ninto exile; he went to live at Rome with his son Cardinal Domenico\nGrimani. On being recalled to Venice he filled the office of Doge\nfrom 1521 to 1523. _Antonio Maria_ probably means Antonio Maria\nGrimani, the Patriarch of Aquileia.]\n\n675.\n\nFame should be depicted as covered all over with tongues instead of\nfeathers, and in the figure of a bird.\n\n676.\n\nPleasure and Pain represent as twins, since there never is one\nwithout the other; and as if they were united back to back, since\nthey are contrary to each other.\n\n[6] Clay, gold.\n\n[Footnote: 7. _oro. fango_: gold, clay. These words stand below the\nallegorical figure.]\n\nIf you take Pleasure know that he has behind him one who will deal\nyou Tribulation and Repentance.\n\n[9] This represents Pleasure together with Pain, and show them as\ntwins because one is never apart from the other. They are back to\nback because they are opposed to each other; and they exist as\ncontraries in the same body, because they have the same basis,\ninasmuch as the origin of pleasure is labour and pain, and the\nvarious forms of evil pleasure are the origin of pain. Therefore it\nis here represented with a reed in his right hand which is useless\nand without strength, and the wounds it inflicts are poisoned. In\nTuscany they are put to support beds, to signify that it is here\nthat vain dreams come, and here a great part of life is consumed. It\nis here that much precious time is wasted, that is, in the morning,\nwhen the mind is composed and rested, and the body is made fit to\nbegin new labours; there again many vain pleasures are enjoyed; both\nby the mind in imagining impossible things, and by the body in\ntaking those pleasures that are often the cause of the failing of\nlife. And for these reasons the reed is held as their support.\n\n[Footnote: 676. The pen and ink drawing on PI. LIX belongs to this\npassage.]\n\n[Footnote: 8. _tribolatione_. In the drawing caltrops may be seen\nlying in the old man's right hand, others are falling and others\nagain are shewn on the ground. Similar caltrops are drawn in MS.\nTri. p. 98 and underneath them, as well as on page 96 the words\n_triboli di ferro_ are written. From the accompanying text it\nappears that they were intended to be scattered on the ground at the\nbottom of ditches to hinder the advance of the enemy. Count Giulio\nPorro who published a short account of the Trivulzio MS. in the\n\"_Archivio Storico Lombardo_\", Anno VIII part IV (Dec. 31, 1881) has\nthis note on the passages treating of \"_triboli_\": \"_E qui\naggiunger\u00f2 che anni sono quando venne fabbricata la nuova\ncavallerizza presso il castello di Milano, ne furono trovati due che\nio ho veduto ed erano precisamente quali si trovano descritti e\ndisegnati da Leonardo in questo codice_\".\n\nThere can therefore be no doubt that this means of defence was in\ngeneral use, whether it were originally Leonardo's invention or not.\nThe play on the word \"_tribolatione_\", as it occurs in the drawing\nat Oxford, must then have been quite intelligible.]\n\n[Footnote: 9--22. These lines, in the original, are written on the\nleft side of the page and refer to the figure shown on PI. LXI. Next\nto it is placed the group of three figures given in PI. LX No. I.\nLines 21 and 22, which are written under it, are the only\nexplanation given.]\n\nEvil-thinking is either Envy or Ingratitude.\n\n677.\n\nEnvy must be represented with a contemptuous motion of the hand\ntowards heaven, because if she could she would use her strength\nagainst God; make her with her face covered by a mask of fair\nseeming; show her as wounded in the eye by a palm branch and by an\nolive-branch, and wounded in the ear by laurel and myrtle, to\nsignify that victory and truth are odious to her. Many thunderbolts\nshould proceed from her to signify her evil speaking. Let her be\nlean and haggard because she is in perpetual torment. Make her heart\ngnawed by a swelling serpent, and make her with a quiver with\ntongues serving as arrows, because she often offends with it. Give\nher a leopard's skin, because this creature kills the lion out of\nenvy and by deceit. Give her too a vase in her hand full of flowers\nand scorpions and toads and other venomous creatures; make her ride\nupon death, because Envy, never dying, never tires of ruling. Make\nher bridle, and load her with divers kinds of arms because all her\nweapons are deadly.\n\nToleration.\n\nIntolerable.\n\nNo sooner is Virtue born than Envy comes into the world to attack\nit; and sooner will there be a body without a shadow than Virtue\nwithout Envy.\n\n[Footnote: The larger of the two drawings on PI. LXI is explained by\nthe first 21 lines of this passage. L. 22 and 23, which are written\nabove the space between the two drawings, do not seem to have any\nreference to either. L. 24-27 are below the allegorical twin figure\nwhich they serve to explain.]\n\n678.\n\nWhen Pluto's Paradise is opened, then there may be devils placed in\ntwelve pots like openings into hell. Here will be Death, the Furies,\nashes, many naked children weeping; living fires made of various\ncolours....\n\n679.\n\n  John the Baptist\n  Saint Augustin\n  Saint Peter\n  Paul\n  Elisabeth\n  Saint Clara.\n  Bernardino\n  Our Lady  Louis\n  Bonaventura\n  Anthony of Padua.\n  Saint Francis.\n  Francis,\n  Anthony, a lily and book;\n  Bernardino with the [monogram of] Jesus,\n  Louis with 3 fleur de lys on his breast and\n              the crown at his feet,\n  Bonaventura with Seraphim,\n  Saint Clara with the tabernacle,\n  Elisabeth with a Queen's crown.\n\n[Footnote: 679. The text of the first six lines is written within a\nsquare space of the same size as the copy here given. The names are\nwritten in the margin following the order in which they are here\nprinted. In lines 7--12 the names of those saints are repeated of\nwhom it seemed necessary to point out the emblems.]\n\nList of drawings.\n\n680.\n\n  A head, full face, of a young man\n  with fine flowing hair,\n  Many flowers drawn from nature,\n  A head, full face, with curly hair,\n  Certain figures of Saint Jerome,\n  [6] The measurements of a figure,\n  Drawings of furnaces.\n  A head of the Duke,\n  [9] many designs for knots,\n  4 studies for the panel of Saint Angelo\n  A small composition of Girolamo da Fegline,\n  A head of Christ done with the pen,\n  [13] 8 Saint Sebastians,\n  Several compositions of Angels,\n  A chalcedony,\n  A head in profile with fine hair,\n  Some pitchers seen in(?) perspective,\n  Some machines for ships,\n  Some machines for waterworks,\n  A head, a portrait of Atalanta raising her\n  face;\n  The head of Geronimo da Fegline,\n  The head of Gian Francisco Borso,\n  Several throats of old women,\n  Several heads of old men,\n  Several nude figures, complete,\n  Several arms, eyes, feet, and positions,\n  A Madonna, finished,\n  Another, nearly in profile,\n  Head of Our Lady ascending into Heaven,\n  A head of an old man with long chin,\n  A head of a gypsy girl,\n  A head with a hat on,\n  A representation of the Passion, a cast,\n  A head of a girl with her hair gathered in a knot,\n  A head, with the brown hair dressed.\n\n[Footnote: 680. This has already been published by AMORETTI _Memorie\nstoriche_ cap. XVI. His reading varies somewhat from that here\ngiven, _e. g._ l. 5 and 6. _Certi Sangirolami in su d'una figura_;\nand instead of I. 13. _Un San Bastiano_.]\n\n[Footnote: 680. 9. _Molti disegni di gruppi_. VASARI in his life of\nLeonardo (IV, 21, ed. MILANESI 1880) says: \"_Oltrech\u00e9 perse tempo\nfino a disegnare_ gruppi _di corde fatti con ordine, e che da un\ncapo seguissi tutto il resto fino all' altro, tanto che s'empiessi\nun tondo; che se ne vede in istampa uno difficilissimo e molto\nbello, e nel mezzo vi sono queste parole: Leonardus Vinci\nAccademia_\". _Gruppi_ must here be understood as a technical\nexpression for those twisted ornaments which are well known through\nwood cuts. AMORETTI mentions six different ones in the Ambrosian\nLibrary. I am indebted to M. DELABORDE for kindly informing me that\nthe original blocks of these are preserved in his department in the\nBiblioth\u00e8que Nationale in Paris. On the cover of these volumes is a\ncopy from one of them. The size of the original is 23 1/2\ncentimetres by 26 1/4. The centre portion of another is given on p.\n361. G. Govi remarks on these ornaments (_Saggio_ p. 22): \"_Codesti\ngruppi eran probabilmente destinati a servir di modello a ferri da\nrilegatori per adornar le cartelle degli scolari (?). Fregi\nsomigliantissimi a questi troviamo infatti impressi in oro sui\ncartoni di vari volumi contemporanei, e li vediam pur figurare nelle\nlettere iniziali di alcune edizioni del tempo._\"\n\nD\u00fcrer who copied them, omitting the inscription, added to the second\nimpressions his own monogram. In his diary he designates them simply\nas \"_Die sechs Knoten_\" (see THAUSING, Life of A. D\u00fcrer I, 362,\n363). In Leonardo's MSS. we find here and there little sketches or\nsuggestions for similar ornaments. Compare too G. MONGERI, _L'Arte\nin Milano_, p. 315 where an ornament of the same character is given\nfrom the old decorations of the vaulted ceiling of the Sacristy of\nS. Maria delle Grazie.]\n\n[Footnote: 680, 17. The meaning in which the word _coppi_, literally\npitchers, is here used I am unable to determine; but a change to\n_copie_ seems to me too doubtful to be risked.]\n\n681.\n\n  Stubborn rigour.\n  Doomed rigour.\n\n[Footnote: See PI. LXII, No. 2, the two upper pen and ink drawings.\nThe originals, in the Windsor collection are slightly washed with\ncolour. The background is blue sky; the plough and the instrument\nwith the compass are reddish brown, the sun is tinted yellow].\n\n682.\n\n  Obstacles cannot crush me\n  Every obstacle yields to stern resolve\n  He who is fixed to a star does not change\n  his mind.\n\n[Footnote: This text is written to elucidate two sketches which were\nobviously the first sketches for the drawings reproduced on PL LXII,\nNo. 2.]\n\n683.\n\nIvy is [a type] of longevity.\n\n[Footnote: In the original there is, near this text, a sketch of a\ncoat wreathed above the waist with ivy.]\n\n684.\n\n  Truth      the sun.\n  falsehood   a mask.\n  innocence,\n  malignity.\n\n  Fire destroys falsehood,\n  that is sophistry, and\n  restores truth, driving out\n  darkness.\n\n  Fire may be represented as the destroy of\n  all sophistry, and as the\n  image and demonstration of truth;\n  because it is light and drives\n  out darkness which conceals\n  all essences [or subtle things].\n\n[Footnote: See PI. LXIII. L. 1-8 are in the middle of the page; 1.\n9-14 to the right below; 1. 15-22 below in the middle column. The\nrest of the text is below the sketches on the left. There are some\nother passages on this page relating to geometry.]\n\nTRUTH.\n\n  Fire destroys all sophistry, that is deceit;\n  and maintains truth alone, that is gold.\n\n  Truth at last cannot be hidden.\n  Dissimulation  is of no avail. Dissimulation is\n  to no purpose before\n  so great a judge.\n  Falsehood puts on a mask.\n  Nothing is hidden under the sun.\n\n  Fire is to represent truth because it\n  destroys all sophistry and lies; and the\n  mask is for lying and falsehood\n  which conceal truth.\n\n685.\n\n  Movement will cease before we are\n  weary\n  of being useful.\n\n  Movement will fail sooner than usefulness.\n  Death sooner than        I am never weary   of\n  weariness.               being useful,\n  In serving others I      is a motto for carnval.\n  cannot do enough.        Without fatigue.\n\n  No labour is\n  sufficient to tire me.\n\n  Hands into which\n  ducats and precious\n  stones fall like snow; they\n  never become tired by serving,\n  but this  service is only for its\n  utility and not for our      I am never weary\n  own benefit.                 of being useful.\n\n  Naturally\n  nature has so disposed me.\n\n686.\n\n  This shall be placed in the\n  hand of Ingratitude.\n  Wood nourishes the fire that\n  consumes it.\n\n687.\n\nTO REPRESENT INGRATITUDE.\n\n  When the sun appears\n  which dispels darkness in\n  general, you put out the\n  light which dispelled it\n  for you in particular\n  for your need and convenience.\n\n688.\n\n  On this side Adam and Eve on the other;\n  O misery of mankind, of how many things do\n  you make yourself the slave for money!\n\n[Footnote: See PI. LXIV. The figures of Adam and Eve in the clouds\nhere alluded to would seem to symbolise their superiority to all\nearthly needs.]\n\n689.\n\nThus are base unions sundered.\n\n[Footnote: A much blurred sketch is on the page by this text. It\nseems to represent an unravelled plait or tissue.]\n\n690.\n\n  Constancy does not begin, but is that\n  which perseveres.\n\n[Footnote: A drawing in red chalk, also rubbed, which stands in the\noriginal in the middle of this text, seems to me to be intended for\na sword hilt, held in a fist.]\n\n691.\n\n  Love, Fear, and Esteem,--\n  Write these on three stones. Of servants.\n\n692.\n\nPrudence Strength.\n\n693.\n\n  Fame alone raises herself to Heaven,\n  because virtuous things are in favour with God.\n\n  Disgrace should be represented upside\n  down, because all her deeds are contrary to\n  God and tend to hell.\n\n694.\n\nShort liberty.\n\n695.\n\n  Nothing is so much to be feared as Evil\n  Report.\n  This Evil Report is born of life.\n\n696.\n\nNot to disobey.\n\n697.\n\n  A felled tree which is shooting\n  again.\n\n  I am still hopeful.\n  A falcon,\n  Time.\n\n[Footnote: I. _Albero tagliato_. This emblem was displayed during\nthe Carnival at Florence in 1513. See VASARI VI, 251, ed. MILANESI\n1881. But the coincidence is probably accidental.]\n\n698.\n\n  Truth here makes Falsehood torment\n  lying tongues.\n\n699.\n\n  Such as harm is when it hurts me not,\n  is good which avails me not.\n\n[Footnote: See PI. LX, No. 2. Compare this sketch with that on PI.\nLXII, No. 2. Below the two lines of the text there are two more\nlines: _li g\u00f9chi (giunchi) che rit\u00e9g\u00f2 le paglucole (pagliucole)\nchelli (che li) anniegano_.]\n\n700.\n\nHe who offends others, does not secure himself.\n\n[Footnote: See PI. LX, No. 3.]\n\n701.\n\nIngratitude.\n\n[Footnote: See PI. LX, No. 4. Below the bottom sketches are the\nunintelligible words \"_sta stilli_.\" For \"_Ingratitudo_\" compare\nalso Nos. 686 and 687.]\n\n702.\n\nOne's thoughts turn towards Hope.\n\n[Footnote: 702. By the side of this passage is a sketch of\na cage with a bird sitting in it.]\n\nOrnaments and Decorations for feasts (703-705).\n\n703.\n\nA bird, for a comedy.\n\n[Footnote: The biographies say so much, and the author's notes say\nso little of the invention attributed to Leonardo of making\nartificial birds fly through the air, that the text here given is of\nexceptional interest from being accompanied by a sketch. It is a\nvery slight drawing of a bird with outspread wings, which appears to\nbe sliding down a stretched string. Leonardo's flying machines and\nhis studies of the flight of birds will be referred to later.]\n\n704.\n\nA DRESS FOR THE CARNIVAL.\n\nTo make a beautiful dress cut it in thin cloth and give it an\nodoriferous varnish, made of oil of turpentine and of varnish in\ngrain, with a pierced stencil, which must be wetted, that it may not\nstick to the cloth; and this stencil may be made in a pattern of\nknots which afterwards may be filled up with black and the ground\nwith white millet.[Footnote 7: The grains of black and white millet\nwould stick to the varnish and look like embroidery.]\n\n[Footnote: Ser Giuliano, da Vinci the painter's brother, had been\ncommissioned, with some others, to order and to execute the garments\nof the Allegorical figures for the Carnival at Florence in 1515--16;\nVASARI however is incorrect in saying of the Florentine Carnival of\n1513: \"_equelli che feciono ed ordinarono gli abiti delle figure\nfurono Ser Piero da Vinci, padre di Lonardo, e Bernardino di\nGiordano, bellissimi ingegni_\" (See MILANESI'S ed. Voi. VI, pg.\n251.)]\n\n705.\n\nSnow taken from the high peaks of mountains might be carried to hot\nplaces and let to fall at festivals in open places at summer time.","title":"The Notebooks of Leonardo Da Vinci \u2014 Volume 1","tradition":"philosophy-ethics","translated_text":null,"word_count":107402}