Harmonies of the World, by Johannes Kepler, tr. Charles Glenn Wallis [1939]
Therefore by now I have proved by means of numbers gotten on one side from astronomy and on the other side from harmonics that, taken in every which way, harmonic ratios hold between these twelve termini or movements of the six planets revolving around the sun or that they approximate such ratios within an imperceptible part of least concord. But just as in Book III in the first chapter, we first built up the single…