Note 40 — Chapter I · SPECULATIVE PHILOSOPHY IN GREECE, BEFORE AND IN THE TIME OF SOKRATES.

Playfair observes (in his dissertation on the Progress of Natural Philosophy, p. 87) respecting Kepler — “Kepler was perhaps the first person who conceived that there must be always a law capable of being expressed by arithmetic or geometry, which connects such phenomena as have a physical dependence on each other”. But this seems to be exactly the fundamental conception of the Pythagoreans: or rather a part of their fundamental conception, for they also considered their numbers as active forces bringing such law into reality. To illustrate the determination of the Pythagoreans to make up the number of Ten celestial bodies, I transcribe another passage from Playfair (p. 98). Huygens, having discovered one satellite of Saturn, “believed that there were no more, and that the number of the planets was now complete. The planets, primary and secondary, thus made up twelve — the double of six, the first of the perfect numbers.”