Eduard Zeller on Philolaus

“The importance of the decuple system in relation to the Pythagoreans is much greater. For as they considered numbers over ten to be only the repetition of the first ten numbers, all numbers and all powers of numbers appeared to them to be comprehended in the decad, which is therefore called by Philolaus, great all-powerful and all-producing, the beginning and the guide of the divine and heavenly, as of the terrestrial life.”

“In regard to Philolaus, we are told... that he derived geometrical determinations (the point, the line, the surface, the solid) from the first four numbers, so he derived physical qualities from five, the soul from six; reason, health, and light, from seven; love, friendship, prudence, and inventive faculty from eight. Herein (apart from the number schematism) is contained the thought that things represent a graduated scale of increasing perfection; but we hear nothing of any attempt to prove this in detail, or to seek out the characteristics proper to each particular region.”