Metaphysics (1.4.11-1.5.3)

These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination .[*](Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from N[*] in position.

As for motion, whence and how it arises in things,

At the same time, however, and even earlier the so-called[*] Pythagoreans applied themselves to mathematics, and were the first to develop this science[*]; and through studying it they came to believe that its principles are the principles of everything.

And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues[*] of what is and comes into being—such and such a property of number being justice ,[*] and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,[*] and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe,

and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine[*] that are visible, they make the antichthon[*] the tenth.