Life of Pythagoras — Iamblichus, trans. Thomas Taylor (1818)

“Since also separate numbers possess a demiurgic or fabricative power, which mathematical numbers imitate, the sensible world likewise contains images of those numbers by which it is adorned; so that all things are in all, but in an appropriate manner in each. ‘The sensible world, therefore, subsists from immaterial and energetic reasons, and from more ancient causes. But those who do not admit that nature herself is full of productive powers, lest they should be obliged to double things themselves, these wonder how from things void of magnitude and gravity, magnitude and gravity are composed; though they are never composed from things of this kind which are void of gravity and magnitude, as from parts. But magnitude is generated from essentially impartible elements; since form and matter are the elements of bodies; and still much more is it generated from those truer causes which are considered in demiurgic reasons and forms. Is it not therefore necessary that all dimensions, and all moving masses,

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must from these receive their generation? For either bodies are unbegotten, like incorporeal natures; or of things with interval, things without interval are the causes; of partibles impartibles; and of sensibles and contraries, things insensible and void of contact: and we must assent to those who assert that things possessing magnitude are thus generated from impartibles.

Hence the Pythagorean Eurytus, and his followers, beholding the images of things themselves in numbers, rightly attributed certain numbers to certain things, according to their peculiarity. In consequence of this, he said that a particular number is the boundary of this plant, and again, another number of this animal; just as of a triangle 6 is the boundary, of a square 9, and of a cube 8.

As the musician, too, harmonizes his lyre through mathematical numbers, so nature through her own natural numbers, orderly arranges, and modulates her productions.

“Indeed, that numbers are participated by the heavens, and that there is a solar number, and also a lunar number, is manifest according to the adage, even tothe blind. For the restitutions of the heavenly bodies to their pristine state (aroxatacracets) would not always be effected through the same things, and in the same manner, unless one and the same number had dominion in each. Yet all these contribute to the procession of the celestial spheres, and are contained by their perfect number. But there is also a certain natural number belonging to every animal. For things of the same species would not be distinguished by organs after the same manner, nor would they arrive at puberty and old age about the same time, or generate, nor would the feetus be nourished or increase, according to regular periods, unless they were detained by the same measure of nature. According to the best of the Pythagoreans also, Plato himself, number is the cause of better and worse generations. Hence though the Pythagoreans sometimes speak of the squares andp. 227 cubes of natural numbers, they do not make them to be monadic, such as the number 9, and the number 27; but they signify through these names, from similitude, the progression of natural numbers into, and dominion about, generations. In like manner, though they call them equal or double, they exhibit the dominion and symphony of ideas in these numbers. Hence different things do not use the same number, so far as they are different, nor do the same things use a different number, so far as they are the same.