Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

val things without interval are the causes, of partibles impartible~,
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 to the blind. For the restitutions
of the heavenly bodies to their pristine state (a~oxa.raa.ra-
OW) 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 foetus 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 and cubes of natural numbers, they do not make
them to be monadic, such as the number 9, and the number