Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK Two 85
from the monad, are said to be definite, and to possess a sameness
of subsistence. These, however, are such as increase from
equal numbers, as squares, or those which unity forms, i.e. odd
numbers. But the binary, and all the numbers that are longer
in the other part, in consequence of departing from a definite
essence, are said to be of a variable and infinite nature. Every
number, therefore, consists of the odd and the even, which are
very remote from and contrary to each other. For the former
rs stability; but the latter unstable variation. The former possesses
the strength of an immoveable essence; but the latter is
a moveable permutation. And the former is definite; but the
latter is an infinite accumulation of multitude. These, however,
though contrary, are after a manner mingled in friendship
and alliance; and through the forming power and dominion
of unity, produce one body of number. Those, therefore,
who have reasoned about the world, and this common
nature of things, have neither uselessly, nor improvidently
made this to be the first division of the essence of the universe.
And Plato, indeed, in the Timaeus, calls every thing that the
world contains the progeny of sameness and difference; and
asserts, that there is one thing which is always real being, and
indivisible without generation, but another which is generated,
or continually rising into existence, and divisible, but never
truly is. But Philolaus says, it is necessary that whatever exists
should be either infinite or finite; for he wished to demonstrate
that all things consists of either infinites or finites, according
to the similitude of number. For this is formed from
the junction of the monad and duad, and from the odd and
the even; which evidently belong to the same series as equality
and inequality, sameness and difference, the definite and the
indefinite. Hence, it is not without reason asserted, that all
things that consist of contraries, are conjoined and composed
by a certain harmony. For harmony is a union of many
things, and the consent of discordant natures.