Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

parts of these wholes have sometimes a natural, and sometimes
an unnatural subsistence; for thus alone can the circle of generation
unfold all the variety which it contains.
The different periods in which these mutations happen, are
called by Plato, with great propriety, periods of fertility and
sterility. For in these periods, a fertility or sterility of men,
animals, and plants, takes place; so that in fertile periods, mankind
will be both more numerous, and upon the whole, superior
in mental and bodily endowments, to the men of a barren
period. And a similar reasoning must be extended to animals
and plants. The so much celebrated heroic age, was the
result of one of these fertile periods, in which men transcending
the herd of mankind, both in practical and intellectual
virtue, abounded on the earth.
With respect to the epithet divinely generated, it is well observed
by the Greek scholiast, "that Plato does not mean by
this either the whole world, though the epithet is primarily
applicable to it, nor the celestial regions only, nor the sublunary
world, but every thing which is perpetually and circularly
moved, whether in the heavens, or under the moon; so far as
it is corporeal calling it generated, (for no body is self-subsistent),
but so far as it is perpetually moved, divine. For it imt
tates the most divine of things, which possess an ever-vigilant
life. But with respect to the perfect number mentioned here
by Plato, we must not only direct our attention to a perfect
number in vulgar arithmetic,-for this is rather numbered
than number, tends to perfection and is never perfect, as being
always in generation,-but we must survey the cause of this
number, which is indeed intellectual, but comprehends the
definite boundary of every period of the world."
In the third place, let us consider what Plato means by augmentations
surpassing and surpassed; things assimilating and