Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

all perfectly as well as all imperfectly amicable numbers, are
contained in it; so that it corresponds in this respect, to the
series before delivered, in which all perfect and partially perfect
numbers are contained.
CHAPTER XLI
On the geometric number, in the eighth book of the Republic
of Plato.
THE obscurity of what Plato says respecting the geometric
number, is so great, as to have become proverbial among the
ancients; and it is not elucidated in any of those invaluable
remains of Grecian philosophy, which have been transmitted
to the present time. What follows, is an attempt to remove the
veil, in which it has been so long concealed.
In the first place, the whole passage in the Republic respecting
this number is as follows: "It is indeed difficult for a city
thus constituted, to be changed; but as every thing which is
generated is obnoxious to corruption, neither will such a constitution
as this remain for ever, but be dissolved. And its dissolution
is this. Not only with respect to terrestrial plants, but
likewise in terrestrial animals, a fertility and sterility of soul as
well as of body takes place, when the revolutions of the heavenly
bodies complete the periphery of their respective orbits,
which are shorter, to the shorter-lived, and contrarywise to
such as are the contrary. And with reference to the fertility
and sterility of our race, although those are wise that you have
educated to be governors of cities, yet will they never by reason
in conjunction with sense, observe the proper seasons, but overlook
them, and sometimes generate children when they ought
not. But the period to that which is divinely generated, is
that which the perfect number comprehends; and to that which