Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK Two 121
which is 18416, we must multiply the third prime number 1151
by 16, the same double of the cube 8.
"If you still want other amicable numbers, instead of 2 or its
cube 8, make use of its square cube 64; for it has the same
quality, and will answer as above."
Thus far Ozanam. But the two amicable numbers produced
from 64, which he has omitted in this extract are, 9363584, and
9437056. And the three prime numbers which are the remainders
are 191, 383, and 73727.
CHAPTER XXXIV
On lateral and diametrical n urn hers.*
As numbers have trigonic, tetragonic, and pentagonic reasons,
(or productive principles) and the reasons of all other figures
in power (i.e. causally) so likewise we shall find lateral and
diametrical reasons, spermatically as it were presenting themselves
to the view in numbers. For from these, figures are elegantly
arranged. As therefore, the monad is the principle of all
figures, according to a supreme and seminal reason, thus also
the reason of a diameter and a side, are found in the monad or
unity. Thus for instance, let there be two units, one of which
we suppose to be a diameter, but the other a side; since it is
necessary that the monad which is the principle of all figures,
should be in power, or causally both a side and a diameter.
And let the diameter be added to the side, but two sides to the
diameter; since the diameter is once in power what the side is
twice.? The diameter therefore will be made more, but the
* Vid. Theon. Smyrn. Mathemat. p. 67.
For in a square figure, the square of the diagonal is twice the square of one
of the sides, by 47. 1, of Euclid.