Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK Two 83
the principles of things, and who have given a twofold division
to the nature of all beings,-these assert that the essences
of all things consist of sameness and difference, the former of
which is the cause of an immutable, and the latter of a variable
mode of subsistence. These two principles likewise, pertain to
the monad and the duad, the latter of which being the first
number that departs from the monad, becomes on this account
different. And because all odd numbers are formed according
to the nature of the monad, and the numbers arising from the
addition of these are squares, hence squares are said to be
participants of sameness in a twofold respect, because they are
formed from equality, each being produced by the multiplication
of a number into itself, and both angles and sides being
equal to each other, and because they are generated from the
coacervation of odd numbers. But even numbers, because
they are the forms of the binary number, and the aggregates of
these form the numbers that are longer in the other pmt, are
said, through the nature of the duad to depart from the nature
of sameness, and to be participants of difference. Hence,
since the sides of squares proceeding from equality tend to
equality, the numbers that are longer in the other part, by the
addition of unity depart from the equality of sides, and on
this account are conjoined from sides that are dissimilar, and
in a certain respect different from each other. Every thing
incorporeal therefore, form its immutability participates of the
nature of saneness, and every thing corporeal, from its mutable
and variable essence, participates of the nature of difference,
It must now therefore be shown, that all the species of numbers,
and all habitudes, whether of relative discrete quantity,
final number; but 6 in the multiplications by itself, has either 1, 3, 5, 7, or 9,
preceding the final number, as is evident in the following numbers, 36, 216, 1296,
7776, 46656, 279936, 1679616, &c.