Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

speaking accurately. Farther still, it has been shown that the
odd number derives its completion from unity alone; but the
even number from the duad alone. Hence, it must be said,
that, the odd number participates of the essence which possesses
an invariable sameness of subsistence, because it is formed
by unity ; but that the even number is full of the nature of difference,
because it derives its completion from the duad.
CHAPTER XV.
That squares are generated from odd numbers; but the HETE-
ROMEKEIS from even numbers.
IF all the odd numbers are arranged from unity, and under
these are placed the even numbers from the duad, the coacervation
of the odd numbers forms squares, but the coacervation of
the even numbers produces the above mentioned numbers
called heteromekeis. Hence, because this is the nature of
squares, that they are generated from odd numbers, which
participate of the monad, i.e. of an essence invariably the same,
and because they are equal in all their parts, angles being equal
to angles, sides to sides, and breadth to length, it must be said
that numbers of this kind participate of the immutable essence.
But we must aasert that those numbers which parity or evenness
generates longer in the other part, participate of the nature
of difference. For as 1 differs only from 2 by 1, so the
sides of these numbers differ only from each other by unity.
Let therefore all the odd numbers be disposed in order from
unity, and under these all the even numbers from 2, viz.
The leader therefore of the odd series is unity, which is itself
the efficient cause, and after a manner a certain form of im-