Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

such as those of multiples, or superparticulars, etc., or of discrete
quantity considered by itself, are comprehended in this
twofold nature of numbers, viz. of squares, and numbers longer
in the other part. Hence as the world consists of an immutable
and mutable essence, so every number is formed from squares
which partake of immutability, and from numbers longer in
the other part, which participate of mutability. And in the
first place, the numbers that are promekeis or oblong, must
be distinguished from those that are heteromekeis, or longer
in the other part. For the latter is produced by the multiplication
of two numbers that differ from each other by unity, such
as 6 which is produced by 2 multiplied by 3, or 12 which is produced
by 4 multiplied by 3. But the oblong number is produced
by the multiplication of two numbers that differ from
each other by more than unity, such as thrice five, or thrice six,
or four times seven. Hence, because it is more extended in
length than in breadth, it is very properly called prome&s, or
longer in the anterior part. But squares, because their breadth
is equal to their length, may aptly be denominated of a proper
length, or of the same breadth. And the heteromekeis because
they are not extended in the same length, are called of another
length, and longer in the other part.
CHAPTER XVIII.
That all things consist of sameness and difference; and that
the truth of this is primarily to be seen in numbers.
EVERY thing, however, which in its proper nature and essence
is immoveable, is terminated and definite; since that
which is changed by no variation, never ceases to be, and
never can be that which it was not. The monad is a thing of
this kind: and those numbers which derive their formation