Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

monad is either even or odd. It cannot however be even; for
it cannot be divided into equal parts, nor in short does it admit
of any division. The monad therefore is odd. If also the
even is added to the even, the whole becomes even; but if the
monad is added to an even number, it makes the whole to be
odd. And hence the monad is not even, but odd. Aristotle
however, in his treatise called Pythagoric says, that the one or
unity participates of both these natures; for being added to
the odd it makes the even, and to the even the odd; which it
would not be able to effect if it did not participate of both
these natures. And hence the one is called evenly-odd. Archytas
likewise is of the same opinion. The monad therefore
is the first idea of the odd number, just as the Pythagoreans
adapt the odd number to that which is definite and orderly in
the world. But the indefinite duad is the first idea of the even
number; and hence the Pythagoreans attribute the even number
to that which is indefinite, unknown, and inordinate in
the world. Hence also the duad is called indefinite, because it
is not definite like the monad. The terms, however, which
follow these in a continued series from unity, are increased by
an equal excess; for each of them surpasses the former number
by the monad. But being increased, their ratios to each other
are diminished. Thus in the numbers 1, 2, 3, 4, 5, 6, the ratio
of 2 to 1 is double; but of 3 to 2 sesquialter; of 4 to 3 sesqut
tertain; of 5 to 4 sesquiquartan; and of 6 to 5 sesquiquintan.
This last ratio, however, is less than the sesquiquartan, the sesquiquartan
is less than the sesquitertian, the sesquitertian than
the sequialter, and the sesquialter than the double. And the
like takes place in the remaining numbers. The odd and the
even numbers also surveyed about unity alternately succeed
each other.+
+ Vid. Theo. Smym. Mathanat. p. 29, 6.