Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK THREE
CHAPTER I
On the manner in which the Pythagoreans philosophized
about numbers.
HE Pythagoreans, turning from the vulgar paths,
and delivering their philosophy in secret to those
alone who were worthy to receive it, exhibited
it to others through mathematical names. Hence
they called forms, numbers, as things which are
the first separated from impartible union; for the natures
which are above forms, are also above separation.+ The allperfect
multitude of forms, therefore, they obscurely signified
through the duad; but they indicated the first formal principles
by the monad and duad, as not being numbers; and also
by the first triad and tetrad, as being the first numbers, the
one being odd, and the other even, from which by addition
the decad is generated; for the sum of 1, 2, 3, and 4, is ten.
But after numbers, in secondary and multifarious lives, introducing
geometrical prior to physical magnitudes; these also
they referred to numbers, as to formal causes and the princi-
+ Forms subsist at the extremity of the intelligible triad, which triad consists of
being, life, and intellect. But being and life, with all they contain, subsist here
involved in impartible union. See my Proclus on the Theology of Plato.