Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

since it is not possible for division to proceed beyond the
monad. For if we divide the one which is in sensibles into
parts, again the one becomes multitude and many; and by a
subtraction of each of the parts we end in one. And if we
again divide this one into parts, the parts will become multitude;
and by an ablation of each of the parts, we shall at
length arrive at unity. So that the one so far as one is impartible
and indivisible. For another number indeed when divided
is diminished, and is divided into parts less than itself. Thus
for instance, 6 may be divided into 3 and 3, or into 4 and 2,
or into 5 and 1. But the one in sensibles, if it is divided indeed,
as body it is diminished, and by section is divided into
parts less than itself, but as number it is increased; for instead
of the one it becomes many. So that according to this the one
is impartible. For nothing (in sensibles) which is divided, is
divided into parts greater than itself; but that which is divided
into parts greater than the whole, and into parts equal to the
whole, is divided as number. Thus if the one which is in sensibles,
be divided into six equal parts, as number indeed, it will
be divided into parts equal to the whole, viz. into 1.1.1.1.1.1.
and also into parts greater than the whole, viz. into 4 and 2;
for 4 and 2 as numbers are more than one. Hence the monad
as number is indivisible. But it is called the monad, either
from remaining immutable, and not departing from its own
nature; for as often as the monad is multiplied into itself, it
remains the monad; since once one is one; and if we multiply
the monad to infinity, it still continues to be the monad. Or it
is called the monad, because it is separated, and remains by
itself alone apart from the remaining multitude of numbers.*
Archytas and Philolaus, as we are informed by Theo, called indiscriminately
the one, the monad, and the monad, the one. But according to the best of the
Platonists, Proclus, Dunrscius, & in divine natures the mod is that which contains
distinct, but at cbe same time profoundly-unied multitude; and the one is
the summit of the many, so that thk one is more simple than the monad. Observe