Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

27, but they signify through these names from similitude, the
progression of natural numbers into, and dominion about,
generations In like manner, though they call them equal or
double, they exhibit the dominion and symphony of ideas in
these numbers. Hence different things do not use the same
number, so far as they are different, nor do the same things use
a different, so far as they are the same.
In short, physical numbers are material forms divided about
the subject which receives them. But material powers are the
sources of connection and modification to bodies. For form is
one thing, and the power proceeding from it another. For
form itself is indeed impartible and essential; but being extended,
and becoming bulky, it emits from itself, as if it werc
a blast, material powers which are certain qualities. Thus, for
instance, in fire, the form and essence of it is impartible, and
is truly the image of the cause of fire: for in partible natures,
the impartible has a subsistence. But from form which is impartible
in fire, and which subsists in it as number, an extension
of it accompanied with interval, takes place about matter, from
which the powers of fire are emitted, such as heat, or refrigeration,
or moisture, or something else of the like kind. And
these qualities are indeed essential, but are by no means the
essence of fire. For essences do not proceed from qualities,
nor are essence and power the same thing. But the essential
every where precedes power. And from this being one the
multitude of powers proceeds, and the distributed from that
which is undistributed; just as many energies are the progeny
of one power.
CHAPTER
On the monad.
THE monad, as we learn from the extracts preserved by
Photius from Nicomachus, was called by the Pythagoreans