Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

mon the term first is adapted to all of them), viz. to the triad
itself, and the tetrad itself.
Again, the Pythagoreans and Plato did not denominate idea
from one thing, and ideal number from another. But since the
assertion is eminently true, that all things are similar to number,
it is evident that number, and especially every ideal number,
was denominated on account of its paradigmatic peculiarity.
If any one, however, wishes to apprehend this from the
appellation itself, it is easy to infer that idea was called, from
rendering as it were its participants similar to itself, and imparting
to them form, order, beauty, and unity; and this in
consequence of always preserving the same form, expanding its
own power to the infinity of particulars, and investing with
the same species its eternal participants. Ntrmber also, since it
imparts proportion and elegant arrangement to all things, was
allotted this appellation. For the ancients, says Syrianus," call
to adapt or compose a~gac arsai, whence is derived aptepoc
arzthrn oz ntlmber. Hence avap~tov anarsion among the Greeks
signifies incomposite. Hence too, those Grecian sayings, you
will adapt the balance, they placed nrrmber together with
them, and also number and friendship. From all which number
was called by the Greeks arithmos, as that which measures
and orderly arranges all things, and unites them in amicable
league.
Farther still, some of the Pythagoreans discoursed about
inseparable numbers alone, i.e. numbers which are inseparable
from mundane natures, but others about such as have a subsistence
separate from the universe, in which as paradigms they
saw those numbers are contained, which are perfected by
nature. But others, making a distinction between the two,
unfolded their doctrine in a more clear and perfect manner.
* In Aristot. Metaphys. Lib. 13.