Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

sav7ov. Syrianus adds, "But Philolaus declared that number
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QP~~ILOV. "And Hippasus, and all those who were
destined to a quinquennial silence, called number the judicial
instrument of the maker of the universe, and the first paradigm
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But how is it possible they could have spoken thus sublimely
of number, unless they had considered it as possessing an
essence separate from sensibles, and a transcendency fabricative,
and at the same time paradigmatic?
CHAPTER 11
On mathematical and ph ysicd number.
As in every thing, according to the doctrine of Aristotle, one
thing corresponds to matter, and another to form, in any number,
as for instance the pentad, its five monads, and in short its
quantity, and the number which is the subject of participation,
are derived from the duad itself; but its form, i.e. the pentad
itself, is from the monad: for every form is a monad, and
unites its subject quantity. The pentad itself, therefore, which
is a monad, proceeds from the principal monad, or that which
ranks as the highest principle after the ineffde one, forms its
subject quantity, which is itself formless, and connects it to its
own form. For there are two principles of mathematical numbers
in our souls, the monad which comprehends in itself all
the forms of numbers, and corresponds to the monad in intellectual
natures, and the duad which is a certain generative
principle of infinite power, and which on this account, as being