Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

titude, and communion with itself, it produces geometry. Understanding
itself likewise to be both one and many, it pre
duces numbers, and the knowledge of these. But it procures
for itself music, according to the bond by which it is held together.
Hence arithmetic is more ancient than music, since
the soul was first divided in a fabricative way, and afterwards
was bound together by harmonic ratios, as Plato narrates in
the Timaeus. And again, the discursive energy of reason being
established according to a permanent energy in itself, unfolds
from itself geometry, and the fabricative principles of all figures."
But according to its inherent motion, it produces the
spheric science. For it also is moved according to circles; but
is established in invariable sameness, according to the causes
of circles. On this account, here also geometry precedes
spherics, just as permanency is prior to motion.
"Sihce however the scientifically-reasoning power generates
these sciences, not by looking to its evolution of forms which
possesses an infinite power, but to the generic comprehension
of bound, hence the Pythagoreans say that the mathematical
sciences taking away the infinite, are now conversant with
finite quantity. For intellect has established in the scientificaC
ly-reasoning power all the principles both of multitude and
magnitude; since this power wholly consists with reference to
itself of similar parts, is one and indivisible, and again divisible.
Unfolding into light likewise the world of forms, it participates
of bound and infinity essentially from intelligibles. But it perceives
intellectually indeed from its participation of bound, and
generates vital energies, and various productive principles from
the nature of infinity. The intellections therefore of the reasoning
power, constitute these sciences according to the bound
which they contain, and not according to the infinity of life.
For they bring with them an image of intellect, but not of life.
+ 1.c. a right and circular line.