Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

that all motion is after rest, and that permanency is always
naturally prior to mobility. But astronomy is the doctrine of
moveable, and geometry of immoveable natures. The motion
of the stars likewise is celebrated as being accompanied with
harmonic modulations. Whence also it appears that the power
of music precedes in antiquity the course of the stars. And it
cannot be doubted that arithmetic naturally surpasses astronomy,
since it appears to be more ancient than geometry and
music which are prior to it. For by numbers we collect the
rising and setting of the stars, the swiftness and slowness of
the planets, and the eclipses and manifold variations of the
moon.
CHAPTER 11.
On the definition of number and the monad.
THALES* defined number conformably to the doctrine of
the Egyptians by whom he was instructed, to be a collection
of monads. But Pythagoras defined it to be the extension and
energy of the spermatic reasons contained in the monad. Or
otherwise, to be that which prior to all things subsists in a
divine intellect, by which and from which all things are coordinated,
and remain connumerated in an indissoluble order.
Others, however, of his followers defined it to be a progression
from unity through the magnitude of it. But Eudoxus the
Pythagorean says, that number is definite multitude, in which
definition he distinguishes the species from the genus. The
followers of Hippasus who were called Acousmatici said that
number is the first paradigm of the fabrication of the world;
Vid. Iamblich. in Nicomach. Arithrnet. p. 11.