Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

ples of these; referring the point indeed, as being impartible
to the monad, but a line as the first interval to the duad; and
again, a superficies, as having a more abundant interval to the
triad; and a solid to the tetrad. They also called, as is evident
from the testimony of Aristotle, the first length the duad; for
it is not simply length, but the first length, in order that by
this they might signify cause. In a similar manner also, they
denominated the first breadth, the triad; and the first depth
the tetrad. They also referred to formal principles all psychical
knowledge. And intellectual knowledge indeed, as being
contracted according to impartible union, they referred to the
monad; but scientific knowledge, as being evolved, and as
proceeding from cause to the thing caused, yet through the
inerratic, and always through the same things, they referred
to the duad; and opinion to the triad, because the power of it
is not always directed to the same thing, but at one time inclines
to the true, and at another to the false. And they referred
sense to the tetrad, because it has an apprehension of
bodies; for in the duad indeed, there is one interval from one
monad to the other; but in the triad there are two intervals
from any one monad to the rest; and in the tetrad there are
three. They referred, therefore, to principles every thing
knowable, viz. beings, and the gnostic powers of these. But
they divided beings not according to breadth, but according
to depth; into intelligibles, objects of science, objects of opinion,
and sensibles. In a similar manner, also they divided
knowledge into intellect, science, opinion, and sense. The
extremity, therefore, of the intelligible triad, or animal itself,
as it is called by Plato in the Timaeus, is assumed from the
division of the objects of knowledge, manifesting the intelligible
order, in which forms themselves, viz. the first forms
and the principles of these, are contained, viz. the idea of the
one itself, of the first length, which is the duad itself, and also
the ideas of the first breadth and the first depth; (for in com-