Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

adytum of god-nourished silence, as it is called in the Chaldean
oracles, may be said, metaphorically speaking, to be an audacious
undertaking. But the duad was called matter, as being
indefinite, and the cause of bulk and division, as Simplicius
observes in his comment on the Physics. And it is the cause of
dissimilitude, as being in its first subsistence the infinite, from
which dissimilitude is suspended, in the same manner as similitude
is suspended from bound. But it is the interval between
multitude and the monad, because it is yet perfect multitude,
but is as it wereparturient with it, and almost unfolding it into
light. Of this we see an image in the duad of arithmetic.
For as Proclus beautifully observes in his Comment on the
20th kc. definition of the first book of Euclid's Elements:
"The duad is the medium between unity and number. For
unity, by addition, produces more than by multiplication; but
number, on the contrary, is more increased by multiplication
than by addition; and the duad, whether multiplied into, or
compounded with itself, produces an equal quantity." The
duad was also called equal, because, says the anonymous author,
"two and two are equal to twice two:" that is, the addition
of two to itself, is equal to the multiplication of it by itself.
But it is unequal, defect and abundance, as the same author
observes, according to the conception of matter. For he adds,
the Pythagoreans call matter homonymously with this, the indefinite
duad, because so far as pertains to itself, it is deprived
of morphe, form, and a certain definition, and is defined and
bounded by reason and art. It is likewise alone unfigured,
because, as the anonymous writer observes, "From the triangle
and the triad polygonous figures proceed in energy, ad infiniturn;
from the monad all figures subsist at once according
to power; but from two things, whether they are right lines,
or angles, a right-lined figure can never be composed."* But
The latter part of this extract in the original is defective; for it is uxo $6