Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

of the hebdomad 3 and 4 necessarily impart the right angle,
this hebdomad may justly be considered as the fountain of
every figure and of every quality. To what has been said also,
it may be properly added, that 3 is the number of a plane figure,
since a point is arranged according to the monad, but a
line according to the duad, and a superficies according to the
triad. But 4 is the number of a solid, by the addition of unity
giving depth to superficies. Hence it is manifest, that the essence
of the hebdomad is the principle of geometry and stereometry:
and in short, it is the principle of incorporeal and corporeal
natures.
There is also naturally so much of what is adapted to sacred
concerns in the hebdomad, that it has a pre-eminence with reference
to all the numbers that are within the decad. For of
these some beget, not being themselves begotten; but others are
begotten indeed, but do not beget; and others both beget and
are begotten. The hebdomad however alone is beheld in no
part of these; which may be confirmed by demonstration as
follows: Unity therefore generates all the numbers that are posterior
to it, but is by no means generated by any number. Eight
is indeed generated by twice four, but generates no number
within the decad. Again, 4 ranks among those natures that
both beget and are begotten. For it generates 8 by being multiplied
by 2, and is generated by twice two. But 7 alone, as I
have said, is neither naturally adapted to generate, nor to be
generated. Hence other philosophers indeed assimilate this
number to Victory, who is motherless and a virgin, and who is
said to have sprung to light from the head of Jupiter. But the
Pythagoreans assimilate it to the leader and ruler of all things.
For that which neither generates nor is generated, remains immoveable;
for generation subsists in motion, since that also
which is generated is not without motion. For that which
generates is in motion, in order that it may generate, and also