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Chapter XVIII.—Pythagoras’ System of Numbers.

Pythagoras, then, declared the originating
principle of the universe to be the unbegotten monad, and the generated
duad, and the rest of the numbers. And he says that the monad is
the father of the duad, and the duad the mother of all things that are
being begotten—the begotten one (being mother) of the things that
are begotten. And Zaratas, the pupil of Pythagoras, was in the
habit of denominating unity a father, and duality a mother. For
the duad has been generated from the monad, according to Pythagoras;
and the monad is male and primary, but the duad female (and
secondary). And from the duad, again, as Pythagoras states, (are
generated) the triad and the succeeding numbers up to ten. For
Pythagoras is aware that this is the only perfect number—I mean
the decade—for that eleven and twelve are an addition and
repetition of the decade; not, however, that what is added^{653}^{653} Miller
would read for προστιθέμενον,
νομιστέον or
νομίζει. constitutes the generation of another
number. And all solid bodies he generates from incorporeal
(essences). For he asserts that an element and principle of both
corporeal and incorporeal entities is the point which is
indivisible. And from a point, he says, is generated a line, and
from a line a surface; and a surface flowing out into a height becomes,
he says, a solid body. Whence also the Pythagoreans have a
certain object of adjuration, viz., the concord of the four
elements. And they swear in these words:—

“By him who to our head quaternion gives,

A font that has the roots of everlasting
nature.”^{654}^{654}
Respecting these lines, Miller refers us to Fabricius, *in
Sextum Empiricum*, p. 332.

Now the quaternion is the originating principle of natural and
solid bodies, as the monad of intelligible ones. And that
likewise the quaternion generates,^{655}^{655} The Abbe
Cruice adduces a passage from Suidas (on the word ἀριθμός) which contains a
similar statement to that furnished by Hippolytus.
he says, the perfect number, as in the case of intelligibles (the
monad) does the decade, they teach thus. If any, beginning to
number, says one, and adds two, then in like manner three, these
(together) will be six, and to these (add) moreover four, the entire
(sum), in like manner, will be ten. For one, two, three, four,
become ten, the perfect number. Thus, he says, the quaternion in
every respect imitated the intelligible monad, which was able to
generate a perfect number.

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