Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

lastly, according to Chalcidius on the Timaeus of Plato, the decad
was called by the Pythagoreans the first square, because it
consists of the first four numbers, 1, 2, 3, and 4.
We have already observed that all numbers revolve within
the number 9, and that on this account it was called by the
Pythagoreans the ocean and the horizon; so that it is in reality
paronymous to the monad. This being the case, it may seem
wonderful that the decad also should be considered as analogous
to the monad. The reason however of this is, that the
first offspring of a monad is likewise a monad, which contains
in a more expanded manner all that subsists more contractedly,
and as it were spermatically in the prior monad. Hence both
the ennead and the decad are monads; but in the former all
numbers subsist more unitedly, and the latter with more
abundant diffusion and separation.
CHAPTER
On the properties of the monad.
HAVING thus unfolded the meaning of most of the appellations
given by the Pythagoreans to numbers as far as to the decad,
I shall in the next place present the reader with such properties
of these numbers as have been discovered partly by the
ancients and partly by myself; and shall begin as order requires
with the properties of the monad.
We have shown then from Aristotle in his Pythagorics that
the monad is virtually i.e. causally, both odd and even; for
added to the odd it produces the even number, and to the even
the odd number. In the next place, Plutarch in his Platonic
Questions observes, that the monad is a triangular number (in
power) ; for if any triangular number is multiplied by 8, and