Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

monad. Thus if from each of the numbers 10, 11, 12, 13, 14,
15, 16, 17, 18, and 19, the number 9 is subtracted, the numbers
that remain will be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And vice versa
the progression will receive an increase by the addition of 9.
For if to each of the numbers 1,2, 3, 4, 5, kc. 9 is added, the
numbers produced will be 10, 11, 12, 13, 14, kc. Likewise
by subtracting from 20, twice 9, from 30, thrice 9, from 40,
four times 9, from 50, five times 9, &c. the numbers 2, 3, 4, 5,
6, &c. will be produced. By taking likewise from 100, eleven
times 9, we again return to the monad. And after the same
manner we may proceed to infinity. Hence it is not possible
there should be any elementary number beyond the ennead.
Hence the Pythagoreans called it ocean and the horizon, because
all numbers are comprehended by and revolve within
it. Hence too, it was called by them Halios, (xapa TO ahcl;erv)
concord, and Perseia, because it congregates all numbers, and
collects them into one, and does not permit the conspiration of
the numbers beyond it to be dissipated."
With respect to the appellation Prometheus, we are informed
by the anonymous writer, that the ennead was thus called,
"from not suffering a number to proceed in the anterior part
of it." (viz. from not suffering any number besides the nine
that are in the place of units to be anterior to it.) ~~o PT
7 1 ~PQOW ~ ~ ~ J V G XUP~~V ap ce~ov. He adds: "And this reasonably;
for being triply perfect, it does not admit of any increase; but
consisting of two cubes, viz. 1 and 8, and being also a square,
it is the only number as far as to itself that has a triangle* for
its side."
The same author likewise informs us, that the ennead was
called freedom from strife, on account of the retribution and
permutation of numbers from it as far as to the monad. By
* 1.e. a triangular number.