Note 159 — Chapter XXXI

The meaning of Proclus in asserting that the ennead proceeds from the monad as far as to the extremities without retrogression is as follows: The ennead, according to the Pythagoreans, circulates all numbers within itself, and there can be no number beyond it. For the natural progression of numbers is as far as to 9, but after it their retrogression takes place. For 10 becomes as it were again the 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, &c. 9 is added, the numbers produced will be 10, 11, 12, 13, &c. 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 too the Pythagoreans, called it Ocean and the Horizon, because all numbers are comprehended by and revolve within it. On this account likewise, it was called by them Halios, (παρα το αλιζειν) and Concord and Perseïa because it congregates all numbers, and collects them into one, and does not permit the conspiration of the numbers beyond it to be dissipated. Vid. Anonym. in opere quod inscripsit τα θεολογουμενα της αριθμητικης.