Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

as far as to the monad which is naturally indivisible.*
From Macrobius too we learn that "the ogdoad was called
by the Pythagoreans justice, because it is the first number that
is so resolved into evenly-even numbers, viz. into two fours,
that each of these can nevertheless be divided into numbers
equally evenly-even, i.e. into two twos. Its composition also is
of the same quality as its analysis; for it is twice two twice.
Since therefore its composition proceeds by an even equality,
and its analysis equally returns as far as to the monad, which
does not receive division in an arithmetical ratio, the ogdoad
deservedly obtains the appellation of justice on account of its
equal division."
CHAPTER XI
On the ennead.
ACCORDING to the extracts from Nicomachus, the ennead
was celebrated by the Pythagoreans as "flowing round the
other numbers within the decad like the ocean. It was also
called by them the horizon, Prometheus and Concord, Perseia
and Halios, freedom from strife and similitude, Vulcan and
Juno, the sister and wife of Jupiter, Hecaergus and Paan,
Nysseis and Agyica, Enyalius and Agelia, Tritogenia and Persuasion,
Curetis and Proserpine, Hyperion, and of the Muses
Terpsichore."
Of these appellations, ocean and the horizon are unfolded as
follows by the anonymous writer: "That there can be no number
beyond the ennead, but that it circulates all numbers within
itself, is evident from the regression of numbers. For the natural
progression of them is as far as to 9, but after it their
retrogression takes place. For 10 becomes as it were again the
* Viz. It can be divided by 2 as far as to unity.