Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

one side, and 1 on the other, each of which is equally distant
from 5. Thus too, if 3 is added to 5, and is also subtracted
from it, on the one side 8 will be produced, and on the other 2.
If 2 is added to 5, and likewise taken from it, 7 and 3 will be
produced. And by adding 1 to 5 and subtracting 1 from it, 6
and 4 will be the result; in all which instances the numbers
produced are equidistant from 5, and the sum of each couple
is equal to 10.
We are likewise informed by Plutarch in his treatise On the
Generation of the Soul according to Plato, that the Pythagoreans
called the pentad ~QO~~OC, which signifies a sound, because
they were of opinion that the first of the intervals of a tone
which is capable of producing a sound is the fifth.
The same Plutarch also in his treatise On Ec at Delphi, farther
informs us that the pentad was called by the Pythagoreans
nature, "because," says he, "by the multiplication of itself, it
again terminates in itself. For as nature receiving wheat in the
seed, and becoming expanded in the middle produces many
figures and forms, through which she brings her work to the
(desired) end, but at last exhibits wheat, restoring the principle
at the end of the whole mutation, thus also, while other
numbers, when multiplied into themselves, terminate by increase
in other numbers, five and six alone as often as they are
multiplied into themselves, exhibit and preserve themselves."
CHAPTER VIII
On the hexad.
THE Pythagoreans, as we learn from the extracts from Nicomachus,
denominated the hexad, "the form of form, the only
number adapted to the soul, the distinct union of the parts of
the universe, the fabricator of the soul, and the producing
cause of the vital habit. Hence also, it is harmony, the perfec-