Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

pass the sum of the whole number, is called superabundant.
On the contrary, that number is called deficient, the parts of
which are surpassed by the multitude of the whole; and such
are the numbers 8 and 14. For the half of 8 is 4; the fourth
is 2; and the eighth is 1; the aggregate of all which is 7; a sum
less than the whole number. Again, the half of 14 is 7; the
seventh is 2; and the fourteenth is 1; the aggregate of which
is 10; a sum less than the whole term. Such therefore are these
numbers, the former of which in consequence of being surpassed
by its parts, resembles one born with a multitude of
hands in a manner different from the common order of nature,
such as the hundred-handed giant Briareus, or one whose
body is formed from the junction of three bodies, such as the
triple Gerion, or any other production of nature which has
been deemed monstrous by the multiplication of its parts. But
the latter of these numbers resembles one who is born with a
deficiency of some necessary part, as the one-eyed Cyclops,
or with the want of some other member.
Between these however, as between things equally immoderate,
the number which is called perfect is alloted the temperament
of a middle limit, and is in this respect the emulator of
virtue; for it is neither extended by a superfluous progression,
nor remitted by a contracted diminution; but obtaining the
limit of a medium, and being equal to its parts, it is neither
overflowing through abundance, nor deficient through poverty.
Of this kind are the numbers 6 and 28. For the half of 6
is 3; the third is 2; and the sixth is 1, which if reduced into one
sum, the whole body of the number will be found to be equal
to its parts. Again, the half of 28 is 14; the seventh is 4; the
fourth is 7; the fourteenth is 2; and the twenty-eighth is 1 ; the
aggregate of which is 28.
Nor must we omit to observe, that all the multiples of a
perfect number are superabundant, but on the contrary all the