Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

tained of what kind they are when compared with each other.
Again therefore, from the greater number 21 let the less number
9 be taken, and 12 will remain. From 12 let 9 be taken,
and there will remain 3. But if 3 be taken from 9, 6 will remain;
from which if 3 be taken, 3 will be the remainder. And
from this 3 cannot be taken so as to leave any remainder.
Hence these numbers are commensurable, and 3 is their common
measure.
CHAPTER XIV.
Another division of the even number according to the perfect,
deficient, and superperfect, or stlperabundant.
AGAIN, of even numbers a second division is as follows. Of
these, some are superperfect, and others are deficient, according
to each habitude of inequality. For all inequality is considered
either in greater or less terms. But the superperfect
numbers are such as by an immoderate plenitude, exceed, as
it were, by the numerosity of their parts, the measure of their
proper body. On the contrary, the deficient numbers being as
it were, oppressed by poverty, are less than the sum of their
parts. And the superperfect numbers indeed, are such as 12
and 24; for these will be found to be more than the aggregate
of their parts. For the half of 12 is 6; the third part is 4; the
fourth part is 3; the sixth part is 2; and the twelfth part is 1.
And the aggregate of all these parts is 16, which surpasses the
multitude of its whole body. Again, of the number 24, the
half is 12; the third 8; the fourth 6; the sixth 4; the eighth 3;
the twelfth 2; and the twenty-fourth 1; the aggregate of all
which is 36. And it is evident in this instance also, that the
sum of the parts is greater than, and overflows as it were, its
proper body. And this number indeed, because the parts sur-