Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

submultiples deficient. Thus, for instance, 3 the subduple of
6 is a deficient, but 12 the double of 6 is superabundant. Thus
also 2 which is subtriple of 6 is a deficient, but 18 which is
the triple of it is a superabundant number. And the like will
take place in other multiples, and submultiples. Hence also it
is evident that a perfect number is a geometric medium between
the superabundant and the deficient number. Thus in
the three numbers 3. 6. 12, 6 is the geometrical mean between
3 and 12; for as 3 is to 6, so is 6 to 12. Thus, too, 28 is the geometric
mean between 14 and 56, the former of which is a deficient,
and the latter a superabundant number.
Perfect numbers therefore, are beautiful images of the virtues
which are certain media between excess and defect, and
are not summits, as by some of the ancients they were supposed
to be. And evil indeed is opposed to evil, but both are
opposed to one good. Good however, is never opposed to
good, but to two evils at one and the same time. Thus timidity
is opposed to audacity, to both which the want of true
courage is common; but both timidity and audacity are opposed
to fortitude. Craft also is opposed to fatuity, to both
which the want of intellect is common; and both these are opposed
to prudence. Thus too profusion is opposed to avarice,
to both which illiberality is common; and both these are op
posed to liberality. And in a similar manner in the other virtues;
by all which it is evident that perfect numbers have a
great similitude to the virtues. But they also resemble the virtues
on another account; for they are rarely found, as being
few, and they are generated in a very constant order. On the
contrary, an infinite multitude of superabundant and diminished
numbers may be found, nor are they disposed in any
orderly series, nor generated from any certain end; and hence
they have a great similitude to the vices, which are numerous,
inordinate, and indefinite.