Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

as those of greater inequality, with the addition of the preposition
sub. For they are denominated submultiple, subsuperparticular,
subsuperpartient, multiple-subsuperparticular, and
multiple-subsuperpartient.
CHAPTER XVII.
On multiple inequality, its species, and the generation of them.
AGAIN, the multiple is the first part of greater inequality,
being more ancient than all the others, and naturally more excellent,
as we shall shortly demonstrate. This number however
is such, that when compared with another, it contains the
number with which it is compared more than once.
This multiple inequality also is first seen in the natural series
of number. For all the numbers that follow unity have the
relation of multiples to it. Thus 2 with relation to unity is
duple; 3 is triple; 4 quadruple; and thus proceeding in order,
all multiple quantities are produced.
The inequality however, which is contra-distinguished to
this, is called submultiple, and this also is the first species of
less quantity. But this number is such that when compared
with another, it measures the sum of the greater number more
than once. If therefore, the less number measures the greater
only twice, it is called subduple: but if three times, subtriple:
if four times, subquadruple; and so on ad infiniturn. And
they are always denominated with the addition of the preposition
sub.
Since, however, multiplicity and submultiplicity are naturally
infinite, the proper generations of the species also admit
of infinite speculation. For if numbers are arranged in a
natural series, and the several even numbers are selected in a