Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

superquadripartient, may likewise be denominated superquadriquintan.
And names maybe produced ad infinitum according
to the same similitude.
CHAPTER XXI.
On the multiple superparticular and superpartient ratio.
THESE, therefore, are the simple and first species of relative
quantity. There are, however, two other species which are
composed from these as from certain principles. And these
are, the multiple superparticular, and multiple superpartient;
and the attendants of these the submultiple superparticular,
and the submultiple superpartient. For in these, as in the before-mentioned
ratios, the less numbers and their species are
denominated with the addition of the preposition sub. But the
definition of them is as follows: Multiple superparticular ratio
is produced, when one number being compared to another,
contains it more than once, and one part of it besides; viz. it
contains either the double, or triple, or quadruple, or some
other multiple of it, and a certain part of it besides, as the half,
third, fourth, or some other part. Hence this ratio consists
both of multiple and superparticular. The number, therefore,
which contains another number twice, and the half of it besides,
is called duple sesquialter. That which contains the
double and a third, is duple sesquitertian. But that which contains
the double and a fourth, is duple sesquiquartan, and so
on. If also, one number contains the whole of another thrice,
and its half, third, or fourth part, it is called triple sesquialter,
triple sesquitertian, triple sesquiquartan, and after the same
manner in the rest. And as often as it contains the whole of
the less number in itself, it is denominated by the species of
multiple number; but from the part of the compared number
which it contains, it will be denominated according to a super-