Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

number besides containing the whole, contained two halves of
the other, the ratio would be duple instead of superpartient.
And if the greater, besides containing the whole, has only two
third parts of the less, the greater will surpass the less by odd
numbers. For if it contained the whole and two fourths of it,
the ratio would necessarily be superparticular; since two fourths
are the same as half, and the comparison will be sesquialter.
But if it contained two sixths, again the ratio is superparticular;
for two sixths are the same as a third part. And this
in the comparison will produce the form of the sesquitertian
habitude. After these, the attendants arise which are called
subsuperpartient. These, however, are such as are contained in
another number, and two, three, four, or any other parts of
them besides. If, therefore, a number containing another number
in itself, has also two parts of it, it is called superbipartient;
if three, supertripartient ; if four, superquadripartient, and sc,
on ad infiniturn.
But the order of them is natural, as often as all the even and
odd numbers naturally constituted, are disposed from 3; and
under these others are adapted, which are all odd numbers beginning
from 5. These, therefore, being thus disposed, if the
first is compared to the first, the second to the second, the
third to the third, and the rest to the rest, a superpartient
habitude will be produced; as is evident from the following
arrangement :
If, therefore, the comparison of 5 to 3 is considered, it will be
that superpartient which is called superbipartient; for 5 contains
in itself the whole of 3, and two parts of it besides, viz.
2. But if 7 is compared to 4, the ratio will be supertripartient;
for 7 contains in itself the whole of 4, and three parts of it be-