Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

particular comparison and habitude. Examples of these are
as follow: Duple sesquialter ratio is such as that of 5 to 2; for
5 contains 2 twice, and the half of it, which is 1. But duple
sesquitertian ratio, is such as that of 7 to 3. Duple sesquiquartan
ratio is such as that of 9 to 4. And duple sesquiquintan,
such as that of 11 to 5.
These ratios too will always be produced, if the numbers
which are naturally even and odd, being disposed in order
from 2, the odd numbers beginning from 5 are compared to
them; viz. if the first is compared to the first, the second to
the second, the third to the third, and so on, as in the following
table:
But if even numbers being disposed from 2 are compared to
those which, beginning from 5, surpass each other by 5, duple
sesquialter ratios will be produced, as will be evident from the
following diagram.
If the series begins from 3, and the numbers that follow surpass
each other by 3, and if those that begin from 7, and exceed
each other by 7, are compared to them, duple sesquitertian
ratios will be formed, as below:
If also the quadruplicates of the natural numbers 1, 2, $4,
etc. beginning from 4 are disposed in order, and numbers beginning
from 9, and surpassing each other by 9, are compared