Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

Multiple superpartient ratio however is, when one number
on being compared to another, contains the whole of it more
than once, and two, three, or some other number of parts,
according to the species of the superpartient number. Here
too, from the cause before mentioned, there will not be two
halves, nor two fourths, nor two sixths; but there will be two
thirds, or two fifths, or two sevenths. Nor will it be difficult
according to the examples before adduced, to discover these
numbers also. These are denominated according to their proper
parts, duple superbipartient, or duple supertripartient, or
duple superquadripartient, and so on. And again, they are
called triple superbipartient, triple supertripartient, triple superquadripartient,
and the like. Thus 8, compared to 3, produces
a duple superbipartierit ratio. This is also the case with
16 compared to 6; and with all those numbers that beginning
from 8, and surpassing each other by 8, are compared to those
that begin from 3, and surpass each other by 3. It will likewise
be easy to find other parts of these numbers according to the
before mentioned mode. Here too, the less numbers are not
denominated without the preposition sub, as subduple superbipartient,
subduple supertripartient. And after a similar manner
in the rest.
CHAPTER XXII.
A demonstration that all ineqality proceeds from equality.
IT now remains for us to deliver a certain profound discipline,
which especially pertains to all the power of nature and
integrity of things. For it is highly advantageous in this science,
not to be ignorant that the nature of good is definite, but
that of evil indefinite. That the more indefinite the nature of
evil is, the worse it is; and that it is goodness alone, which by