Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

CHAPTER XVI.
On relative quantity, and the species of greater and less inequality.
THE first division of relative quantity is twofold: for whatever
is measured by comparison with another quantity, is either
equal or unequal. And that indeed is equal which when
compared to something else is neither less nor greater. This
part however, of relative quantity, viz. equality, is naturally
indivi.sible: for it cannot be said that one portion of equality
is different from another. For all equality in its proper measurement
preserves one measure. The quantity too which is
compared, has not an appellation different from that to which
it is compared. For as a friend is the friend of a friend, and 3
neighbour is the neighbour of a neighbour, so the equal is
said to be equal to the equal. But of unequal quantity there is
a twofold division: for that which is unequal may be cut
into the greater and the less, which have a denomination contrary
to each other. For the greater is greater than the less,
and the less is less than the greater. Hence both have not the
same appellations as was observed to be the case with equal
quantity, but they are distinguished by different names, in the
same manner as those of teacher and learner, or of any other
relatives which are compared to contraries that are differently
denominated.
Of greater inequality however, there are five parts. For one
part is that which is called multiple; another is superparticular
; a third superpartient ; a fourth multiple-superparticular ;
and a fifth multiple-superpartient. To these five parts, therefore,
of greater inequality, other five parts of less inequality
are opposed, just as the greater is always opposed to the less.
These species also of less inequality have the same appellations