Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

CHAPTER VII.
On the unevenly-even number, and its properties, etc.
THE unevenly-even number is composed from both the
evenly-even, and the evenly-odd number, and is a medium between
both. But this number is such as may be divided into
equal parts, and each of these into other equal parts, and sometimes
the parts of these parts may again be divided, but this
equable division does not proceed as far as to unity. And of
this kind are the numbers 24 and 28. For each of these may
be divided into two equal parts, and also the parts of these
parts, and again the parts of these, but the division does not
extend as far as to unity. Hence, because this number receives
more than one division, it resembles the evenly-even, and is
separated from the evenly-odd number. But because the section
does not proceed as far as to unity, it associates with the
evenl y-odd, but is separated from the evenl y-even number.
It happens however to this number, that it possesses that
which both the above-mentioned numbers have not, and obtains
that which both of them receive. And it as that indeed
which both do not possess; for in the evenly-odd number, the
major term alone is divided into two equal parts; but in the
evenly-even number on the contrary, the minor term alone is
deprived of this division. In the unevenly-even number however,
neither the major term alone admits of this section, nor
the minor alone is deprived of such a division; for the parts
also are divided, and the section does not arrive as far as to
unity, but prior to unity a term is found which cannot be divided.
It also obtains what both the others receive; for some
of its parts are of the same quantity and denomination, according
to a similitude of the evenly-even number ; but other parts
of it receive a denomination contrary to their proper quantity