For example every triad possesses the
attributes number, odd, and prime in both senses, i.e. not only as
possessing no divisors, but also as not being a sum of numbers.
This, then, is precisely what triad is, viz. a number, odd, and
prime in the former and also the latter sense of the term: for these
attributes taken severally apply, the first two to all odd numbers,
the last to the dyad also as well as to the triad, but, taken
collectively, to no other subject. Now since we have shown above' that
attributes predicated as belonging to the essential nature are
necessary and that universals are necessary, and since the
attributes which we select as inhering in triad, or in any other
subject whose attributes we select in this way, are predicated as
belonging to its essential nature, triad will thus possess these
attributes necessarily. Further, that the synthesis of them
constitutes the substance of triad is shown by the following argument.
If it is not identical with the being of triad, it must be related
to triad as a genus named or nameless. It will then be of wider extent
than triad-assuming that wider potential extent is the character of
a genus.
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