Moreover, every
demonstration proves a predicate of a subject as attaching or as not
attaching to it, but in definition one thing is not predicated of
another; we do not, e.g. predicate animal of biped nor biped of
animal, nor yet figure of plane-plane not being figure nor figure
plane. Again, to prove essential nature is not the same as to prove
the fact of a connexion. Now definition reveals essential nature,
demonstration reveals that a given attribute attaches or does not
attach to a given subject; but different things require different
demonstrations-unless the one demonstration is related to the other as
part to whole. I add this because if all triangles have been proved to
possess angles equal to two right angles, then this attribute has been
proved to attach to isosceles; for isosceles is a part of which all
triangles constitute the whole. But in the case before us the fact and
the essential nature are not so related to one another, since the
one is not a part of the other.
So it emerges that not all the definable is demonstrable nor all the
demonstrable definable; and we may draw the general conclusion that
there is no identical object of which it is possible to possess both a
definition and a demonstration.
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