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It is an evident corollary of these conclusions that if the same
attribute A inheres in two terms C and D predicable either not at all,
or not of all instances, of one another, it does not always belong
to them in virtue of a common middle term. Isosceles and scalene
possess the attribute of having their angles equal to two right angles
in virtue of a common middle; for they possess it in so far as they
are both a certain kind of figure, and not in so far as they differ
from one another. But this is not always the case: for, were it so, if
we take B as the common middle in virtue of which A inheres in C and
D, clearly B would inhere in C and D through a second common middle,
and this in turn would inhere in C and D through a third, so that
between two terms an infinity of intermediates would fall-an
impossibility. Thus it need not always be in virtue of a common middle
term that a single attribute inheres in several subjects, since
there must be immediate intervals. Yet if the attribute to be proved
common to two subjects is to be one of their essential attributes, the
middle terms involved must be within one subject genus and be
derived from the same group of immediate premisses; for we have seen
that processes of proof cannot pass from one genus to another.
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