Hence each of these can be the middle term of a proof, for
(a) though the inference from antecedent to necessary consequent
does not hold if only one premiss is assumed-two is the
minimum-still when there are two it holds on condition that they
have a single common middle term. So it is from the assumption of this
single middle term that the conclusion follows necessarily. The
following example will also show this. Why is the angle in a
semicircle a right angle?-or from what assumption does it follow
that it is a right angle? Thus, let A be right angle, B the half of
two right angles, C the angle in a semicircle. Then B is the cause
in virtue of which A, right angle, is attributable to C, the angle
in a semicircle, since B=A and the other, viz. C,=B, for C is half
of two right angles. Therefore it is the assumption of B, the half
of two right angles, from which it follows that A is attributable to
C, i.e. that the angle in a semicircle is a right angle. Moreover, B
is identical with (b) the defining form of A, since it is what A's
definition signifies. Moreover, the formal cause has already been
shown to be the middle. (c) 'Why did the Athenians become involved
in the Persian war?' means 'What cause originated the waging of war
against the Athenians?' and the answer is, 'Because they raided Sardis
with the Eretrians', since this originated the war.
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