The Complete Aristotle (eng.)

conclusion is converted into its
contradictory, both premisses can be refuted. Suppose that A
belongs to no B, and to some C: the conclusion is BC. If then it is
assumed that B belongs to some C, and the statement AB stands, the
conclusion will be that A does not belong to some C. But the
original statement has not been refuted: for it is possible that A
should belong to some C and also not to some C. Again if B belongs
to some C and A to some C, no syllogism will be possible: for
neither of the premisses taken is universal. Consequently the
proposition AB is not refuted. But if the conclusion is converted
into its contradictory, both premisses can be refuted. For if B
belongs to all C, and A to no B, A will belong to no C: but it was
assumed to belong to some C. Again if B belongs to all C and A to
some C, A will belong to some B. The same proof can be given if the
universal statement is affirmative.
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    In the third figure when the conclusion is converted into its
contrary, neither of the premisses can be refuted in any of the
syllogisms, but when the conclusion is converted into its
contradictory, both premisses may be refuted and in all the moods.
Suppose it has been proved that A belongs to some B, C being taken
as middle, and the premisses being universal. If then it is assumed
that A does not belong to some B, but B belongs to all C, no
syllogism is formed about A and C. Nor if A does not belong to some
B, but belongs to all C, will a syllogism be possible about B and
C. A similar proof can be given if the premisses are not universal.
For either both premisses arrived at by the conversion must be
particular, or the universal premiss must refer to the minor
extreme. But we found that no syllogism is possible thus either in
the first or in the middle figure. But if the conclusion is
converted into its contradictory, both the premisses can be
refuted. For if A belongs to no B, and B to all C, then A belongs
to no C: again if A belongs to no B, and to all C, B belongs to no
C. And similarly if one of the premisses is not universal. For if A
belongs to no B, and B to some C, A will not belong to some C: if A
belongs to no B, and to C, B will belong to no C.
    Similarly if the original syllogism is negative. Suppose it has
been proved that A does not belong to some B, BC being affirmative,
AC being negative: for it was thus that, as we saw, a syllogism
could be made. Whenever then the contrary of the conclusion is
assumed a syllogism will not be possible. For if A belongs to some
B, and B to all C, no syllogism is possible (as we saw) about A and
C. Nor, if A belongs to some B, and to no C, was a syllogism
possible concerning B and C. Therefore the premisses are not
refuted. But when the contradictory of the conclusion is assumed,
they are refuted. For if A belongs to all B, and B to C, A belongs
to all C: but A was supposed originally to belong to no C. Again if
A belongs to all B, and to no C, then B belongs to no C: but it was
supposed to belong to all C. A similar proof is possible if the
premisses are not universal. For AC becomes universal and negative,
the other premiss particular and affirmative. If then A belongs to
all B, and B to some C, it results that A belongs to some C: but it
was supposed to belong to no C. Again if A belongs to all B, and to
no C, then B belongs to no C: but it was assumed to belong to some
C. If A belongs to some B and B to some C, no syllogism results:
nor yet if A belongs to some B, and to no C. Thus in one way the
premisses are refuted, in the other way they are not.
    From what has been said it is clear how a syllogism results in
each figure when the conclusion is converted; when a result
contrary to the premiss, and when a result contradictory to the
premiss, is obtained. It is clear that in the first figure the
syllogisms are formed through the middle and the last figures, and
the premiss which concerns the minor extreme is alway refuted
through the middle figure, the premiss which concerns the major
through the last figure. In the second figure syllogisms proceed
through the first and the last figures, and the premiss which
concerns the minor extreme is always refuted through the first
figure, the premiss which concerns the major extreme through the
last. In the third figure the refutation proceeds through the first
and the middle figures; the premiss which concerns the major is
always refuted through the first figure, the premiss which concerns
the minor through the middle