
Prior Analytics  Book II
if A belongs to no C, and B to some C: the conclusion is that A does
not belong to some B. If then it is assumed that C belongs to some
of that to some of which does not belong, it is necessary that C
should belong to some of the Bs. In no other way is it possible by
converting the universal premiss to prove the other: for in no other
way can a syllogism be formed.
It is clear then that in the first figure reciprocal proof is made
both through the third and through the first figureif the
conclusion is affirmative through the first; if the conclusion is
negative through the last. For it is assumed that that belongs to
all of that to none of which this belongs. In the middle figure,
when the syllogism is universal, proof is possible through the
second figure and through the first, but when particular through the
second and the last. In the third figure all proofs are made through
itself. It is clear also that in the third figure and in the middle
figure those syllogisms which are not made through those figures
themselves either are not of the nature of circular proof or are
imperfect.
8
To convert a syllogism means to alter the conclusion and make
another syllogism to prove that either the extreme cannot belong to
the middle or the middle to the last term. For it is necessary, if the
conclusion has been changed into its opposite and one of the premisses
stands, that the other premiss should be destroyed. For if it should
stand, the conclusion also must stand. It makes a difference whether
the conclusion is converted into its contradictory or into its
contrary. For the same syllogism does not result whichever form the
conversion takes. This will be made clear by the sequel. By
contradictory opposition I mean the opposition of 'to all' to 'not
to all', and of 'to some' to 'to none'; by contrary opposition I
