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the universal concerns the minor extreme； proof will be possible；
but when it concerns the other extreme； impossible。 Let A belong to
all C and B to some C： the conclusion is the statement AB。 If then
it is assumed that C belongs to all A； it has been proved that C
belongs to some B； but that B belongs to some C has not been proved。
And yet it is necessary； if C belongs to some B； that B should
belong to some C。 But it is not the same that this should belong to
that； and that to this： but we must assume besides that if this
belongs to some of that； that belongs to some of this。 But if this
is assumed the syllogism no longer results from the conclusion and the
other premiss。 But if B belongs to all C； and A to some C； it will
be possible to prove the proposition AC； when it is assumed that C
belongs to all B； and A to some B。 For if C belongs to all B and A
to some B； it is necessary that A should belong to some C； B being
middle。 And whenever one premiss is affirmative the other negative；
and the affirmative is universal； the other premiss can be proved。 Let
B belong to all C； and A not to some C： the conclusion is that A
does not belong to some B。 If then it is assumed further that C
belongs to all B； it is necessary that A should not belong to some
C； B being middle。 But when the negative premiss is universal； the
other premiss is not except as before； viz。 if it is assumed that that
belongs to some of that； to some of which this does not belong； e。g。
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 figure…if 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
mean the opposition of 'to all' to 'to none'； and of 'to some' to 'not
to some'。 Suppose that A been proved of C； through B as middle term。
If then it should be assumed that A belongs to no C； but to all B； B
will belong to no C。 And if A belongs to no C； and B to all C； A
will belong； not to no B at all； but not to all B。 For （as we saw） the
universal is not proved through the last figure。 In a word it is not
possible to refute universally by conversion the premiss which
concerns the major extreme： for the refutation always proceeds through
the third since it is necessary to take both premisses in reference to
the minor extreme。 Similarly if the syllogism is negative。 Suppose
it has been proved that A belongs to no C through B。 Then if it is
assumed that A belongs to all C； and to no B； B will belong to none of
the Cs。 And if A and B belong to all C； A will belong to some B： but
in the original premiss it belonged to no B。
If the conclusion is converted into its contradictory； the
syllogisms will be contradictory and not universal。 For one premiss is
particular； so that the conclusion also will be particular。 Let the
syllogism be affirmative； and let it be converted as stated。 Then if A
belongs not to all C； but to all B； B will belong not to all C。 And if
A belongs not to all C； but B belongs to all C； A will belong not to
all B。 Similarly if the syllogism is negative。 For if A belongs to
some C； and to no B； B will belong； not to no C at all； but…not to
some C。 And if A belongs to some C； and B to all C； as was
originally assumed； A will belong to some B。
In particular syllogisms when the conclusion is converted into its
contradictory； both premisses may be refuted； but when it is converted
into its contrary； neither。 For the result is no longer； as in the
universal syllogisms； refutation in which the conclusion reached by O；
conversion lacks universality； but no refutation at all。 Suppose
that A has been proved of some C。 If then it is assumed that A belongs
to no C； and B to some C； A will not belong to some B： and if A
belongs to no C； but to all B； B will belong to no C。 Thus both
premisses are refuted。 But neither can be refuted if the conclusion is
converted into its contrary。 For if A does not belong to some C； but
to all B； then B will not belong to some C。 But the original premiss
is not yet refuted： for it is possible that B should belong to some C；
and should not belong to some C。 The universal premiss AB cannot be
affected by a syllogism at all： for if A does not belong to some of
the Cs； but B belongs to some of the Cs； neither of the premisses is
universal。 Similarly if the syllogism is negative： for if it should be
assumed that A belongs to all C； both premisses are refuted： but if
the assumption is that A belongs to some C； neither premiss is
refuted。 The proof is the same as before。
9
In the second figure it is not possible to refute the premiss
which concerns the major extreme by establishing something contrary to
it； whichever form the conversion of the conclusion may take。 For
the conclusion of the refutation will always be in the third figure；
and in this figu