with every A, and with no G, so that B must necessarily be identical with some H. For the impossibility of B and G being in the same thing, does not differ from B being the same as a certain H, since every thing is assumed which cannot be with E.
From these observations, then, it is shown that no syllogism arises; but if B and F are contraries, B must necessarily be identical with a certain H, and a syllogism arises through these. Nevertheless it occurs to persons thus inspecting, that they look to a different way than the necessary, from the identity of B and H escaping them.
Chapter 29
Syllogisms which lead to the impossible subsist in the same manner as ostensive, for these also arise through consequents, and those (antecedents) which each follows, and the inspection is the same in both, for what is ostensively demonstrated may also syllogistically inferred per impossibile, and through the same terms, and what is demonstrated per impossibile, may be also proved ostensively, as that A is with no E. For let it be supposed to be with a certain E, therefore since B is with every A, and A with a certain E, B also will be with a certain E, but it was present with none; again, it may be shown that A is with a certain E, for if A is with no E, but E is with every H, A will be with no H, but it was supposed to be with every H. It will happen the same in other problems, for always and in all things demonstration per impossibile will be from consequents, and from those which each follows. In every problem also there is the same consideration, whether a man wishes to syllogize ostensively, or to lead to the impossible, since both demonstrations are from the same terms, as for example, if A were shown to be with no E, because B happens to be with a certain E, which is impossible, if it is assumed that B is with no E, but with every A, it is evident that A will be with no E. Again, if it is ostensively collected that A
