Prior Analytics - Book II   

And the original premisses form the first figure. Similarly if the

demonstration establishes a particular proposition: the hypothesis

then must have been that A belongs to no B, and the original premisses

that C belongs to some B, and A to all C. If the syllogism is

negative, the hypothesis must have been that A belongs to some B,

and the original premisses that C belongs to no A and to all B, and

this is the middle figure. Similarly if the demonstration is not

universal. The hypothesis will then be that A belongs to all B, the

premisses that C belongs to no A and to some B: and this is the middle

figure.

It is clear then that it is possible through the same terms to prove

each of the problems ostensively as well. Similarly it will be

possible if the syllogisms are ostensive to reduce them ad impossibile

in the terms which have been taken, whenever the contradictory of

the conclusion of the ostensive syllogism is taken as a premiss. For

the syllogisms become identical with those which are obtained by means

of conversion, so that we obtain immediately the figures through which

each problem will be solved. It is clear then that every thesis can be

proved in both ways, i.e. per impossibile and ostensively, and it is

not possible to separate one method from the other.



15



In what figure it is possible to draw a conclusion from premisses

which are opposed, and in what figure this is not possible, will be

made clear in this way. Verbally four kinds of opposition are

possible, viz. universal affirmative to universal negative,

universal affirmative to particular negative, particular affirmative

to universal negative, and particular affirmative to particular

negative: but really there are only three: for the particular

affirmative is only verbally opposed to the particular negative. Of

the genuine opposites I call those which are universal contraries, the