for B reciprocates with C. But if B is with every C, and A with a certain C, B must be taken as the first term, for B is with every C, but C with a certain A, so that B is with a certain A; since however the particular is convertible, A will also be with a certain B. If the syllogism be negative, when the terms are universal, we must assume in like manner, for let B be with every C, but A with no C, wherefore C will be with a certain B, but A with no C, so that C will be the middle term. Likewise, if the negative is universal, but the affirmative particular, for A will be with no C, but C with a certain B; if however the negative be taken as particular, there will not be a resolution, e.g. if B is with every C, but A not with a certain C, for by conversion of the proposition B C, both propositions will be partial.

It is clear then, that in order mutually to convert these figures, the minor premise must be converted in either figure, for this being transposed a transition is effected; of syllogisms in the middle figure, one is resolved, and the other is not resolved into the third, for when the universal is negative there is a resolution, for if A is with no B, but with a certain C, both similarly reciprocate with A, wherefore B is with no A, but C with a certain A, the middle then is A. When however A is with every B, and is not with a certain C, there will not be resolution, since neither proposition after conversion is universal.

Syllogisms also of the third figure may be resolved into the middle, when the negative is universal, as if A is with no C, but B is with some or with every C, for C will be with no A, but will be with a certain B, but if the negative be particular, there will not be a resolution, since a particular negative does not admit conversion.

We see then that the same syllogisms are not resolved in these figures, which were not resolved into the first figures, and that when syllogisms are reduced to the first figure, these only are conducted per impossibile.

How therefore we must reduce syllogisms, and