is with no E, to those who suppose that it is with a certain E, it may be shown per impossibile to be with no E. The like will also occur in other cases, for in all we must assume some common term different from the subject terms to which there will appertain a syllogism of the false, so that this proposition being converted, but the other remaining the same, there will be an ostensive syllogism through the same terms. But an ostensive syllogism differs from that per impossibile, because in the ostensive both premises are laid down according to truth, but in that which leads to the impossible one is laid down falsely.
These things however will more fully appear by what follows, when we come to speak of the impossible, for the present let so much be manifest to us, that both he who wishes to syllogize ostensively, and per impossibile, must observe these things. In other syllogisms indeed which are hypothetical, such as those which are according to transumption, or according to quality, the consideration will be in the subject terms, not in the original ones, but in those taken afterwards, but the mode of inspection will be the same; but it is necessary also to consider, and distinguish, in how many ways hypothetical syllogisms arise.
Each problem then is demonstrated thus, and some of them we may infer syllogistically after another method, for example, universals by an hypothetical inspection of particulars, for if C and H are the same, and if E is assumed to be with H alone,
