It appears then that when a pure minor is assumed the syllogisms are perfect, but that when it is of a contrary character it may be shown per impossibile that there would be also syllogisms, though at the same time it would be evident that they are imperfect, since the demonstration will not arise from the assumed propositions. First, however, we must show that if A exists, B must necessarily exist, and that if A is possible, B will necessarily be possible; let then under these circumstances A be possible but B impossible, if therefore the possible, since it is possible to be, may be produced, yet the impossible, because it is impossible, cannot be produced. But if at the same time A is possible and B impossible, it may happen that A may be produced without B; if it is produced also, that it may exist, for that which has been generated, when it has been so generated, exists. We must however assume the possible and impossible, not only in generation, but also in true assertion, and in the inesse, and in as many other ways as the possible is predicated, for the case will be the same in all of them. Moreover (when it is said) if A exists B is, we must not understand as if A being a certain thing B will be, for no necessary consequence follows from one thing existing; but from there being two at least, as in the case of propositions subsisting in the manner we have stated in syllogism. For if C is predicated of D, but D of F, C will also necessarily be predicated of F; and if each be possible, the conclusion will be possible, just as if one should take A as the premises, but B the conclusion; it will not only happen that A being necessary, B is also necessary, but that when the former is possible, the latter also will be possible.
This being proved, it is manifest that when there is a false and not impossible hypothesis, the consequence of the hypothesis will also be false and not impossible, e. g. if A is false yet not impossible, but when A is, B also is,—here B will also be false yet not impossible. For since it has been shown that A ex-
