Chapter 22
If one premise be necessary, but the other contingent, the terms being affirmative there will be always a syllogism of the contingent; but when one is affirmative but the other negative, if the affirmative be necessary there will be a syllogism of the contingent non-inesse; if however it be negative, there will be one both of the contingent and of the absolute non-inesse. There will not however be a syllogism of the necessary non-inesse, as neither in the other figures. Let then, first, the terms be affirmative, and let A be necessarily with every C, but B happen to be with every C; therefore since A is necessarily with every C, but C is contingent to a certain B, A will also be contingently, and not necessarily, with some certain B; for thus it is concluded in the first figure. It can be similarly proved if B C be assumed as necessary, but A C contingent.
Again, let one premise be affirmative, but the other negative, and let the affirmative be necessary; let also A happen to be with no C, but let B necessarily be with every C; again there will be the first figure;
