when the universal is affirmative. For let A be with every B, but not with every C, the conclusion that B is not with a certain C, if then B is assumed present with every A, but not with every C, A will not be with a certain C, the middle is B. But if the universal is negative, the proposition A C will not be demonstrated, A B being converted, for it will happen either that both or that one proposition will be negative, so that there will not be a syllogism. Still in the same manner there will be a demonstration, as in the case of universals, if A is assumed present with a certain one, with which B is not present.
Chapter 7
In the third figure, when both propositions are assumed universal, we cannot demonstrate reciprocally, for the universal is shown through universals, but the conclusion in this figure is always particular, so that it is clear that in short we cannot demonstrate an universal proposition by this figure. Still if one be universal and the other particular, there will be at one time and not at another (a reciprocal demonstration); when then both propositions are taken affirmative, and the universal belongs to the less extreme, there will be, but when to the other, there will not be. For let A be with every C, but B with a certain (C), the conclusion A B, if then C is assumed present with every A, C has been shown to be with a certain B, but B has not been shown to be with a certain C. But it is necessary if C is with a certain B, that B should be with a certain C, but it is not the same thing, for this to be with that, and that with this, but it mast be assumed that if this is present with a certain that, that also is with a certain this, and from this assumption there is no longer a syllogism from the conclusion and the other proposition. If
