we use the same thing demonstrated for the purpose of a demonstration. For C is demonstrated of B, and B of A, assuming C to be predicated of A, but C is demonstrated of A by these propositions, so that we use the conclusion for demonstration.
In negative syllogisms a demonstration through each other is produced thus: let B be with every C, but A present with no B, the conclusion that A is with no C. If then it is again necessary to conclude that A is with no B, which we took before, A will be with no C, but C with every B, for thus the proposition becomes converted. But if it is necessary to conclude that B is with C, the proposition A B must no longer be similarly converted, for it is the same proposition, that B is with no A, and that A is with no B, but we must assume that B is present with every one of which A is present with none. Let A be present with no C, which was the conclusion, but let B be assumed present with every of which A is present with none, therefore B must necessarily be present with every C, so that each of the assertions which are three becomes a conclusion, and this is to demonstrate in a circle, namely, assuming the conclusion and one premise converse to infer the other. Now in particular syllogisms we cannot demonstrate universal proposition through others, but we can the particular, and that we cannot demonstrate universal is evident, for the universal is shown by universals, but the conclusion is not universal, and we must demonstrate from the conclusion, and from the other proposition. Besides, there is no syllogism produced at all when the proposition is converted, since both premises become particular.
