however B is with every C, but A with a certain C, it will be possible to demonstrate A C, when C is assumed present with every B, but A with a certain (B). For if C is with every B, but A with a certain B, A must necessarily be with a certain C, the middle is B. And when one is affirmative, but the other negative, and the affirmative universal, the other will be demonstrated; for let B be with every C, but A not be with a certain (C), the conclusion is, that A is not with a certain B. If then C be assumed besides present with every B, A must necessarily not be with a certain C, the middle is B. But when the negative is universal, the other is not demonstrated, unless as in former cases, if it should be assumed that the other is present with some individual, of what this is present with none, as if A is with no C, but B with a certain C, the conclusion is, that A is not with a certain B. If then C should be assumed present with some individual of that with every one of which A is not present, it is necessary that C should be with a certain B. We cannot however in any other way, converting the universal proposition, demonstrate the other, for there will by no means be a syllogism.
It appears then, that in the first figure there is a reciprocal demonstration effected through the ihird and through the first figure, for when the conclusion is affirmative, it is through the first, but when it is negative through the last, for it is assumed that with what this is present with none, the other is present with every individual. In the middle figure however, the syllogism being uni-
