dle, and in the third, but is not in the first. For let A be supposed not present with every B, or present with no B, and let the other proposition be assumed from either part, whether C is present with every A, or B with every D, for thus there will be the first figure. If then A is supposed not present with every B, there is no syllogism, from whichever part the proposition is assumed, but if (it is supposed that A is present with) no (B), when the proposition B D is assumed, there will indeed be a syllogism of the false, but the thing proposed is not demonstrated. For if A is with no B, but B with every D, A will be with no D, but let this be impossible, therefore it is false that A is with no B. If however it is false that it is present with no B, it does not follow that it is true that it is present with every B. But if C A is assumed, there is no syllogism, neither when A is supposed not present with every B, so that it is manifest that the being present with every, is not demonstrated in the first figure per impossibile. But to be present with a certain one, and with none, and not with every is demonstrated, for let A be supposed present with no B, but let B be assumed to be present with every or with a certain C, therefore is it necessary that A should be with no or not with every C, but this is impossible, for let this be true and manifest, that A is with every C, so that if this is false, it is necessary that A should be with a certain B. But if one proposition should be assumed to A, there will not be a syllogism, neither when the contrary to the conclusion is supposed as not to be with a certain one, wherefore it appears that the contradictory must be supposed. Again, let A be supposed present with a certain B, and C assumed present with every A, then it is necessary that C should be with a certain B, but let this be impossible, hence the hypothesis is false, and if this be the case, that A is present with no B is true.
