In like manner, if C A is assumed negative; if however the proposition be assumed to B, there will not be a syllogism, but if the contrary be supposed, there will be a syllogism, and the impossibile (demonstration), but what was proposed will not be proved. For let A be supposed present with every B, and let C be assumed present with every A, then it is necessary that C should be with every B, but this is impossible, so that it is false that A is with every B, but it is not yet necessary that if it is not present with every, it is present with no B. The same will happen also if the other proposition is assumed to B, for there will be a syllogism, and the impossible (will be proved), but the hypothesis is not subverted, so that the contradictory must be supposed. In order however to prove that A is not present with every B, it must be supposed present with every B, for if A is present with every B, and C with every A, C will be with every B, so that if this impossible, the hypothesis is false. In the same manner, if the other proposition is assumed to B, also if C A is negative in the same way, for thus there is a syllogism, but if the negative be applied to B, there is no demonstration. If however it should be supposed not present with every, but with some one, there is no demonstration that it is not present with every, but that it is present with none, for if A is with a certain B, but C with every A, C will be with a certain B, if then this is impossible it is false that A is present with a certain B, so that it is true that it is present with none. This however being demonstrated, what is true is subverted besides, for A was present with a certain B, and with a certain one was not present. Moreover, the impossibile does not result from the hypothesis, for it would be false, since we cannot conclude the false from the true, but now it is true, for A is with a certain B, so that it must not be supposed present with a certain, but with every B. The like also will occur, if we should show that A is not present with a certain B, since if it is the same thing not to be with a certain individual, and to be not with every, there is the same demonstration of both.
