are not universal, for either both must be particular by conversion, or the universal be joined to the minor, but thus there was not a syllogism neither in the first nor in the middle figure. If however they are converted contradictorily, both propositions are subverted; for if A is with no B, but B with every C, A will be with no C; again, if A is with no B, but with every C, B will be with no C. In like manner if one proposition is not universal; since if A is with no B, but B with a certain C, A will not be with a certain C, but if A is with no B, but with every C, B will be present with no C. So also if the syllogism be negative, for let A be shown not present with a certain B, and let the affirmative proposition be B C, but the negative A C, for thus there was a syllogism; when then the proposition is taken contrary to the conclusion, there will not be a syllogism. For if A were with a certain B, but B with every C, there was not a syllogism of A and C, nor if A were with a certain B, but with no C was there a syllogism of B and C, so that the propositions are not subverted. When however the contradictory (of the conclusion is assumed) they are subverted. For if A is with every B, and B with C, A will be with every C, but it was with none. Again if A is with every B, but with no C, B will be with no C, but it was with every C. There is a similar demonstration also, if the propositions are not universal, for A C becomes universal negative, but the other, particular affirmative. If then A is with every B, but B with a certain C, A happens to a certain C, but it was with none; again, if A is with every B, but with no C, B is with no C, but if A is with a certain B, and B with a certain C, there is no syllogism, nor if A is with a certain B, but with no C, (will there thus be a syllogism): Hence in that way, but not in this, the propositions are subverted.
