under B or C, for if D is in the whole of B, but B in the whole of A, D will also be in the whole of A. Again, if E is in the whole of C, and C is in A, E will also be in the whole of A, and in like manner if the syllogism be negative; but in the second figure it will be only possible to form a syllogism of that which is under the conclusion. As, if A is with no B, but is with every C, the conclusion will be that B is with no C; if therefore D is under C, it is clear that B is not with it, but that it is not with things under A, does not appear by the syllogism, though it will not be with E, if it is under A. But it has been shown by the syllogism that B is with no C, but it was assumed without demonstration that it is not with A, wherefore it does not result by the syllogisms that B is not with E. Nevertheless in particular syllogisms of things under the conclusion, there is no necessity incident, for a syllogism is not produced, when this is assumed as particular, but there will be of all things under the middle, yet not by that syllogism, e.g. if A is with every B, but B with a certain C, there will be no syllogism of what is placed under C, but there will be of what is under B, yet not through the antecedent syllogism. Similarly also in the case of the other figures, for there will be no conclusion of what is under the conclusion, but there will be of the other, yet not through that syllogism; in the same manner, as in universals, from an undemonstrated proposition, things under the middle were shown, wherefore either there will not be a conclusion there, or there will be in these also.
Chapter 2
It is therefore possible that the propositions may be true, through which a syllogism arises, also that one may be true and the other false; but the conclusion must of
