From what has been said then it seems clear how, when the conclusion is converted, a syllogism arises in each figure, both when contrarily and when contradictorily to the proposition, and that in the first figure syllogisms are produced through the middle and the last, and the minor premise is always subverted through the middle (figure), but the major by the last (figure): in the second figure, however, through the first and the last, and the minor premise (is) always (subverted) through the first figure, but the major through the last: but in the third (figure) through the first and through the middle, and the major premise is always (subverted) through the first, but the minor premise through the middle (figure). What therefore conversion is, and how it is effected in each figure, also what syllogism is produced, has been shown.
A syllogism through the impossible is shown, when the contradiction of the conclusion is laid down, and another proposition is assumed, and it is produced in all the figures, for it is like conversion except that it differs insomuch as that it is converted indeed, when a syllogism has been made, and both propositions have been assumed, but it is deduced to the impossible, when the opposite is not previously acknowledged but is manifestly true. Now the terms subsist similarly in both, the assumption also of both is the same, as for instance, if A is present with every B, but the middle is C, if A is supposed present with every or with no B, but with every C, which was true, it is necessary that C should be with no or not with every B. But this is impossible, so that the supposition is false, wherefore the opposite is true. It is a similar case with other figures, for whatever are capable of conversion, are also capable of the syllogism per impossibile.
All other problems then are demonstrated through the impossible in all the figures, but the universal affirmative is demonstrated in the mid-