in this figure are imperfect, for all of them are produced from certain assumptions, which are either of necessity in the terms, or are admitted as hypotheses, as when we demonstrate by the impossible. Lastly, it appears that an affirmative syllogism is not produced in this figure, but all are negative, both the universal and also the particular.
Chapter 6
When with the same thing one is present with every, but the other with no individual, or both with every, or with none, such I call the third figure; and the middle in it, I call that of which we predicate both, but the predicates the extremes, the greater extreme being the one more remote from the middle, and the less, that which is nearer to the middle. But the middle is placed beyond the extremes, and is last in position; now neither will there be a perfect syllogism, even in this figure, but there may be one, when the terms are joined to the middle, both universally, and not universally. Now when the terms are universally so, when, for instance, P and R are present with every S, there will be a syllogism, so that P will necessarily be present with some certain R, for since an affirmative is convertible, S will be present to a certain R. Wherefore since P is present to every S, but S to some certain R, P must necessarily be present with some R, for a syllogism arises in the first figure. We may also make the demonstration through the impossible, and by exposition. For if both are present with every S, if some S is assumed, (e. g.) N, both P and R
