Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/108

 a figure of this kind I call the second figure. The middle term also in it, I call that which is predicated of both extremes, and the extremes I denominate those of which this middle is predicated, the greater extreme being that which is placed near the middle, but the less, that which is farther from the middle. Now the middle is placed beyond the extremes, and is first in position; wherefore by no means will there be a perfect syllogism in this figure. There may however be one, both when the terms are, and are not, universal, and if they be universal there will be a syllogism when the middle is present with all and with none, to which ever extreme the negation is added, but by no means in any other way. For let M be predicated of no N, but of every O; since then a negative proposition is convertible, N will be present with no M; but M was supposed to be present with every O, wherefore N will be present with no O, for this has been proved before. Again, if M be present with every N, but with no O, neither will O be present with any N, for if M be present with no O, neither will be O present with any M; but M was present with every N, hence also O will be present with no N; for again the first figure is produced; since however a negative proposition is converted, neither will N be present with any O; hence there will be the same syllogism. We may also demonstrate the same things, by a deduction to the impossible; it is evident therefore, that when the terms are thus, a syllogism, though not a perfect one, is produced, for the necessary is not only perfected from first assumptions, but from other things also. If also M is predicated of every N and of every O, there