Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/228

 negative, but it will happen the same about both. Now whatever is concluded ostensively can also be proved per impossibile, and what is concluded per impossibile may be shown ostensively through the same terms, but not in the same figures. For when the syllogism is in the first figure, the truth will be in the middle, or in the last, the negative indeed in the middle, but the affirmative in the last. When however the syllogism is in the middle figure, the truth will be in the first in all the problems, but when the syllogism is in the last, the truth will be in the first and in the middle, affirmatives in the first, but negatives in the middle. For let it be demonstrated through the first figure that A is present with no, or not with every B, the hypothesis then was that A is with a certain B, but C was assumed present with every A, but with no B, for thus there was a syllogism, and also the impossible. But this is the middle figure, if C is with every A, but with no B, and it is evident from these that A is with no B. Likewise if it has been demonstrated to be not with every, for the hypothesis is that it is with every, but C was assumed present with every A, but not with every B.  Also in a similar manner if C A were assumed negative, for thus also there is the middle figure. Again, let A be shown present with a certain B, the hypothesis then is, that it is present with none, but B was assumed to be with every C, and A to be with every or with a certain C, for thus (the conclusion) will be impossible, but this is the last figure, if A and B are with every C. From these then it appears that A must necessarily be with a certain B, and similarly if B or A is assumed present with a certain C.

Again, let it be shown in the middle figure that A is with every B, then the hypothesis was that A is not with every B, but A was assumed present with