Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/211

 existing, it is necessary that A should not be, thus B not being great, it is impossible that A should be white.

But if when A is not white, it is necessary that B should be great, it will necessarily happen that B not being great, B itself is great, which is impossible. For if B is not great, A will not be necessarily white, and if A not being white, B should be great, it results, as through three (terms), that if B is not great, it is great.

Chapter 5
demonstration of things in a circle, and from each other, is by the conclusion, and by taking one proposition converse in predication, to conclude the other, which we had taken in a former syllogism. As if it were required to show that A is with every C, we should have proved it through B; again, if a person should show that A is with B, assuming A present with C, but C with B, and A with B; first, on the contrary, he assumed B present with C. Or if it is necessary to demonstrate that B is with C, if he should have taken A (as predicated) of C, which was the conclusion, but B to be present with A, for it was first assumed conversely, that A was with B.  It is not however possible in any other manner to demonstrate them from each other, for whether another middle is taken, there will not be (a demonstration) in a circle, since nothing is assumed of the same, or whether something of these (is assumed), it is necessary that one alone should (be taken), for