Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/187

 Of syllogisms, however, in the middle figure, the universal will be reduced to the first, but only one of the particular, for let A be with no B, but with every C, then by conversion of the negative there will be the first figure, since B will be with no A, but A with every C. Now if the affirmative be added to B, and the negative to C, we must take C as the first term, since this is with no A, but A is with every B, wherefore C is with no B, neither will B be with any C, for the negative is converted. If however the syllogism be particular, when the negative is added to the major extreme, it will be reduced to the first figure, as if A is with no B, but with a certain C, for by conversion of the negative there will be the first figure, since B is with no A, but A with a certain C. When however the affirmative (is joined to the greater extreme), it will not be resolved, as if A is with every B, but not with every C, for the proposition A B does not admit conversion, nor if it were made would there be a syllogism.

Again, not all in the third figure will be resolvable into the first, but all in the first will be into the third, for let A be with every B, but B with a certain C, since then a particular affirmative is convertible, C will be with a certain B, but A was with every B, so that there is the third figure. Also if the syllogism be negative, there will be the same result, for the particular affirmative is convertible, wherefore A will be with no B, but with a certain C. Of the syllogisms in the last figure, one alone is not resolvable into the first, when the negative is not placed universal, all the rest however are resolved. For let A and B be predicated of every C, C therefore is convertible partially to each extreme, wherefore it is present with a certain B, so that there will be the first figure, if A is with every C, but C with a certain B. And if A is with every C, but B with a certain C, the reasoning is the same,