Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/151

 A C be contingent, and if A C be negative, but B C affirmative, and either of them be pure; in both ways the conclusion will be contingent, since again there arises the first figure. Now it has been shown that where one premise in that figure signifies the contingent, the conclusion also will be contingent; if however the negative be annexed to the minor premise, or both be assumed as negative, through the propositions laid down themselves, there will not indeed be a syllogism, but by their conversion there will be, as in the former cases.

Nevertheless if one premise be universal and the other particular, yet both affirmative, or the universal negative but the particular affirmative, there will be the same mode of syllogisms; for all are completed by the first figure, so that it is evident there will be a syllogism of the contingent and not of the inesse. If however the affirmative be universal and the negative particular, the demonstration will be per impossibile; for let B be with every C and A happen not to be with a certain C, it is necessary then that A should happen not to be with a certain B, since if A is necessarily with every B, but B is assumed to be with every C, A will necessarily be with every C, which was demonstrated before, but by hypothesis A happens not to be with a certain C.

When both premises are assumed indefinite, or particular, there will not be a syllogism, and the demonstration is the same as in universals, and by the same terms.