Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/158



Chapter 25
appears that every demonstration will be by three terms and no more, unless the same conclusion should result through different arguments, as E through A B, and through C D, or through A B, A C, and B C, for there is nothing to prevent many media subsisting of the same conclusions). But these being (many), there is not one syllogism, but many syllogisms; or again, when each of the propositions A B is assumed by syllogism, as A through D E, and again B through F G, or when the one is by induction, but the other by syllogism.  Thus in this manner indeed there are many syllogisms, for there are many conclusions, as A and B and C, and if there are not many but one, it is thus possible, that the same conclusion may arise through many syllogisms, but in order that C may be proved through A B, it is impossible.  For let the conclusion be E, collected from A B C D, it is then necessary that some one of these should be assumed with reference to something else, as a whole, but another as a part, for this has been shown before, that when there is a syllogism, some of the terms should necessarily thus subsist; let then A be thus with reference to B, from these there is a certain conclusion, which is either E or C or D, or some other different from these.