Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/161

 takes place, it is also manifest to us, what kind of problem is difficult, and what easy of proof, for that which is concluded in many figures, and through many cases, is more easy, but what is in fewer figures, and by fewer cases, is more difficult. An universal affirmative then is proved through the first figure alone, and by this in one way only; but a negative, both through the first and through the middle, through the first in one way, but through the middle in two ways; the particular affirmative again through the first and through the last, in one way through the first figure, but in three ways through the last; lastly, the particular negative is proved in all the figures, but in the first in one way, in the middle in two ways, and in the last in three ways. Hence it appears most difficult to construct an universal affirmative, but most easy to subvert it, in short, universals are easier to subvert than particulars, because the former are subverted, whether a thing is present with nothing, or is not with a certain thing, of which the one, namely, the not being with a certain thing, is proved in all the figures, and the other, the being with nothing, is proved in two. The same mode also prevails in the case of negatives, for the original proposition is subverted, whether a thing is with every, or with a certain individual, now this was in two figures. In particular problems there is one way (of confutation), either by showing a thing to be with every, or with no individual, and particular problems are easier of construction, for they are in more figures, and through more modes. In short, we ought not to forget that it is possible to confute universal mutually through particular problems, and these through universal, yet we cannot construct universal through particular, but the latter may be through the former, at the same time that it is easier to subvert than to construct is plain.

In what manner then every syllogism arises, through how