They collect then that the odd would be equal to the even, but show from hypothesis that the diameter is incommensurate, since a falsity occurs by contradiction. This then it is, to syllogize per impossibile, namely, to show an impossibility from the original hypothesis, so that as by reasonings leading to the impossible, an ostensive syllogism of the false arises, but the original proposition is proved by hypothesis; and we have before said about ostensive syllogisms, that they are perfected by these figures—it is evident that syllogisms also per impossibile will be formed through these figures. Likewise all others which are by hypothesis, for in all there is a syllogism of that which is assumed, but the original proposition is proved by confession, or some other hypothesis. Now if this is true, it is necessary that every demonstration and syllogism should arise through the three figures before named, and this being shown, it is manifest that every syllogism is completed in the first figure, and is reduced to universal syllogisms in it.
Chapter 24
Moreover it is necessary in every syllogism, that one term should be affirmative and one universal, for without the universal there will not be a syllogism, or one not pertaining to the thing proposed, or the original (question) will be the subject of petition. For let it be proposed that pleasure from music is
