Now if E is concluded, the syllogism would be from A B alone, but if C D are so as that the one is universal, and the other particular, something also will result from these which will either be E or A or B, or something else different from these, and if E is collected, or A or B, there will be either many syllogisms, or, as it was shown possible, the same thing will happen to be collected through many terms. If, however, any thing else different from these is collected, there will be many syllogisms unconnected with each other; but if C is not so with respect to D, as to produce a syllogism, they will be assumed to no purpose, except for the sake of induction or concealment, or something of the sort. Still if from A B, not E, but some other conclusion is produced, and from C D, either one of these, or something different from these, many syllogisms arise, yet not of the subject, for it was supposed that the syllogism is of E. If, again, there is no conclusion from C D, it will happen that they are assumed in vain, and the syllogism is not of the primary problem, so that it is evident that every demonstration and every syllogism will be through three terms only.
This then being apparent, it is also clear that a syllogism consists of two premises and no more; for three terms are two premises, unless something is assumed over and above, as we observed at first, for the perfection of the syllogisms. Hence it appears, that in the syllogistic discourse, in which the premises, through which the principal conclusion is collected, are not even,—(for it is requisite that some of the former conclusions should be premises,)—this discourse is either not syllogistically constructed, or has required more than is necessary to the thesis.
When then the syllogisms are taken according to the principal propositions, every syllogism will consist of propositions
