which are even, but of terms which are odd for the terms exceed the premises by one, and the conclusions will be half part of the premises. When, however, the conclusion results through pro-syllogisms, or through many continued middles, as A B through C D, the multitude of terms, in like manner, will exceed the premises by one, (for the term interpolated will be added either externally or in the middle; but in both ways it will happen that the intervals are fewer than the terms by one,) but the propositions are equal to the intervals, the former, indeed, will not always be even, but the latter odd, but alternately, when the propositions are even the terms are odd, but when the terms are even the propositions are odd; for together with the term, one proposition is added wherever the term is added. Hence, since the propositions were even, but the terms odd, it is necessary they should change when the same addition is made; but the conclusions will no longer have the same order, neither with respect to the terms, nor to the propositions, for one term being added, conclusions will be added less than the pre-existent terms by one, because to the last term alone there is no conclusion made; but to all the rest, e.g. if D is added to A B C, two conclusions are immediately added, the one to A and the other to B. The same occurs in the other cases also, if the term be inserted in the middle after the same manner, for it will not make a syllogism to one term alone, so that the conclusions will be many more than the terms, and than the propositions.
Chapter 26
Since we have those particulars with which syllogisms are conversant, and what is their quality in each figure, and in how many ways demon-
