a certain A, if A is necessarily present with every B. Hence, it is necessary that C should not be present with a certain A; there is, however, nothing to prevent such an A being assumed, with which universally C may be present. Moreover, it can be shown by exposition of the terms, that the conclusion is not simply necessary, but necessary from the assumption of these, e. g. let A be "animal," B "man," C "white," and let the propositions be similarly assumed: for it is possible for an animal to be with nothing "white," then neither will "man" be present with any thing white, yet not from necessity, for it may happen for "man" to be "white," yet not so long as "animal" is present with nothing "white," so that from these assumptions there will be a necessary conclusion, but not simply necessary.

The same will happen in particular syllogisms, for when the negative proposition is universal and necessary, the conclusion also will be necessary, but when the affirmative is universal and necessary, and the negative particular, the conclusion will not be necessary. First, then, let there be an universal and necessary negative, and let A not possibly be present with any B, but with a certain C. Since, therefore, a negative proposition is convertible, B can neither be possibly present with any A, but A is with a certain C, so that of necessity B is not present with a certain C. Again, let there be an universal and necessary affirmative, and let the affirmative be attached to B, if then A is necessarily present with every B, but is not with a certain C, B is not with a certain C it is clear, yet not from necessity, since there will be the same terms for the demonstration, as were taken in the case of universal syllogisms. Neither, moreover, will the conclusion be necessary, if a particular necessary negative be taken as the demonstration is through the same terms.

### Chapter 11

In the last figure, when the terms are universally joined to the middle, and both premises are affirmative, if either of them be necessary, the