but B only be present with a certain C; it is necessary therefore that A should of necessity be present with a certain C, for C is under B, and A was of necessity present with every B. The same will occur if the syllogism be negative, for the demonstration will be the same, but if the particular be necessary, the conclusion will not be necessary, for nothing impossible results, as neither in universal syllogisms. A similar consequence will result also in negatives; (let the terms be) "motion," "animal," "white."

### Chapter 10

In the second figure, if the negative premise be necessary, the conclusion will also be necessary, but if the affirmative (be necessary, the conclusion) will not be necessary. For first, let the negative be necessary, and let it not be possible for A to be in any B, but let it be present with C alone; as then a negative proposition may be converted, B cannot be present with any A, but A is with every C, hence B cannot be present with any C, for C is under A. In like manner also, if the negative be added to C, for if A cannot be with any C, neither can C be present with any A, but A is with every B, so neither can C be present with any B, as the first figure will again be produced; wherefore, neither can B be present with C, since it is similarly converted. If, however, the affirmative premise be necessary, the conclusion will not be necessary; for let A necessarily be present with every B, and alone not be present with any C, then the negative being converted, we have the first figure; but it was shown in the first, that when the major negative (proposition) is not necessary, neither will the conclusion be necessary, so that neither in these will there be a necessary conclusion. Once more, if the conclusion is necessary, it results that C is not necessarily present with a certain A, for if B is necessarily present with no C, neither will C be necessarily present with any B, but B is present necessarily with