be "good," B "animal," and C "horse," it happens therefore that "good" is with no "horse," but "animal" is necessarily present with every "horse," but it is not however necessary that a certain "animal" should not be "good," for every "animal" may possibly be "good." Or if this is not possible, (viz. that every animal is good,) we must assume another term, as "to wake," or "to sleep," for every "animal" is capable of these. If then the terms are universal in respect to the middle, it has been shown when there will be a necessary conclusion.
But if one term is universally but the other particularly (predicated of the middle), and both propositions are affirmative, when the universal is necessary the conclusion will also be necessary, for the demonstration is the same as before, since the particular affirmative is convertible. If therefore B is necessarily present with every C, but A is under C, B must also necessarily be present with a certain A, and if B is with a certain A, A must also be present necessarily with a certain B, for it is convertible; the same will also occur if A C be a necessary universal proposition, for B is under C. But if the particular be necessary, there will not be a necessary conclusion, for let B C be particular and necessary, and A present with every C, yet not of necessity, B C then being converted we have the first figure, and the universal proposition is not necessary, but the particular is necessary, but when the propositions are thus there was not a necessary conclusion, so that neither will there be one in the case of these. Moreover this is evident from the terms, for let A be "wakefulness," B "biped," but C, "animal;" B then must necessarily be present with a cer-
