conclusion will also be necessary; and if one be negative, but the other affirmative, when the negative is necessary, the conclusion will be also necessary, but when the affirmative (is so, the conclusion) will not be necessary. For first, let both propositions be affirmative, and let A and B be present with every C, and let A C be a necessary (proposition). Since then B is present with every C, C will also be present with a certain B, because an universal is converted into a particular: so that if A is necessarily present with every C, and C with a certain B, A must also be necessarily present with a certain B, for B is under C, hence the first figure again arises. In like manner, it can be also demonstrated if B C is a necessary (proposition), for C is converted with a certain A, so that if B is necessarily present with every C, (but C with a certain A,) B will also of necessity be present with a certain A. Again let A C be a negative (proposition), but B C affirmative, and let the negative be necessary; as therefore an affirmative proposition is convertible, C will be present with some certain B, but A of necessity with no C, neither will A necessarily be present with some B, for B is under C. But if the affirmative is necessary, there will not be a necessary conclusion; for let B C be affirmative and necessary, but A C negative and not necessary; since then the affirmative is converted C will also be with a certain B of necessity; wherefore if A is with no C, but C with a certain B, A will also not be present with a certain B, but not from necessity, for it has been shown by the first figure, that when the negative proposition is not necessary, neither will the conclusion be necessary. Moreover this will also be evident from the terms, for let A
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