But we can demonstrate a particular proposition, for let A be demonstrated of a certain C through B, if then B is taken as present with every A, and the conclusion remains, B will be present with a certain C, for the first figure is produced, and A will be the middle. Nevertheless if the syllogism is negative, we cannot demonstrate the universal proposition for the reason adduced before, but a particular one cannot be demonstrated, if A B is similarly converted as in universals, but we may show it by assumption, as that A is not present with something, but that B is, since otherwise there is no syllogism from the particular proposition being negative.
Chapter 6
In the second figure we cannot prove the affirmative in this mode, but we may the negative; the affirmative therefore is not demonstrated, because there are not both propositions affirmative, for the conclusion is negative, but the affirmative is demonstrated from propositions both affirmative, the negative however is thus demonstrated. Let A be with every B, but with no C, the conclusion B is with no C, if then B is assumed present with every A, it is necessary that A should be present with no C, for there is the second figure, the middle is B. But if A B be taken negative, and the other proposition affirmative, there will be the first figure, for C is present with every A, but B with no C, wherefore neither is B present with any A, nor A with B, through the conclusion then and one proposition a syllogism is not produced, but when another proposition is assumed there will be a syllogism. But if the syllogism is not universal, the universal proposition is not demonstrated for the reason we have given before, but the particular is demonstrated
