Part III, Chapter 3: General Rules of Simple Incomplex Syllogisms
Rule 6
From two particular propositions nothing follows. For if there are two affirmatives, the middle will be taken twice particularly, whether it be the subject (by the 2d axiom) or whether it be the attribute (by the 3d axiom). Now, by the first rule, nothing can be concluded from a syllogism whose middle term is taken twice particularly.
And if there be a negative, the conclusion being negative also, by the rule preceding, there must be at least two universal terms in the premises (according to the 2d corollary). Therefore there ought to be a universal proposition in these two premises, since it is impossible to arrange three terms in two terms, where two terms must be taken universally, without having either two negative attributes, which would be contrary to the 3d rule, or one of the subjects universal, which makes the proposition universal.