All the As make up a part of the Xs
All the Bs make up a part of the Xs
And, before we can know that there is any common term of comparison at all, we must have some means of shewing that the two parts are the same; or the preceding premises by themselves are inconclusive.
2. No term must enter the conclusion more generally than it is found in the premises; thus, if A be spoken of partially in the premises, it must enter partially into the conclusion. This is obvious, since the conclusion must assert no more than the premises imply.
3. From premises both negative no conclusion can be drawn. For it is obvious, that the mere assertion of disagreement between each of two things and a third, can be no reason for inferring either agreement or disagreement between these two things. It will not be difficult to reduce any case which falls under this rule to a breach of the first rule: thus, No A is X, No B is X, gives
Every A is (something which is not X)
Every B is (something which is not X)
in which the middle term is not spoken of universally in either. Again, ‘No X is A, Some X is not B,’ may be converted into
Every A is (a thing which is not X)
Some (thing which is not B) is X