This also follows from the function of the middle term.
For the more convenient application of these canons to the testing of syllogisms, it is usual to derive from them three Corollaries: (i) Two particular premises yield no conclusion.
For if both premises be affirmative, _all_ their terms are undistributed, the subjects by predesignation, the predicates by position; and therefore the middle term must be undistributed, and there can be no conclusion.
If one premise be negative, its predicate is distributed by position: the other terms remaining undistributed.

But, by Canon 6, the conclusion (if any be possible) must be negative; and therefore its predicate, the major term, will be distributed.

In the premises, therefore, both the middle and the major terms should be distributed, which is impossible: e.g., Some M is not P; Some S is M: .'.

Some S is not P.
Here, indeed, the major term is legitimately distributed (though the negative premise might have been the minor); but M, the middle term, is distributed in neither premise, and therefore there can be no conclusion.
Still, an exception may be made by admitting a bi-designate conclusion: Some P is M; Some S is not M: .'.

Some S is not some P.
(ii) If one premise be particular, so is the conclusion.
For, again, if both premises be affirmative, they only distribute one term, the subject of the universal premise, and this must be the middle term.