Aristotle

“ In cases where one term is predicated or denied of another not immediately but by means of a middle term, when the conclusion is attained by the help of the proper middle term wrongly expressed, both premises cannot be false, but only the premise containing the major term. ”

“ Here the premise DB must remain unaltered, while AD must be converted, and the fallacy is the same as the preceding. When however the proper middle is not used, if D be included in A the major premise containing those terms will be true, the other will be false. It is in fact possible that A should be predicable of several terms, no one of which is included under another. But if D be not included in A the premise containing them must clearly be false, for it is expressed affirmatively. The premise BD on the contrary may be either true or false ”

“ It is plain then that, when the middle term is not included in A, both or either of the premises may be false. It is now therefore possible to see in how many ways and from what causes syllogistic fallacies may arise, both in the case of immediate assertions and of those attained mediately through demonstration. ”