Aristotle

“ Now in the case of the simple or immediate supposition the mistake is simple, in the case of that which is produced by the syllogism it may assume several forms. Suppose it to be proved immediately that no B is A; then if one conclude, with the help of a middle term C, that B is A, one’s reasoning will have led one astray. Here it is possible for both premises to be false or else for only one. Thus if no C be A, and no B be C, and if each of these premises be transposed, both will be false. ”

“ In the second figure it is not possible for both the premises to be entirely false; for when all B is A no third term can be found which will be predicable of the whole of one and not predicable of any part of the other term. If one want a syllogism at all one ought to select the premises in such a way that the middle term will be affirmed of one of the other two terms and denied of the second. If then, when thus stated, the premises are false, it is clear that the contrary of them will be true. ”