Aristotle - The Organon - index for ANALYTICA POSTERIORA Book 1 Part 23

Some corollaries

Paragraph 1 It is an evident corollary of these conclusions that if the same attribute A inheres in two terms C and D predicable either not at all, or not of all instances, of one another, it does not always belong to them in virtue of a common middle term.
Paragraph 2 It is also clear that when A inheres in B, this can be demonstrated if there is a middle term.
Paragraph 3 When we are to prove a conclusion, we must take a primary essential predicate - suppose it C - of the subject B, and then suppose A similarly predicable of C.
Paragraph 4 (2) If we have to show that E is not D by means of the premisses, all D is C;
Paragraph 5 (3) In the third figure the middle will never fall beyond the limits of the subject and the attribute denied of it.

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