Aristotle

“ Certain Corollaries Several terms may have only one thing in common, but one middle term uniting attribute and subject is necessary for demonstration; for immediate propositions are indemonstrable and serve as the basis for demonstrating other propositions. Such elementary principles need not be everywhere identical; for ‘Unit’ in different sciences is only analogously the same. ”

“ If then one term be common to two others it is not necessary that it should be common to several additional terms, since there are also ultimate propositions. It is, however, necessary for the terms which have something in common with one another to be in the same genus and derived from the same series, if there is to be any community of essential attributes, for demonstration cannot pass from one genus to another. ”

“ Unity is attained when the proposition is immediate and simply forms one immediate premise. Just as in other subjects the primary element is simple, though not identical in all cases, being in Weight a Mina, in Music a Semitone, and elsewhere something different, so in Syllogism the Unit is Immediate Premise, in Demonstration and Science it is Reason. Now in affirmative demonstration the middle term never falls outside the attributes of the predicate, and the same is sometimes the case in negative syllogisms, as in the case where A is not predicable of B because of C ”