Note 51a

Whereas the assertion  Socrates ( = individual) is rational  can be proved (see NOTE 52b), the present assertion  Socrates is a human being  cannot be proved. This is because there is no middle term (no middle term [qua extension] between  Socrates  and  human being ).  By definition the species immediately follws upon the individual (if there were something in between, then this something would be the species [in the logical sense] ).
On the other hand, in the assertion  Socrates ( = individual) is rational  we have the term 'rational' of which the range of reference (extension) not necessarily stops at the boundary of the extension of the term 'human being' (that is, it is not beforehand excluded that there are other beings that are rational too). So the term with the largest extension is 'rational', then comes 'human being'.  The individual, Socrates, is just a point, although there is nothing between Socrates and human being. And so we have 'human being' as middle term in the syllogism :

a human being ( = species) is rational
Socrates ( = individual) is a human being
Therefore :
Socrates is rational



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