Note 157

Because no middle term can be placed between the extreme superior term (maius) and extreme inferior term (minus), because subject and predicate have precisely the same significatum (they both refer to the same thing).
Indeed, the definition itself is the middle term for the demonstration of the proprium:

Every organism is mortal
Man is an organism
Ergo :  Man is mortal

Here 'mortal' is a proprium for organisms.
'organism' is (part of the) definition of 'man', and is the middle term of this syllogism.
'organism' is part of the (complete) definition of 'man', because it is a higher genus of 'man'. The direct genus of 'man' is 'animal', and 'organism' figures in the definition of 'animal'.
The supreme genus of 'man' is 'substance' (first Predicament).

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