For instance, between dog and the alledged first middle term mammal (that can bark) we can insert yet another middle term, namely carnivore (that can bark) (thereby changing the differentia part of the former : (mammal) with fangs).
So we then get for dog :
A carnivore that can bark is a dog (definition of the term ' dog ' ).
This thing is a carnivore that can bark.
Therefore, this thing is a dog.
A mammal with fangs is a carnivore (definition of the term ' carnivore ' ).
This thing is a mammal with fangs.
Therefore, this thing is a carnivore.
A vertebrate with hairs is a mammal (definition of the term ' mammal ' ).
This thing is a vertebrate with hairs.
Therefore, this thing is a mammal.
etc.