3) that 'any apparent syllogism, having one premise a verbal proposition, is really an Immediate Inference'; but that, if both premises are real propositions, the Inference is Mediate, and demands for its explanation something more than the Laws of Thought.
The fact is that to prove the minor to be a case of the middle term may be an exceedingly difficult operation (chap.xiii.Sec.

7).

The difficulty is disguised by ordinary examples, used for the sake of convenience.
Sec.5.Other kinds of Mediate Inference exist, yielding valid conclusions, without being truly syllogistic.

Such are mathematical inferences of Equality, as-- A = B = C .'.

A = C.
Here, according to the usual logical analysis, there are strictly four terms--( 1) A, (2) equal to B, (3) B, (4) equal to C.
Similarly with the argument _a fortiori_, A > B > C .'.