Three propositions with more than three terms do not show that connection of two terms by means of a third, which is requisite for proving a Mediate Inference.

If we write-- All authors are vain; Cicero is a statesman-- there are four terms and no middle term, and therefore there is no proof.

Or if we write-- All authors are vain; Cicero is an author: .'.

Cicero is a statesman-- here the term 'statesman' occurs without any voucher; it appears in the inference but not in the evidence, and therefore violates the maxim of all formal proof, 'not to go beyond the evidence.' It is true that if any one argued-- All authors are vain; Cicero wrote on philosophy: .'.

Cicero is vain-- this could not be called a bad argument or a material fallacy; but it would be a needless departure from the form of expression in which the connection between the evidence and the inference is most easily seen.
Still, a mere adherence to the same form of words in the expression of terms is not enough: we must also attend to their meaning.