For if the same word be used ambiguously (as 'author' now for 'father' and anon for 'man of letters'), it becomes as to its meaning two terms; so that we have four in all.

Then, if the ambiguous term be the Middle, no connection is shown between the other two; if either of the others be ambiguous, something seems to be inferred which has never been really given in evidence.
The above two Canons are, indeed, involved in the definition of a categorical syllogism, which may be thus stated: A Categorical Syllogism is a form of proof or reasoning (way of giving reasons) in which one categorical proposition is established by comparing two others that contain together only three terms, or that have one and only one term in common.
The proposition established, derived, or inferred, is called the Conclusion: the evidentiary propositions by which it is proved are called the Premises.
The term common to the premises, by means of which the other terms are compared, is called the Middle Term; the subject of the conclusion is called the Minor Term; the predicate of the conclusion, the Major Term.
The premise in which the minor term occurs is called the Minor Premise; that in which the major term occurs is called the Major Premise.

And a Syllogism is usually written thus: Major Premise--All authors (Middle) are vain (Major); Minor Premise--Cicero (Minor) is an author (Middle): Conclusion--.'.

Cicero (Minor) is vain (Major).
Here we have three propositions with three terms, each term occurring twice.

The minor and major terms are so called, because, when the conclusion is an universal affirmative (which only occurs in Barbara; see chap.x.Sec.