Noun
An argument consisting of only two propositions, an antecedent and consequent deduced from it; a syllogism with one premise omitted; as, We are dependent; therefore we should be humble. Here the major proposition is suppressed. The complete syllogism would be, Dependent creatures should be humble; we are dependent creatures; therefore we should be humble.
Source: Webster's dictionaryAn "enthymeme" would follow today's form of a syllogism; however it would exclude either the major or minor premise. Source: Internet
An enthymeme is persuasive because the audience is providing the missing premise. Source: Internet
However, the enthymeme based upon logic (especially, based upon the syllogism) was viewed as the basis of rhetoric. Source: Internet