syllogism

Definitions:

Form of argument consisting of two propositions called the premisses, and the third which follows from them, called the conclusion.
- The Clarendon dictionary. By William Hand Browne, Samuel Stehman Haldeman. Published 1894. (noun) (n.) (noun)
An argument stated in a logical form, consisting of three propositions, the first two being called the premises, and the last the conclusion, which contains the matter to be proved.
- The Winston Simplified Dictionary. By William Dodge Lewis, Edgar Arthur Singer. Published 1919. (noun) (n.) (noun)
A form of reasoning or argument, consisting of three propositions, of which the first two are called the premises, and the last, which necessarily follows from them, the conclusion.
- Nuttall's Standard dictionary of the English language. By Nuttall, P.Austin. Published 1914. (noun) (n.) (noun)
Syllogistic.
- The Winston Simplified Dictionary. By William Dodge Lewis, Edgar Arthur Singer. Published 1919. (adjective) (adj.) (adjective)
Logical form of every argument, consisting of three propositions, of which the first two are called the premises, and the last, which follows from them, the conclusion.
- The american dictionary of the english language. By Daniel Lyons. Published 1899. (noun) (n.) (noun)

Usage examples:

A series of statements such as the above is called a syllogism
- Composition-Rhetoric by Stratton D. Brooks
Fulke asserted that it could, and did; and made a syllogism Whatsoever error is incident to every member, is incident to the whole.
- By What Authority? by Robert Hugh Benson
All pure mathematics- Arithmetic, Analysis, and Geometry- is built up by combinations of the primitive ideas of logic, and its propositions are deduced from the general axioms of logic, such as the syllogism and the other rules of inference.
- Mysticism and Logic and Other Essays by Bertrand Russell