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ARGUMENT, a word meaning "proof," "evidence," corresponding in English to the Latin word argumentum, from which it is derived; the originating Latin verb arguere, to make clear, from which comes the English " argue," is from a root meaning bright, appearing in Greek apyils, white. From its primary sense are derived such applications of the word as a chain of reasoning, a fact or reason given to support a proposition, a discussion of the evidence or reasons for or against some theory or proposition and the like. More particularly " argument " means a synopsis of the contents of a book, the outline of a novel, play, &c. In logic it is used for the middle term in a syllogism, and for many species of fallacies, such as the argumentum ad hominem, ad baculum, &c. (see FALLACY). In mathematics the term has received special meanings ; in mathematical tables

the " argument " is the quantity upon which the other quantities in the table are made to depend; in the theory of complex variables, e.g. such as a+ib where i=V% the " argument " (or " amplitude ") is the angle 8 given by tan 8 = b/a. In astronomy, the term is used in connexion with the Ptolemaic theory to denote the angular distance on the epicycle of a planet from the true apogee of the epicycle; and the " equation to the argument " is the angle subtended at the earth by the distance of a planet from the centre of the epicycle.