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 ap-yin, 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 ad-ib where i=1/ - i, the "argument" (or "amplitude") is the angle 0 given by tan 0 = 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.