Axiom
a Greek word meaning a decision or assumption, is commonly used to signify a general proposition which the understanding recognizes as true, as soon as the import of the words conveying it is apprehended. Such a proposition is, therefore, known directly, and does not need to be deduced from any other. Mathematicians used the word axiom to denote those propositions which they must assume as known from some other source than deductive reasoning, and employ in proving all the other truths of the science. The rigor of method requires that no more be assumed than are absolutely necessary. Every self-evident proposition, therefore, is not an axiom in this sense, though, of course, it is desirable that every axiom be self-evident; thus, Euclid rests the whole of geometry on 15 assumptions, but he proves propositions that are at least as self-evident as some that he AXIS takes for granted. Euclid's assumptions are divided into three postulates, or demands, and 12 common notions; the term axiom is of later introduction. The distinction between axioms and postulates is usually stated in this way: an axiom is "a theorem granted without demonstration;" a postulate is "a problem granted without construction"-as, to draw a straight line between two given points.