Axiom
2 of the 7 encyclopedias on this shelf carry an entry for Axiom. Both are reproduced below, so you can see where they agree and where they differ.
Collier's New Encyclopedia (1921)
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 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.
Aiton's Encyclopedia (1910)
a truth requiring no proof. The term is sometimes applied to any important and generally accepted truth, as, in political economy , "cheap money drives good money out of circulation"; in logic, "he who admits a principle admits its consequence"; in natural history, "mountain ranges restrict and direct migrations"; in geography, "an increased altitude lowers the temperature"; in sociology, "character is affected by associations," etc. The term is restricted more properly, however, to self-evident mathematical truths, as, for instance: "The whole is greater than any of its parts"; "Things which are equal to the same thing are equal to each other"; "Two straight lines cannot enclose a space," etc. Euclid recognized fifteen geometrical axioms. 2026 Editor's Note: Axioms turned out to be trickier than 'truths requiring no proof': Euclid's parallel postulate proved optional, opening the door to the curved geometries Einstein needed, and in 1931 Gödel stunned mathematics by proving that any system of axioms rich enough for arithmetic must leave some truths forever unprovable within it. (Ed: BR 2026-06-18)