A cutting tool, of various shapes and sizes and worked by hand or machinery, consisting essentially of a thin blade or disk of metal, usually steel, the edge of which is a series of sharp teeth

A statement that explains or makes generalizations about a set of facts or principles, usually forming a basis for possible experiments to confirm its viability.

Find another word for axioms. In this page you can discover 29 synonyms, antonyms, idiomatic expressions, and related words for axioms, like: maxims, principles, witticisms, truths, standards, sentences, sayings, saws, rules, proverbs and propositions.

But Clement always regards the articles of the Christian creed as the axioms of a new philosophy.

The "axioms" of geometry are the fixed conditions which occur in the hypotheses of the geometrical propositions.

The special nature of the "axioms" which constitute geometry is considered in the article Geometry (Axioms).

For the subjects under this heading see the articles CONIC SECTIONS; CIRCLE; CURVE; GEOMETRICAL CONTINUITY; GEOMETRY, Axioms of; GEOMETRY, Euclidean; GEOMETRY, Projective; GEOMETRY, Analytical; GEOMETRY, Line; KNOTS, MATHEMATICAL THEORY OF; MENSURATION; MODELS; PROJECTION; Surface; Trigonometry.

The important thing to notice is that where, in any of these five cases, one statement is followed by another, the second is not to be regarded as obtained from the first by logical reasoning involving such general axioms as that " if equals are taken from equals the remainders are equal "; the fact being that the two statements are merely different ways of expressing the same relation.