Two things that are equal to the same thing are also equal to each other is an example of an axiom.
- a statement universally accepted as true; maxim
- an established principle or law of a science, art, etc.
- a statement or proposition that needs no proof because its truth is obvious, or one that is accepted as true without proof: Euclid's axiom that things equal to the same thing are equal to each other
Origin of axiomFrench axiome ; from Classical Latin axioma ; from Classical Greek axi?ma, authority, authoritative sentence ; from axioun, to think worthy ; from axios, worthy ; from base of agein, to weigh, origin, originally , to lend: see act
- A self-evident or universally recognized truth; a maxim: “It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services” (Albert Jay Nock).
- An established rule, principle, or law.
- A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
Origin of axiomMiddle English, from Old French axiome, from Latin axi&omacron;ma, axi&omacron;mat-, from Greek, from axios, worthy; see ag- in Indo-European roots.
(plural axioms); also axiomata (though, becoming less common and sometimes considered archaic)
- (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
- (mathematics, logic, proof theory) A fundamental assumption that serves as a basis for deduction of theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent".
- An established principle in some artistic practice or science that is universally received.
- The axioms of political economy cannot be considered absolute truths.
From Middle French axiome, from Ancient Greek ἀξίωμα (aksiōma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ἀξίοῦν (aksioun, “to think fit or worthy, require, demand”), from ἄξιος (aksios, “worthy, fit”, literally “weighing as much as, of like value”), from ἄγω (agō, “I drive”).