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 axiōma axiōmat- 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”).