Two things that are equal to the same thing are also equal to each other is an example of an axiom.

## 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 axiom

French*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

## axiom

noun

- 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 axiom

Middle English*from*Old French

*axiome*

*from*Latin

*axiōma*

*axiōmat-*

*from*Greek

*from*

*axios*

*worthy*; see

*ag-*in Indo-European roots.

## axiom

(*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”).