An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

A basic rule in → group theory stating that if a, b and c are members of a group then (a * b) * c and a * (b * c) are members of the group.

→ associative; → axiom.

In any system of mathematics or logic, a statement or proposition from which secondary statements or propositions are derived. The truth of an axiom is either taken for granted or assumed. In modern practice, axiom and → postulate have the same meaning.

M.Fr. axiome, from L. axioma, from Gk. axioma "authority," literally "something worthy," from axioun "to think worthy," from axios "worthy," from PIE adj. *ag-ty-o- "weighty," from base *ag- "to drive, draw, move."

Bondâšt, literally "taking as the base," from bon "root, origin, base" + dâšt "held," from dâštan "to have, to hold, to maintain, to consider."
Arzâqâzé, from arz "value" + âqâzé "beginning, principle," from âqâz "beginning."

An axiom in → statics, stating that any → constrained body can be treated as a → free body detached from its → constraints, provided the latter are represented by their → reactions.

→ axiom; → constraint.

Of, relating to, or resembling an → axiom.

→ axiom; → -ic.

Any system of → logic which explicitly states → axioms from which → theorems can be → deduced.

→ axiomatic; → system.

A basic rule in → group theory stating that if a and b are a group element then a * b is also a group element.

→ closure; → axiom.

A basic rule in → group theory stating that there exists a unit group element e, called the identity, such that for any element a of the group a * e = e * a = a.

→ identity; → axiom.

A basic rule in → group theory stating that for any element a of a group there is an element a^-1 such that a * a^-1 = a^-1 * a = e.

→ inverse; → axiom.