axiom n.

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

1520s, "concise statement of a principle" (especially in reference to the "Aphorisms of Hippocrates"), from French aphorisme (corrected from Old French aufforisme, 14c.), from Late Latin aphorismus, from Greek aphorismos "definition; short, pithy sentence," from aphorizein "to mark off, divide," from apo "from" (see apo-) + horizein "to bound" (see horizon).

The general sense of "short, pithy statement containing a truth of general import" (e.g. "life is short, and art is long") is from 1580s in English. Distinguished from an axiom, which is a statement of self-evident truth; an epigram is like an aphorism, but lacking in general import. Maxim and saying can be used as synonyms for aphorism, but maxims tend to be practical than aphorisms, and sayings tend to be more commonplace and have an author's name attached.

[F]or aphorisms, except they should be ridiculous, cannot be made but of the pith and heart of sciences ; for discourse of illustration is cut off ; recitals of examples are cut off ; discourse of connexion and order is cut off ; descriptions of practice are cut off. So there remaineth nothing to fill the aphorisms but some good quantity of observation : and therefore no man can suffice, nor in reason will attempt, to write aphorisms, but he that is sound and grounded. [Francis Bacon, "The Advancement of Learning," 1605] 

"of the nature of a self-evident truth," 1797, from Greek axiomatikos, from axioma (genitive axiomatos); see axiom. The form axiomatical is attested from 1580s.