axiom vs Euclid's axiom

axiom and Euclid's axiom both are nouns.

Word	Noun	Adjective	Verb	Adverb
axiom	Yes	No	No	No
Euclid's axiom	Yes	No	No	No

As nouns, Euclid's axiom is a hyponym of axiom; that is, Euclid's axiom is a word with a more specific, narrower meaning than axiom:

axiom: (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
Euclid's axiom: (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry

Other hyponyms of axiom include Euclid's postulate, Euclidean axiom.

axiom (noun)	Euclid's axiom (noun)
a saying that is widely accepted on its own merits	(mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry
(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident