Euclid's axiom vs axiom

Euclid's axiom and axiom both are nouns.

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

As nouns, axiom is a hypernym of Euclid's axiom; that is, axiom is a word with a broader meaning than Euclid's axiom:

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

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