eye vs sagacity

eye and sagacity both are nouns.

Word	Noun	Adjective	Verb	Adverb
eye	Yes	No	Yes	No
sagacity	Yes	No	No	No

As nouns, sagacity is a hypernym of eye; that is, sagacity is a word with a broader meaning than eye:

eye: good discernment (either visually or as if visually)
sagacity: the mental ability to understand and discriminate between relations

Other hypernyms of eye include discernment, judgement, judgment, sagaciousness.

eye (noun)	sagacity (noun)
a small hole or loop (as in a needle)	the trait of forming opinions by distinguishing and evaluating
the organ of sight	the mental ability to understand and discriminate between relations
good discernment (either visually or as if visually)
attention to what is seen
an area that is approximately central within some larger region

eye (verb)	sagacity (verb)
look at