urinalysis (n.)

c. 1300, from Old French orine, urine (12c.) and directly from Latin urina "urine," from PIE *ur- (source also of Greek ouron "urine"), variant of root *we-r- "water, liquid, milk" (source also of Sanskrit var "water," Avestan var "rain," Lithuanian jūrės "sea," Old English wær, Old Norse ver "sea," Old Norse ur "drizzling rain"), related to *eue-dh-r (see udder).

1580s, "resolution of anything complex into simple elements" (opposite of synthesis), from Medieval Latin analysis (15c.), from Greek analysis "solution of a problem by analysis," literally "a breaking up, a loosening, releasing," noun of action from analyein "unloose, release, set free; to loose a ship from its moorings," in Aristotle, "to analyze," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart").

The meaning "statement presenting results of an analytic process" is from 1660s. The psychological sense is from 1890. English also formerly had a noun analyse (1630s), from French analyse, from Medieval Latin analysis. Phrase in the final (or last) analysis (1844), translates French en dernière analyse.