early 15c., "boldness, courage, daring; vigor, animation," from Medieval Latin audacitas "boldness," from Latin audacis genitive of audax "bold, daring; rash, foolhardy" (see audacious). In English, the meaning "presumptuous impudence," implying contempt of moral restraint, is from 1530s.
"eager to undertake, prompt to attempt," 1610s, present-participle adjective from the verb enterprise (late 15c.), from the noun enterprise. Until mid-19c. (at least in Britain) mostly in a bad sense: "scheming, ambitious, foolhardy." Earlier (1560s) as a verbal noun meaning "action of undertaking."
1540s, "confident, intrepid, daring," from French audacieux, from audace "boldness," from Latin audacia "daring, boldness, courage," from audax "brave, bold, daring," but more often "bold" in a bad sense, "rash, foolhardy," from audere "to dare, be bold," which de Vaan says is derived from avidus "greedy" (see avarice). In English, the bad sense of "shameless, unrestrained by propriety" is attested from 1590s. Related: Audaciously; audaciousness.