c. 1300, "to go or come near" in place; late 14c. "come near in time," also "come near in quality or character, resemble, become similar," from Anglo-French approcher, Old French aprochier "come closer" (12c., Modern French approcher), from Late Latin appropiare, adpropiare "go nearer to," from Latin ad "to" (see ad-) + Late Latin propiare "come nearer," comparative of Latin prope "near" (see propinquity). Replaced Old English neahlæcan.
mid-15c., "act of drawing near, arrival," from approach (v.). Meaning "way or means by which something is approached" is from 1630s. Figurative sense of "means of handling a problem, etc." is attested by 1905. Sense of "final stage of an aircraft flight before landing" is by 1930.