Is it farther or further?
c.1600, "a buffoon who practices gesticulations" [Johnson], from French mime (16c.) and directly from Latin mimus, from Greek mimos "imitator, mimic, actor, mime, buffoon," of unknown origin. In reference to a performance, 1640s in a classical context; 1932 as "a pantomime."
1610s, "to act without words," from mime (n.). The transferred sense of "to imitate" is from 1733 (Greek mimeisthai meant "to imitate"). Meaning "to pretend to be singing a pre-recorded song" is from 1965. Related: mimed; miming.