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c.1400, famyschen, alteration of famen (late 14c.), a shortening of Old French afamer, from Vulgar Latin *affamare "to bring to hunger," from ad famem, from Latin fames "hunger" (see famine).
Ending changed mid-14c. to -ish under influence of ravish, anguish, etc. The intransitive sense is from 1520s. Related: Famished; famishing.