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late 14c., "to bring to an end;" mid-15c., "to come to an end," from Old French finiss-, present participle stem of fenir (13c.) "stop, finish, come to an end, die," from Latin finire "to limit, set bounds, put an end to, come to an end," from finis "boundary, limit, border, end," of unknown origin, perhaps related to figere "to fasten, fix" (see fix). Meaning "to kill" is from 1755. Related: Finished; finishing. Finishing school is from 1836.
1779, "that which finishes or gives completion," from finish (v.). Meaning "the end" is from 1790. Finish line attested from 1873.
To put a disastrous end to something or to someone's prospects; COOK someone's GOOSE: She finished him off with a passing shot (1755+)