What is the origin of the word "algorithm"?

1690s, "Arabic system of computation," from French "algorithme," refashioned (under mistaken connection with Greek "arithmos" "number") from Old French "algorisme" "the Arabic numeral system" (13c.), from Medieval Latin "algorismus," a mangled transliteration of Arabic "al-Khwarizmi" "native of Khwarazm" (modern "Khiva" in Uzbekistan), surname of the mathematician whose works introduced sophisticated mathematics to the West (cf. algebra). The earlier form in Middle English was "algorism" (early 13c.), from Old French. The meaning broadened to any method of computation; from mid-20c. especially with reference to computing.