c. 1300, sirgirie, "medical treatment of an operative nature, such as cutting-operations, setting of fractures, etc.," from Old French surgerie, surgeure, contraction of serurgerie, from Late Latin chirurgia "surgery," from Greek kheirourgia, from kheirourgos "working or done by hand," from kheir "hand" (from PIE root *ghes- "the hand") + ergon "work" (from PIE root *werg- "to do").
According to OED, the British sense of "session at which a Member of Parliament (or other public servant) is available locally to be consulted by constituents" is by 1951, from an extended sense in medical practice of "regular session at which a doctor receives patients for consultation" in a room or den set aside for that purpose called a surgery (by 1846). The word has been extended in Britain to other free consultations for advice.
c. 1300, majour, "greater, more important or effective, leading, principal," from Latin maior (earlier *magios), irregular comparative of magnus "large, great" (from PIE root *meg- "great"). From 1590s as "greater in quantity, number, or extent." Used in music (of modes, scales, or chords) since 1690s, on notion of an interval a half-tone "greater" than the minor; of modern modes, "characterized by the use of major tonality throughout," by 1811. Major league, in baseball, is attested by 1892.
military rank above captain and below lieutenant colonel, 1640s, from French major, short for sergent-major, originally a higher rank than at present, from Medieval Latin major "chief officer, magnate, superior person," from Latin maior "an elder, adult," noun use of the adjective (see major (adj.)).
His chief duties consist in superintending the exercises of his regiment or battalion, and in putting in execution the commands of his superior officer. His ordinary position in the line is behind the left wing. [Century Dictionary, 1897]
The musical sense is attested by 1797.
of a college or university student, "focus (one's) studies," 1910, American English, from major (n.) in sense of "subject of specialization" (by 1890). Related: Majored; majoring. Earlier as a verb, in Scottish, "to prance about, or walk backwards and forwards with a military air and step" [Jamieson, 1825] a sense derived from the military major.
also majordomo, "man employed to superintend a household, especially that of a sovereign or other dignitary," 1580s, via Italian maggiordomo or Spanish mayordomo, from Medieval Latin major domus "chief of the household," also "mayor of the palace" under the Merovingians, from Latin maior "greater" (see major (adj.)) + genitive of domus "house" (from PIE root *dem- "house, household").
c. 1300, sorgien, cirurgian "person who heals by manual operation on the patient," from Anglo-French surgien (13c.), from Old French surgien, cirurgien (13c.), from cirurgie "surgery," from Latin chirurgia "surgery," from Greek kheirourgia, from kheirourgos "working or done by hand," from kheir "hand" (from PIE root *ghes- "the hand") + ergon "work" (from PIE root *werg- "to do").