mid-13c., "division, portion of a whole, element or constituent (of something)," from Old French part "share, portion; character; power, dominion; side, way, path," from Latin partem (nominative pars) "a part, piece, a share, a division; a party or faction; a part of the body; a fraction; a function, office," related to portio "share, portion," from PIE root *pere- (2) "to grant, allot."
It has replaced native deal (n.) in most senses. Meaning "an allotted portion, a share" is from c. 1300; that of "a share of action or influence in activity or affairs, role, duty" is by late 14c. The theatrical sense (late 15c.) is from an actor's "share" in a performance (The Latin plural partis was used in the same sense). In music, "one of the voices or instruments in a concerted piece" (1520s). Sense of "separate piece of a machine" is by 1813. Meaning "the division of the hair on the head when dressing it" is by 1890, American English; the earlier word for this was parting (1690s).
As an adjective from 1590s. Late Old English part "part of speech" did not survive and the modern word is considered a separate borrowing. Phrase for the most part "most, the greatest part" is from late 14c. To take part "participate" is from late 14c.
Old English sang "voice, song, art of singing; metrical composition adapted for singing, psalm, poem," from Proto-Germanic *songwho- (source also of Old Norse söngr, Norwegian song, Swedish sång, Old Saxon, Danish, Old Frisian, Old High German, German sang, Middle Dutch sanc, Dutch zang, Gothic saggws), from PIE *songwh-o- "singing, song," from *sengwh- "to sing, make an incantation" (see sing (v.)).
Phrase for a song "for a trifle, for little or nothing" is from "All's Well" III.ii.9 (the identical image, por du son, is in Old French. With a song in (one's) heart "feeling joy" is first attested 1930 in Lorenz Hart's lyric. Song and dance as a form of vaudeville act is attested from 1872; figurative sense of "rigmarole" is from 1895.