shirt-sleeves (n.)

Old English scyrte "skirt, tunic," from Proto-Germanic *skurtjon "a short garment" (source also of Old Norse skyrta, Swedish skjorta "skirt, kirtle;" Middle Dutch scorte, Dutch schort "apron;" Middle High German schurz, German Schurz "apron"), perhaps related to Old English scort, sceort "short," etc., from PIE root *sker- (1) "to cut," on the notion of "a cut piece." Lithuanian šarkas "shirt," Old Church Slavonic sraka "tunic," Russian soročka, Finnish sarkki "shirt" perhaps are from Germanic. 

Formerly of the chief garment worn by both sexes, but in modern use long only of that for men; in reference to women's tops, reintroduced 1896. Bloody shirt, exposed as a symbol of outrage, is attested from 1580s. To give (someone) the shirt off one's back is from 1771. To lose one's shirt "suffer total financial loss" is from 1935. To keep one's shirt on "be patient" (1904) is from the notion of (not) stripping down for a fight.

Old English sliefe (West Saxon), slefe (Mercian) "arm-covering part of a garment," probably literally "that into which the arm slips," from Proto-Germanic *slaubjon (source also of Middle Low German sloven "to dress carelessly," Old High German sloufen "to put on or off"). Related to Old English slefan, sliefan "to slip on (clothes)" and slupan "to slip, glide," from PIE root *sleubh- "to slide, slip."

Compare slipper, Old English slefescoh "slipper," slip (n.2) "woman's garment," and expression slip into "dress in." Mechanical sense is attested from 1864. Meaning "the English Channel" translates French La Manche, literally "the sleeve" (from Old French manche "a sleeve," also "a handle," from Latin manicae "long sleeves of a tunic;" see manacle (n.)).

To have something up one's sleeve is recorded from c. 1500 (large sleeves formerly doubled as pockets); to have a card (or ace) up one's sleeve in the figurative sense "have a hidden resource" is from 1863; the cheat itself is mentioned by 1840s. To wear one's heart on (one's) sleeve is from "Othello" (1604).