"the sleeves of one's shirt," 1560s, from shirt (n.) + sleeve (n.). Often indicating "without one's waistcoat."
Entries linking to shirt-sleeves
shirt n.
Middle English shirt, shirte, "garment for the upper body worn next to the skin," from Old English scyrte, from Proto-Germanic *skurtjon "a short garment" (source also of Old Norse skyrta, Swedish skjorta "skirt, kirtle;" Middle Dutch scorte, Dutch schort "apron;" Middle Low German schörte, Middle High German schurz, German Schurz "apron"), which is perhaps related to Old English scort, sceort "short," etc., from PIE root *sker- (1) "to cut," on the notion of "a cut piece."
OED notes that "the meaning of the word in OE. is obscure, as the only instance of its occurrence is a gloss in which the meaning of the Latin word was probably not understood." Lithuanian šarkas "shirt," Old Church Slavonic sraka "tunic," Russian soročka, Finnish sarkki "shirt" perhaps are from Germanic.
Formerly of the chief under-garment worn by both men and women, but in modern use it has long been only that for men; in reference to women's tops, the word was reintroduced 1896.
Bloody shirt, a blood-stained shirt exposed as a symbol of some outrage, to arouse indignation or resentment, is attested from 1580s, usually figurative. Shirt since late 14c. often has been figurative of one's goods or possessions, hence give (someone) the shirt off one's back (1771); lose one's shirt "suffer total financial loss" (1935). To keep one's shirt on "be patient" (1904) is from the notion of (not) stripping down for a fight.
sleeve n.
Middle English sleve, from 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"), from PIE root *sleubh- "to slide, slip."
It is related etymologically to Old English slefan, sliefan "to slip on (clothes)" and slupan "to slip, glide." Also for the sense, compare slipper, Old English slefescoh "slipper," slip (n.2) "woman's garment," and expression slip into "dress in."
The mechanical sense of "tube in which a rod or another tube is inserted" is by 1864. The 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.)).
The figurative expression have something up (or in) one's sleeve, "have ready as occasion demands," is recorded from c. 1500 (the long, pendant sleeves of the late Middle Ages also sometimes doubled as pockets); to have a card (or ace) up one's sleeve in the figurative sense of "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). For laugh in one's sleeve see laugh (v.).