sleeve (n.) Look up sleeve at Dictionary.com
Old English sliefe (West Saxon), slefe (Mercian), from Proto-Germanic *slaubjon (cf. Middle Low German sloven "to dress carelessly," Old High German sloufen "to put on or off"). Related to Old English sliefan "put on (clothes)" and slupan "to slip, glide," from PIE root *sleubh- "to slide, slip." (cf. expression to slip into "to dress in"). Mechanical sense is attested from 1864. To have something up one's sleeve is recorded from c.1500. Meaning "the English Channel" translates French La Manche.