"to separate or divide" (threads, strands, fibers), Old English -slæfan, from stem of -slifan "to separate, split, cleave," from Proto-Germanic *slifanan, perhaps related to the root of slip (v.). Compare German Schleife "a loop, knot, noose." Related: Sleaved; sleaving. As a noun, "knotted, tangled silk or thread," 1590s, from the verb; this is the word in Shakespeare's rauel'd Sleeue of Care ("Macbeth").
