c.1300, "to escape, to move softly and quickly," from Middle Low German slippen "to glide, slide," from Proto-Germanic *slipanan (cf. Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"), from PIE *sleib- "slimy, slippery," from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)). Meaning "to lose one's footing" is from mid-14c. Related: Slipped; slipping. To slip up "make a mistake" is from 1855; to slip through the net "evade detection" is from 1902.
"narrow strip," mid-15c., probably from Middle Low German or Middle Dutch slippe "cut, slit," possibly related to Old English toslifan "to split, cleave." Sense of "sprig for planting or grafting" first recorded in late 15c.; that of "young slender person" (a slip of a girl) in 1580s; that of "narrow piece of paper" (e.g. pink slip) in 1680s. Meaning "boat ramp" is from 1769. The meaning "potter's clay" is a different word, from Old English slyppe "slime," related to slupan "to slip."