slipper n.

early 14c., slippen, "to escape, to move softly and quickly," from an unrecorded Old English word or cognate Middle Low German slippen "to glide, slide," from Proto-Germanic *slipan (source also of Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"). This is probably from PIE *sleib-"slip, slide," from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)). The verb is not found in Old English, which did have related adjective slipor "slippery, having a smooth surface." Related: Slipped; slipping. 

It is attested from mid-14c. in the sense of "lose one's footing, slide suddenly and unawares," also "slide out of place," also "fall into error or fault." The meaning "pass unguarded or untaken" is from mid-15c. That of "slide, glide, pass smoothly and easily" is from 1520s.

The transitive sense of "cause to move with a sliding motion" is from 1510s; the meaning "insert surreptitiously, put or place secretly" is from 1680s. The meaning "let loose, release from restraint" (1580s), is probably from the noun sense of "leash for a (hunting) dog that can be easily released" (1570s).

To slip on "put on (clothing, etc.) loosely or in haste" is from 1580s; to slip off "take off noiselessly or hastily" is from 1590s. To slip up "make a mistake, err inadvertently" is from 1855; to slip through the net "evade detection" is by 1829 (for slip through the cracks see crack (n.)). To let (something) slip originally (1520s) was a reference to hounds on a leash; figurative use for "allow to escape through carelessness" is by 1540s.

in numerous and various senses from slip (v.), late 13c. as a surname. The meaning "sloping landing place for ships between wharves or a dock" is by mid-15c. The meaning "act of slipping" (as walking on ice) is from 1590s. The meaning "mistake, fault, blunder," especially if minor or unintended is from 1570s.

The sense of "woman's sleeveless garment" (1761) is from notion of something easily "slipped" on or off (compare sleeve). Originally an outer garment; in 20c. of a sleeveless undergarment or petticoat.

To give (someone) the slip "escape from" is from 1560s. Slip of the tongue is 1725 (from Latin lapsus linguae); slip of the pen (Latin lapsus calami) is 1650s.

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.).