Old English stol "seat for one person," from Proto-Germanic *stōla- (source also of Old Frisian stol, Old Norse stoll, Old High German stuol, German Stuhl "seat," Gothic stols "high seat, throne"), from PIE *sta-lo-, locative of root *sta- "to stand, make or be firm."(source also of Lithuanian pa-stolas "stand," Old Church Slavonic stolu "stool").
Originally used of thrones (as in cynestol "royal seat, throne"); decline in sense began with adoption of chair (n.) from French, which relegated stool to small seats without arms or backs, then to "privy" (early 15c.) and thence to "bowel movement" (1530s).
The Cucking-stool was a means adopted for the punishment of scolds and incorrigible women by ducking them in the water, after having secured them in a chair or stool, fixed at the end of a long pole, serving as a lever by which they were immersed in some muddy or stinking pond. [Willis's Current Notes, February 1851]
early 13c., from verbal noun from cuck "to void excrement," from Old Norse kuka "feces," from PIE root *kakka- "to defecate." So called because they sometimes resembled the old close stool of the pre-plumbing days, a portable indoor toilet that looked like a chair with a box under the seat. Old folk etymology made the first element a corruption of cotquean. For second element, see stool. Also known as trebucket and castigatory, it was used on fraudulent tradesmen, in addition to disorderly women, either for public exposure to ridicule or for ducking.
*stā-, Proto-Indo-European root meaning "to stand, set down, make or be firm," with derivatives meaning "place or thing that is standing."
It forms all or part of: Afghanistan; Anastasia; apostasy; apostate; armistice; arrest; assist; astatic; astatine; Baluchistan; bedstead; circumstance; consist; constable; constant; constitute; contrast; cost; desist; destination; destine; destitute; diastase; distance; distant; ecstasy; epistasis; epistemology; establish; estaminet; estate; etagere; existence; extant; Hindustan; histidine; histo-; histogram; histology; histone; hypostasis; insist; instant; instauration; institute; interstice; isostasy; isostatic; Kazakhstan; metastasis; obstacle; obstetric; obstinate; oust; Pakistan; peristyle; persist; post (n.1) "timber set upright;" press (v.2) "force into service;" presto; prostate; prostitute; resist; rest (v.2) "to be left, remain;" restitution; restive; restore; shtetl; solstice; stable (adj.) "secure against falling;" stable (n.) "building for domestic animals;" stage; stalag; stalwart; stamen; -stan; stance; stanchion; stand; standard; stanza; stapes; starboard; stare decisis; stasis; -stat; stat; state (n.1) "circumstances, conditions;" stater; static; station; statistics; stator; statue; stature; status; statute; staunch; (adj.) "strong, substantial;" stay (v.1) "come to a halt, remain in place;" stay (n.2) "strong rope which supports a ship's mast;" stead; steed; steer (n.) "male beef cattle;" steer (v.) "guide the course of a vehicle;" stem (n.) "trunk of a plant;" stern (n.) "hind part of a ship;" stet; stoa; stoic; stool; store; stound; stow; stud (n.1) "nailhead, knob;" stud (n.2) "horse kept for breeding;" stylite; subsist; substance; substitute; substitution; superstition; system; Taurus; understand.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tisthati "stands;" Avestan histaiti "to stand;" Persian -stan "country," literally "where one stands;" Greek histēmi "put, place, cause to stand; weigh," stasis "a standing still," statos "placed," stylos "pillar;" Latin sistere "stand still, stop, make stand, place, produce in court," status "manner, position, condition, attitude," stare "to stand," statio "station, post;" Lithuanian stojuos "I place myself," statau "I place;" Old Church Slavonic staja "place myself," stanu "position;" Gothic standan, Old English standan "to stand," stede "place;" Old Norse steði "anvil;" Old Irish sessam "the act of standing."