Etymology
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sedan (n.)

1630s, "a covered chair on poles, serving as a vehicle for one person," a word of uncertain origin, possibly from a southern Italian dialect derivative of Italian sede "chair" (compare Italian seggietta, 1590s; the thing itself was said to have originated in Naples), which is from Latin sedes, a noun related to sedere "to sit" (from PIE root *sed- (1) "to sit").

Since the date of Johnson's conjecture, however, the word has been often derived from the name of the town of Sedan in France, where it was said to have been made or first used, but historical evidence for this connection is lacking and OED frowns on it.

The thing was introduced in England by Sir Sanders Duncombe in 1634 and first called a covered chair. "In Paris the sedan-chair man was usually an Auvergnat, in London an Irishman" ["Encyclopaedia Britannica," 1929]. 

Brit. 'Sfoot where's my wife then?
Sam. If your wife be the gentlewoman o' the house sir, shee's now gone forth in one o' the new Hand-litters : what call yee it, a Sedan.
[Richard Brome, "The Sparagus Garden: A Comedie," 1635]
[T]heir use was greatly extended in the eighteenth century, when they were the common means of transportation for ladies and gentlemen in the cities of England and France. They were often elaborately decorated, with paintings by artists of note, panels of vernis Martin, and the like, and lined with elegant silks. Similar chairs, carried on the shoulders of two or more bearers, have long been in use in China. [Century Dictionary]

Meaning "closed automobile seating four or more" is recorded by 1911, American English, in automotive journals. Middle English had sede (n.) "a chair, seat" (early 14c.), from Latin sedes.

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*sed- (1)

Proto-Indo-European root meaning "to sit."

It forms all or part of: assess; assiduous; assiento; assize; banshee; beset; cathedra; cathedral; chair; cosset; dissident; dodecahedron; Eisteddfod; ephedra; ephedrine; ersatz; icosahedron; inset; insidious; nest; niche; nick (n.) "notch, groove, slit;" nidicolous; nidification; nidus; obsess; octahedron; piezo-; piezoelectric; polyhedron; possess; preside; reside; saddle; sanhedrim; seance; seat; sedan; sedate; (adj.) "calm, quiet;" sedative; sedentary; sederunt; sediment; see (n.) "throne of a bishop, archbishop, or pope;" sessile; session; set (v.); sett; settle (n.); settle (v.); siege; sit; sitz-bath; sitzkrieg; size; soil (n.1) "earth, dirt;" Somerset; soot; subside; subsidy; supersede; surcease; tanist; tetrahedron; Upanishad.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-sadat "sat down," sidati "sits," nidah "resting place, nest;" Old Persian hadis "abode;" Greek ezesthai "to sit," hedra "seat, chair, face of a geometric solid;" Latin sedere "to sit; occupy an official seat, preside; sit still, remain; be fixed or settled," nidus "nest;" Old Irish suide "seat, sitting," net "nest;" Welsh sedd "seat," eistedd "sitting," nyth "nest;" Old Church Slavonic sežda, sedeti "to sit," sedlo "saddle," gnezdo "nest;" Lithuanian sėdėti "to sit;" Russian sad "garden," Lithuanian sodinti "to plant;" Gothic sitan, Old English sittan "to sit."

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go-cart (n.)
also gocart, 1670s, originally "a litter, sedan chair;" also "an infant's walker" (1680s), from go + cart (n.). Later also of hand carts (1759). The modern form go-kart (1959) was coined in reference to a kind of miniature racing car with a frame body and a two-stroke engine.
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palanquin (n.)

"a covered litter, generally for one person, used in India and elsewhere in the East, borne by means of poles on the shoulders of four or six men," 1580s, from Portuguese palanquim (early 16c.), from Malay and Javanese palangki "litter, sedan," ultimately from Sanskrit palyanka-s "couch, bed, litter," from pari "around" + ancati "it bends, curves," related to anka-s "a bend, hook, angle," and meaning, perhaps, "that which bends around the body." Some have noted the "curious coincidence" of Spanish palanca, from Latin phalanga "pole to carry a burden." "The final nasal appears to have been a Portuguese addition as in mandarin, and is often absent from the forms given by early travellers ..." [OED].

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