Etymology
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farewell (interj.)
expression at parting, late 14c., from Middle English faren wel, verbal phrase attested by c. 1200 (see fare (v.) + well (adv.)); usually said to the departing person, who replied with good-bye. As a noun, "a good-bye, a leave-taking," by early 15c. Expression to a fare-thee-well "to the last degree" is by 1884, American English.
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adieu (interj.)
late 14c., adewe, from Old French a Dieu, a Deu, shortened from phrases such as a dieu (vous) commant "I commend (you) to God," from a "to" (see ad-) + dieu "God," from Latin deum, accusative of deus "god," from PIE *deiwos "god" (from root *dyeu- "to shine," in derivatives "sky, heaven, god"). Originally said to the party left (farewell was to the party setting forth), but in English used as a general parting salutation. As a noun, "expression of kind wishes upon departure," late 14c. Compare native parting salutation good-bye, a contraction of God be with ye.
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*per- (2)

Proto-Indo-European root meaning "to lead, pass over." A verbal root associated with *per- (1), which forms prepositions and preverbs with the basic meaning "forward, through; in front of, before," etc.

It forms all or part of: aporia; asportation; comport; deport; disport; emporium; Euphrates; export; fare; farewell; fartlek; Ferdinand; fere; fern; ferry; firth; fjord; ford; Fuhrer; gaberdine; import; important; importune; opportune; opportunity; passport; porch; pore (n.) "minute opening;" port (n.1) "harbor;" port (n.2) "gateway, entrance;" port (n.3) "bearing, mien;" port (v.) "to carry;" portable; portage; portal; portcullis; porter (n.1) "person who carries;" porter (n.2) "doorkeeper, janitor;" portfolio; portico; portiere; purport; practical; rapport; report; sport; support; transport; warfare; wayfarer; welfare.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit parayati "carries over;" Greek poros "journey, passage, way," peirein "to pierce, pass through, run through;" Latin portare "to carry," porta "gate, door," portus "port, harbor," originally "entrance, passage," peritus "experienced;" Avestan peretush "passage, ford, bridge;" Armenian hordan "go forward;" Old Welsh rit, Welsh rhyd "ford;" Old Church Slavonic pariti "to fly;" Old English faran "to go, journey," Old Norse fjörðr "inlet, estuary."

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valediction (n.)
"a farewell, a bidding farewell," 1610s, from past participle stem of Latin valedicere "bid farewell, take leave," from vale "farewell!," second person singular imperative of valere "be well, be strong" (from PIE root *wal- "to be strong") + dicere "to say" (from PIE root *deik- "to show," also "pronounce solemnly").
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send-off (n.)
"a farewell" (especially a funeral), 1872, from verbal phrase (attested by 1660s), from send (v.) + off (adv.).
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ave 
"hail," also "farewell," early 13c. (in reference to the Ave Maria), from Latin ave, second person singular imperative of avere "to be or fare well."
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sayonara 

"farewell, good-bye" 1875, from Japanese, said to mean literally "if it is to be that way," from sayo "that way," + nara "if."

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leave-taking (n.)
late 14c., from the verbal phrase to take leave, originally "obtain or receive formal permission" in any sense (c. 1300); see take (v.) + leave (n.). Sense evolution was through "receive formal permission to depart;" by 16c. it had begun to mean "depart with an expression of farewell," and in some cases came to mean the farewell itself. Give (someone) leave (v.) "allow, permit" is from 12c.
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later (adj., adv.)
"afterward," 16c., comparative of late. A modern formation; the Old English comparative lator developed into latter. As a salutation, "farewell," from 1954, U.S. colloquial, short for adverbial use in (I'll) see you later.
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entanglement (n.)
1630s, "that which entangles," from entangle + -ment. From 1680s as "act of entangling." Foreign entanglements does not appear as such in Washington's Farewell Address (1796), though he warns against them. The phrase is found in William Coxe's 1798 memoirs of Sir Robert Walpole.
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