Etymology
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entertain (v.)
Origin and meaning of entertain

late 15c., "to keep up, maintain, to keep (someone) in a certain frame of mind," from Old French entretenir "hold together, stick together, support" (12c.), from entre- "among" (from Latin inter; see inter-) + tenir "to hold" (from Latin tenere, from PIE root *ten- "to stretch").

Sense of "have a guest" is late 15c.; that of "gratify, amuse" is 1620s. Meaning "to allow (something) to consideration, take into the mind" (of opinions, notions, etc.) is 1610s. Related: Entertained; entertaining.

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entertainer (n.)
"public performer," 1530s, agent noun from entertain.
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entertainment (n.)
1530s, "provision for support of a retainer; manner of social behavior," now obsolete, along with other 16c. senses; from entertain + -ment. Meaning "the amusement of someone" is from 1610s; sense of "that which entertains" is from 1650s; that of "public performance or display meant to amuse" is from 1727.
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inter- 
word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."

A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
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*ten- 
Proto-Indo-European root meaning "to stretch," with derivatives meaning "something stretched, a string; thin."

It forms all or part of: abstain; abstention; abstinence; abstinent; atelectasis; attend; attenuate; attenuation; baritone; catatonia; catatonic; contain; contend; continue; detain; detente; detention; diatonic; distend; entertain; extend; extenuate; hypotenuse; hypotonia; intend; intone (v.1) "to sing, chant;" isotonic; lieutenant; locum-tenens; maintain; monotony; neoteny; obtain; ostensible; peritoneum; pertain; pertinacious; portend; pretend; rein; retain; retinue; sitar; subtend; sustain; tantra; telangiectasia; temple (n.1) "building for worship;" temple (n.2) "flattened area on either side of the forehead;" temporal; tenable; tenacious; tenacity; tenant; tend (v.1) "to incline, to move in a certain direction;" tendency; tender (adj.) "soft, easily injured;" tender (v.) "to offer formally;" tendon; tendril; tenement; tenesmus; tenet; tennis; tenon; tenor; tense (adj.) "stretched tight;" tensile; tension; tensor; tent (n.) "portable shelter;" tenterhooks; tenuous; tenure; tetanus; thin; tone; tonic.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tantram "loom," tanoti "stretches, lasts," tanuh "thin," literally "stretched out;" Persian tar "string;" Lithuanian tankus "compact," i.e. "tightened;" Greek teinein "to stretch," tasis "a stretching, tension," tenos "sinew," tetanos "stiff, rigid," tonos "string," hence "sound, pitch;" Latin tenere "to hold, grasp, keep, have possession, maintain," tendere "to stretch," tenuis "thin, rare, fine;" Old Church Slavonic tento "cord;" Old English þynne "thin."
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invitatory (adj.)

"using or containing invitation," 1640s, from Latin invitatorius "inviting," from invitat-, past-participle stem of invitare "to invite, treat, entertain" (see invitation).

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regale (v.)

"entertain (someone) splendidly," 1650s, from French régaler "to entertain or feast," from Old French regale, rigale, from gale "merriment," from galer "make merry" (see gallant (adj.)). Influenced in Old French by se rigoler "amuse oneself, rejoice," a word of unknown origin. Italian regalo is from French. Originally of food and drink; by 1670s in reference to what pleases or delights the mind. Related: Regaled; regaling.

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beguile (v.)
"delude by artifice," early 13c., from be- + guile (v.). Meaning "entertain with passtimes" is by 1580s (compare the sense evolution of amuse). Related: Beguiled; beguiling.
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wine (v.)
"entertain with wine," 1862, from wine (n.). Earlier "expend in drinking wine" (1620s). Related: Wined; wining.
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invite (v.)

"solicit to come," 1530s, a back-formation from invitation, or else from French inviter (15c.), from Latin invitare "to invite," also "to summon, challenge; to feast, to entertain," a word of uncertain origin. Related: Invited; inviting.

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