Etymology
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Words related to entertain

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."
entertainer (n.)
"public performer," 1530s, agent noun from entertain.
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.