Etymology
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Words related to interpolate

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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*pel- (5)
Proto-Indo-European root meaning "to thrust, strike, drive."

It forms all or part of: anvil; appeal; catapult; compel; dispel; expel; felt (n.) "unwoven fabric matted together by rolling or beating;" filter; filtrate; impel; impulse; interpellation; interpolate; peal; pelt (v.) "to strike (with something);" polish; propel; pulsate; pulsation; pulse (n.1) "a throb, a beat;" push; rappel; repeal; repel; repousse.

It is the hypothetical source of/evidence for its existence is provided by: Greek pallein "to wield, brandish, swing," pelemizein "to shake, cause to tremble;" Latin pellere "to push, drive;" Old Church Slavonic plŭstĭ.
extrapolate (v.)

"make an approximate calculation by inferring unknown values from trends in the known data," 1862 (in a Harvard observatory account of the comet of 1858), from extra- + ending from interpolate. Said in early references to be a characteristic word of Sir George Airy (1801-1892), English mathematician and astronomer. Related: Extrapolated; extrapolating.

interpolation (n.)
1610s, "act of interpolating;" 1670s, "that which is interpolated," from French interpolation (17c.) or directly from Latin interpolationem (nominative interpolatio), noun of action from past participle stem of interpolare "to alter; falsify" (see interpolate).
interpolator (n.)
1650s, from Late Latin interpolator "one who corrupts or spoils," agent noun from past participle stem of Latin interpolare "to polish; to alter; to falsify" (see interpolate).