Etymology
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*ambhi- 
also *mbhi-, Proto-Indo-European root meaning "around;" probably derived from *ant-bhi "from both sides," from root *ant- "front, forehead."

It forms all or part of: abaft; about; alley (n.1) "open passage between buildings;" ambagious; ambassador; ambi-; ambidexterity; ambidextrous; ambience; ambient; ambiguous; ambit; ambition; ambitious; amble; ambulance; ambulant; ambulate; ambulation; ambulatory; amphi-; amphibian; Amphictyonic; amphisbaena; Amphiscians; amphitheater; amphora; amputate; amputation; ancillary; andante; anfractuous; be-; begin; beleaguer; between; bivouac; but; by; circumambulate; embassy; ember-days; funambulist; ombudsman; perambulate; perambulation; preamble; somnambulate; somnambulism; umlaut.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit abhitah "on both sides," abhi "toward, to;" Avestan aibi; Greek amphi "round about;" Latin ambi- "around, round about;" Gaulish ambi-, Old Irish imb- "round about, about;" Old Church Slavonic oba; Lithuanian abu "both;" Old English ymbe, German um "around."
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*ater- 
*āter-, Proto-Indo-European root meaning "fire." It forms all or part of: atrabiliary; atrabilious; atrium; atrocious.

It is the hypothetical source of/evidence for its existence is provided by: Old Persian atar "fire;" Latin ater "black" ("blackened by fire"), atrox "frightful" ("of fiery or threatening appearance").
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*ere- 

*erə-, Proto-Indo-European root meaning "to row." It forms all or part of: row (v.) "propel with oars;" rudder; Russia; Russian; trireme.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit aritrah "oar;" Greek eressein "to row," eretmon "oar," trieres "trireme;" Latin remus "oar;" Lithuanian iriu, irti "to row," irklas "oar;" Old Irish rome "oar," Old English roðor "rudder," rowan "go by water, row."

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*mei- (1)
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."
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*meue- 
*meuə-, Proto-Indo-European root meaning "to push away."

It forms all or part of: commotion; emotion; mob; mobile; moment; momentary; momentous; momentum; motif; motility; motion; motive; moto-; motor; move; movement; mutiny; premotion; promote; remote; remove.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kama-muta "moved by love" and probably mivati "pushes, moves;" Greek ameusasthai "to surpass," amyno "push away;" Latin movere "move, set in motion;" Lithuanian mauti "push on."
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*lois- 

Proto-Indo-European root meaning "furrow, track." 

It forms all or part of: delirious; delirium; last (n.1) "wooden model of a human foot used by shoemakers;" last (v.) "endure, go on existing;" learn; learning; Lehrjahre; lore.

It is the hypothetical source of/evidence for its existence is provided by: Latin lira "furrow;" Old Prussian lyso "field bed;" Old Church Slavonic lexa "field bed, furrow;" Old High German leisa "track," Gothic laistjan "to follow," Old English læran "to teach."

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*gleubh- 

Proto-Indo-European root meaning "to tear apart, cleave." 

It forms all or part of: cleave (v.1) "to split, part or divide by force;" cleft; clever; clevis; clove (n.2)  "slice of garlic;" glyptodon; hieroglyphic; petroglyph.

It is the hypothetical source of/evidence for its existence is provided by: Greek glyphe "a carving," glyphein "to hollow out, cut out with a knife, engrave, carve;" Latin glubere "to peel, shell, strip;" Old High German klioban, Old English cleofan, Old Norse kljufa "to cleave," Old Norse klofi, Middle Dutch clove "a cleft."  

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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.
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*reig- 

Proto-Indo-European root meaning "stretch; be stretched; be stiff" 

It forms all or part of: reach; rigid; rigidity; rigor.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rjyati "he stretches himself," riag "torture" (by racking); Greek oregein "to reach, extend;" Latin rigidus "hard, stiff, rough, severe," rigēre "be stiff;" Lithuanian raižytis "to stretch oneself;" Old Irish ringid "torture," rigim "I stretch;" Middle High German ric "band, string;" Old High German reihhon, Old English ræcan, ræcean "to reach, achieve," on notion of "to stretch out." 

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*g(a)lag- 
also *g(a)lakt-, Proto-Indo-European root meaning "milk."

It forms all or part of: ablactation; cafe au lait; galactic; galaxy; lactate (v.); lactate (n.); lactation; lacteal; lactescence; lactic; lactivorous; lacto-; lactose; latte; lettuce.

It is the hypothetical source of/evidence for its existence is provided by: Latin lac (genitive lactis) "milk;" Greek gala (genitive galaktos), "milk;" Armenian dialectal kaxc' "milk." The initial "g" probably was lost in Latin by dissimilation. This and the separate root *melg-, account for words for "milk" in most of the Indo-European languages. The absence of a common word for it is considered a mystery.
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