Etymology
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*pau- (2)

Proto-Indo-European root meaning "to cut, strike, stamp."

It forms all or part of: account; amputate; amputation; anapest; berate; compute; count (v.); depute; deputy; dispute; impute; pave; pavement; pit (n.1) "hole, cavity;" putative; rate (v.1) "to scold;" reputation; repute.

It is the hypothetical source of/evidence for its existence is provided by: Latin pavire "to beat, ram, tread down," putare "to prune;" Greek paiein "to strike;" Lithuanian pjauti "to cut," pjūklas "saw."

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*ei- 
Proto-Indo-European root meaning "to go."

It forms all or part of: Abitur; adit; ambience; ambient; ambit; ambition; ambitious; andante; anion; cation; circuit; coitus; commence; commencement; concomitant; constable; count (n.1) title of nobility; county; dysprosium; errant; exit; initial; initiate; initiation; introit; ion; issue; itinerant; itinerary; janitor; January; Janus; Jena; Mahayana; obiter; obituary; perish; praetor; Praetorian; preterite; sedition; sudden; trance; transient; transit; transitive; viscount.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit e'ti "goes," imas "we go," ayanam "a going, way;" Avestan ae'iti "goes," Old Persian aitiy "goes;" Greek ienai "to go;" Latin ire "to go," iter "a way;" Old Irish ethaim "I go," Irish bothar "a road" (from *bou-itro- "cows' way"), Gaulish eimu "we go;" Lithuanian eiti "to go;" Old Church Slavonic iti "go;" Bulgarian ida "I go;" Russian idti "to go;" Gothic iddja "went."
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*re- 

*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together." 

It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."

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*leg- (1)

Proto-Indo-European root meaning "to collect, gather," with derivatives meaning "to speak" on the notion of "to gather words, to pick out words."

It forms all or part of: alexia; analects; analogous; analogue; analogy; anthology; apologetic; apologue; apology; catalogue; coil; colleague; collect; college; collegial; Decalogue; delegate; dialect; dialogue; diligence; doxology; dyslexia; eclectic; eclogue; elect; election; epilogue; hapax legomenon; homologous; horology; ideologue; idiolect; intelligence; lectern; lectio difficilior; lection; lector; lecture; leech (n.2) "physician;" legacy; legal; legate; legend; legible; legion; legislator; legitimate; lesson; lexicon; ligneous; ligni-; logarithm; logic; logistic; logo-; logogriph; logopoeia; Logos; -logue; -logy; loyal; monologue; neglect; neologism; philology; privilege; prolegomenon; prologue; relegate; sacrilege; select; syllogism; tautology; trilogy.

It is the hypothetical source of/evidence for its existence is provided by: Greek legein "to say, tell, speak, declare; to count," originally, in Homer, "to pick out, select, collect, enumerate;" lexis "speech, diction;" logos "word, speech, thought, account;" Latin legere "to gather, choose, pluck; read," lignum "wood, firewood," literally "that which is gathered," legare "to depute, commission, charge," lex "law" (perhaps "collection of rules"); Albanian mb-ledh "to collect, harvest;" Gothic lisan "to collect, harvest," Lithuanian lesti "to pick, eat picking;" Hittite less-zi "to pick, gather."

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