Etymology
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*melg- 

Proto-Indo-European root meaning "to rub off," also "to stroke; to milk," in reference to the hand motion involved in milking an animal. Compare *g(a)lag-.

It forms all or part of: emulgent; emulsify; emulsion; milch; milk.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit marjati "wipes off;" Greek amelgein, Latin mulgere, Old Church Slavonic mlesti, Lithuanian melžti "to milk;" Old Irish melg "milk."

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*apo- 
also *ap-, Proto-Indo-European root meaning "off, away."

It forms all or part of: ab-; abaft; ablaut; aft; after; apanthropy; aperitif; aperture; apo-; apocalypse; apocryphal; Apollyon; apology; apoplexy; apostle; apostrophe; apothecary; apotheosis; awk; awkward; ebb; eftsoons; of; off; offal; overt.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit apa "away from," Avestan apa "away from," Greek apo "from, away from; after; in descent from," Latin ab "away from, from," Gothic af, Old English of "away from."
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*tem- 
also *temə-, Proto-Indo-European root meaning "to cut."

It forms all or part of: anatomy; atom; contemplate; contemplation; diatom; dichotomy; -ectomy; entomolite; entomology; entomophagous; epitome; phlebotomy; temple (n.1) "building for worship;" tmesis; tome; -tomy; tonsorial; tonsure.

It is the hypothetical source of/evidence for its existence is provided by: Greek temnein "to cut," tomos "volume, section of a book," originally "a section, piece cut off;" Old Church Slavonic tina "to cleave, split;" Middle Irish tamnaim "I cut off," Welsh tam "morsel."
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*kwel- (2)

Proto-Indo-European root meaning "far" (in space or time). Some sources connect this root with *kwel- (1), forming words to do with turning, via the notion of "completion of a cycle."

It forms all or part of: paleo-; tele-; teleconference; telegony; telegraph; telegram; telekinesis; Telemachus; telemeter; telepathy; telephone; telescope; television.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit caramah "the last;" Greek tele "far off, afar, at or to a distance," palaios "old, ancient," palai "long ago, far back;" Breton pell "far off," Welsh pellaf "uttermost."

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*ghrei- 

ghrēi-, Proto-Indo-European root meaning "to rub." 

It forms all or part of: chrism; Christ; christen; Christian; Christmas; cream; grime; grisly; Kriss Kringle.

It is the hypothetical source of/evidence for its existence is provided by: Greek khriein "to anoint, besmear;" Lithuanian grieju, grieti "to skim the cream off;" Old English grima "mask, helmet, ghost," Middle Low German greme "dirt."

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*kes- 
Proto-Indo-European root meaning "to cut."

It forms all or part of: caret; cashier (v.) "dismiss;" cassation; caste; castellan; castellated; Castile; castle; castigate; castrate; castration; chaste; chastity; chateau; chatelaine; Chester; forecastle; incest; quash (v.) "make void, annul."

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sastra- "knife, dagger;" Greek keazein "to split;" Latin carere "to be cut off from," cassus "empty, void;" Old Church Slavonic kosa "scythe."
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*skei- 
Proto-Indo-European root meaning "to cut, split," extension of root *sek- "to cut."

It forms all or part of: abscissa; conscience; conscious; ecu; escudo; escutcheon; esquire; nescience; nescient; nice; omniscience; omniscient; plebiscite; prescience; prescient; rescind; rescission; science; scienter; scilicet; sciolist; scission; schism; schist; schizo-; schizophrenia; scudo; sheath; sheathe; sheave (n.) "grooved wheel to receive a cord, pulley;" shed (v.) "cast off;" shin (n.) "fore part of the lower leg;" shingle (n.1) "thin piece of wood;" shit (v.); shive; shiver (n.1) "small piece, splinter, fragment, chip;" shoddy; shyster; skene; ski; skive (v.1) "split or cut into strips, pare off, grind away;" squire.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit chindhi, chinatti "to break, split up;" Avestan a-sista- "unsplit, unharmed," Greek skhizein "to split, cleave, part, separate;" Latin scindere "to cut, rend, tear asunder, split;" Armenian c'tim "to tear, scratch;" Lithuanian skiesti "to separate, divide;" Old Church Slavonic cediti "to strain;" Old English scitan, Old Norse skita "to defecate;" Old English sceað, Old High German sceida "sheath;" Old Irish sceid "to vomit, spit;" Welsh chwydu "to break open."
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*sleg- 
*slēg-, also *lēg-, Proto-Indo-European root meaning "be slack, be languid."

It forms all or part of: algolagnia; catalectic; laches; languid; languish; lax; lease; lessor; lush; relax; release; relish; slack (adj.); sleep.

It is the hypothetical source of/evidence for its existence is provided by: Greek legein "to leave off, stop," lagnein "to lust;" Latin languere "to be faint, weary," laxus "wide, spacious, roomy;" Old Church Slavonic slabu "lax, weak;" Lithuanian silpnas "weak."
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*sek- 

Proto-Indo-European root meaning "to cut." It forms all or part of: bisect; dissect; hacksaw; insect; intersect; resect; saw (n.1) "cutting tool;" Saxon; scythe; secant; secateurs; sect; section; sector; sedge; segment; skin; skinflint; skinny; transect.

It is the hypothetical source of/evidence for its existence is provided by: Hittite shakk- "to know, pay attention to;" Latin secare "to cut," sectio "a cutting, cutting off, division;" Old Church Slavonic seko, sešti "to cut," sečivo "ax, hatchet," Russian seč' "to cut to pieces;" Lithuanian įsėkti "to engrave, carve;" Albanian šate "mattock;" Old Saxon segasna, Old English sigðe "scythe;" Old English secg "sword," seax "knife, short sword;" Old Irish doescim "I cut."

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*bheid- 
Proto-Indo-European root meaning "to split," with derivatives in Germanic "referring to biting (hence also to eating and to hunting) and woodworking" [Watkins].

It forms all or part of: abet; bait (n.) "food used to attract prey;" bait (v.) "to torment, persecute;" bateau; beetle (n.1) "type of insect; bit (n.1) "small piece;" bite; bitter; bitter end; boat; boatswain; -fid; fissile; fission; fissure; giblets; pita; pizza; vent (n.).

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhinadmi "I cleave," Latin Latin findere "to split, cleave, separate, divide," Old High German bizzan "to bite," Old English bita "a piece bitten off, morsel," Old Norse beita "to hunt with dogs," beita "pasture, food."
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