Etymology
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*wal- 

Proto-Indo-European root meaning "to be strong."

It forms all or part of: ambivalence; Arnold; avail; bivalent; convalesce; countervail; Donald; equivalent; evaluation; Gerald; Harold; invalid (adj.1) "not strong, infirm;" invalid (adj.2) "of no legal force;" Isold; multivalent; polyvalent; prevalent; prevail; Reynold; Ronald; valediction; valence; Valerie; valetudinarian; valiance; valiant; valid; valor; value; Vladimir; Walter; wield.

It is the hypothetical source of/evidence for its existence is provided by: Latin valere "be strong, be well, be worth;" Old Church Slavonic vlasti "to rule over;" Lithuanian valdyti "to have power;" Celtic *walos- "ruler," Old Irish flaith "dominion," Welsh gallu "to be able;" Old English wealdan "to rule," Old High German -walt, -wald "power" (in personal names), Old Norse valdr "ruler."

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*we- 

wē-, Proto-Indo-European root meaning "to blow." 

It forms all or part of: Nirvana; vent; ventilate; weather; wind (n.1) "air in motion;" window; wing.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit va-, Greek aemi-, Gothic waian, Old English wawan, Old High German wajan, German wehen, Old Church Slavonic vejati "to blow;" Sanskrit vatah, Avestan vata-, Hittite huwantis, Latin ventus, Old English wind, German Wind, Gothic winds, Old Church Slavonic vetru, Lithuanian vėjas "wind;" Lithuanian vėtra "tempest, storm;" Old Irish feth "air;" Welsh gwynt, Breton gwent "wind." 

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*wed- (1)
Proto-Indo-European root meaning "water; wet."

It forms all or part of: abound; anhydrous; carbohydrate; clepsydra; dropsy; hydra; hydrangea; hydrant; hydrargyrum; hydrate; hydraulic; hydro-; hydrogen; hydrophobia; hydrous; Hydrus; inundate; inundation; kirsch-wasser; nutria; otter; redound; redundant; surround; undine; undulant; undulate; undulation; vodka; wash; water (n.1); wet; whiskey; winter.

It is the hypothetical source of/evidence for its existence is provided by: Hittite watar, Sanskrit udrah, Greek hydor, Old Church Slavonic and Russian voda, Lithuanian vanduo, Old Prussian wundan, Gaelic uisge "water;" Latin unda "wave;" Old English wæter, Old High German wazzar, Gothic wato "water."
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*weg- 
Proto-Indo-European root meaning "to be strong, be lively."

It forms all or part of: awake; bewitch; bivouac; invigilate; reveille; surveillance; vedette; vegetable; velocity; vigil; vigilant; vigilante; vigor; waft; wait; wake (v.) "emerge or arise from sleep;" waken; watch; Wicca; wicked; witch.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vajah "force, strength," vajayati "drives on;" Latin vigil "watchful, awake," vigere "be lively, thrive," velox "fast, lively," vegere "to enliven," vigor "liveliness, activity;" Old English wacan "to become awake," German wachen "to be awake," Gothic wakan "to watch."
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*wegh- 

Proto-Indo-European root meaning "to go, move, transport in a vehicle."

The root wegh-, "to convey, especially by wheeled vehicle," is found in virtually every branch of Indo-European, including now Anatolian. The root, as well as other widely represented roots such as aks- and nobh-, attests to the presence of the wheel — and vehicles using it — at the time Proto-Indo-European was spoken. [Watkins, p. 96]

It forms all or part of: always; away; convection; convey; convex; convoy; deviate; devious; envoy; evection; earwig; foy; graywacke; impervious; invective; inveigh; invoice; Norway; obviate; obvious; ochlocracy; ogee; pervious; previous; provection; quadrivium; thalweg; trivia; trivial; trivium; vector; vehemence; vehement; vehicle; vex; via; viaduct; viatic; viaticum; vogue; voyage; wacke; wag; waggish; wagon; wain; wall-eyed; wave (n.); way; wee; weigh; weight; wey; wiggle.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vahati "carries, conveys," vahitram, vahanam "vessel, ship;" Avestan vazaiti "he leads, draws;" Greek okhos "carriage, chariot;" Latin vehere "to carry, convey," vehiculum "carriage, chariot;" Old Church Slavonic vesti "to carry, convey," vozŭ "carriage, chariot;" Russian povozka "small sled;" Lithuanian vežu, vežti "to carry, convey," važis "a small sled;" Old Irish fecht "campaign, journey," fen "carriage, cart;" Welsh gwain "carriage, cart;" Old English wegan "to carry;" Old Norse vegr, Old High German weg "way;" Middle Dutch wagen "wagon."

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*weid- 
Proto-Indo-European root meaning "to see."

It forms all or part of: advice; advise; belvedere; clairvoyant; deja vu; Druid; eidetic; eidolon; envy; evident; guide; guidon; guise; guy (n.1) "small rope, chain, wire;" Gwendolyn; Hades; history; idea; ideo-; idol; idyll; improvisation; improvise; interview; invidious; kaleidoscope; -oid; penguin; polyhistor; prevision; provide; providence; prudent; purvey; purview; review; revise; Rig Veda; story (n.1) "connected account or narration of some happening;" supervise; survey; twit; unwitting; Veda; vide; view; visa; visage; vision; visit; visor; vista; voyeur; wise (adj.) "learned, sagacious, cunning;" wise (n.) "way of proceeding, manner;" wisdom; wiseacre; wit (n.) "mental capacity;" wit (v.) "to know;" witenagemot; witting; wot.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit veda "I know;" Avestan vaeda "I know;" Greek oida, Doric woida "I know," idein "to see;" Old Irish fis "vision," find "white," i.e. "clearly seen," fiuss "knowledge;" Welsh gwyn, Gaulish vindos, Breton gwenn "white;" Gothic, Old Swedish, Old English witan "to know;" Gothic weitan "to see;" English wise, German wissen "to know;" Lithuanian vysti "to see;" Bulgarian vidya "I see;" Polish widzieć "to see," wiedzieć "to know;" Russian videt' "to see," vest' "news," Old Russian vedat' "to know."
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*weik- (2)

also *weig-, Proto-Indo-European root meaning "to bend, to wind."

It forms all or part of: vetch; vicar; vicarious; vice- "deputy, assistant, substitute;" viceregent; vice versa; vicissitude; weak; weakfish; week; wicker; wicket; witch hazel; wych.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit visti "changing, changeable;" Old English wac "weak, pliant, soft," wician "to give way, yield," wice "wych elm," Old Norse vikja "to bend, turn," Swedish viker "willow twig, wand," German wechsel "change."

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*weik- (1)
Proto-Indo-European root meaning "clan, social unit above the household."

It forms all or part of: antoecian; bailiwick; Brunswick; diocese; ecology; economy; ecumenical; metic; nasty; parish; parochial; vicinage; vicinity; viking; villa; village; villain; villanelle; -ville; villein; Warwickshire; wick (n.2) "dairy farm."

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit visah "house," vit "dwelling, house, settlement;" Avestan vis "house, village, clan;" Old Persian vitham "house, royal house;" Greek oikos "house;" Latin villa "country house, farm," vicus "village, group of houses;" Lithuanian viešpats "master of the house;" Old Church Slavonic visi "village;" Gothic weihs "village."
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*weik- (3)

Proto-Indo-European root meaning "to fight, conquer."

It forms all or part of: convict; convince; evict; evince; invictus; invincible; Ordovician; province; vanquish; victor; victory; Vincent; vincible.

It is the hypothetical source of/evidence for its existence is provided by: Latin victor "a conqueror," vincere "to conquer, overcome, defeat;" Lithuanian apveikiu, apveikti "to subdue, overcome;" Old Church Slavonic veku "strength, power, age;" Old Norse vigr "able in battle," Old English wigan "fight;" Welsh gwych "brave, energetic," Old Irish fichim "I fight," second element in Celtic Ordovices "those who fight with hammers."

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*weip- 

Proto-Indo-European root meaning "to turn, vacillate, tremble ecstatically." 

It forms all or part of: gimlet; gimp (n.2) "ornamental trimming material;" vibrant; vibrate; vibration; vibrato; vibrissa; waif; waive; waiver; whip; wimple; wipe.

It is the hypothetical source of/evidence for its existence is provided by: Latin vibrare "set in tremulous motion, move quickly to and fro, quiver, tremble, shake," Lithuanian vyburti "to wag" (the tail), Danish vippe, Dutch wippen "to swing," Old English wipan "to wipe."

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