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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Valerie 
fem. proper name, French, from Latin Valeria, fem. of Valerius, name of a Roman gens, from valere "to be strong" (from PIE root *wal- "to be strong").
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invalid (adj.2)
"of no legal force," 1630s, from special use of Latin invalidus "not strong, infirm, impotent, feeble, inadequate," from in- "not" (see in- (1)) + validus "strong" (from PIE root *wal- "to be strong").
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Vladimir 

masc. proper name, from Old Church Slavonic Vladimiru "Ruling Peace," from vlasti "to rule over" (from PIE root *wal- "to be strong") + miru "peace" (see mir).

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valid (adj.)

1570s, "having force in law, legally binding," from French valide (16c.), from Latin validus "strong, effective, powerful, active," from valere "be strong" (from PIE root *wal- "to be strong"). The meaning "sufficiently supported by facts or authority, well-grounded" is first recorded 1640s.

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Isold 
fem. proper name, French Isolt, Iseut, of Germanic origin, literally "ice-rule," from Proto-Germanic *is "ice" (see ice (n.)) + *waldan "to rule" (from PIE root *wal- "to be strong").
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Arnold 
masc. proper name, from Old High German Arenwald, literally "having the strength of an eagle," from arn "eagle," from Proto-Germanic *aron- "eagle" (from PIE root *or- "large bird;" see erne) + wald "power" (from PIE root *wal- "to be strong").
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Ronald 
masc. proper name, from Old Norse Rögnvaldr "Having the Gods' Power," from rögn "gods," literally "decreeing powers" (plural of regin "decree") + valdr "ruler" (from Proto-Germanic *waldan, from PIE root *wal- "to be strong").
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invalid (adj.1)
"not strong, infirm," also "infirm from sickness, disease, or injury", 1640s, from Latin invalidus "not strong, infirm, impotent, feeble, inadequate," from in- "not" (see in- (1)) + validus "strong" (from PIE root *wal- "to be strong"). With pronunciation from French invalide (16c.).
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valediction (n.)
"a farewell, a bidding farewell," 1610s, from past participle stem of Latin valedicere "bid farewell, take leave," from vale "farewell!," second person singular imperative of valere "be well, be strong" (from PIE root *wal- "to be strong") + dicere "to say" (from PIE root *deik- "to show," also "pronounce solemnly").
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