h₂welh₂-
“to be strong, to prevail”Source of Latin valēre, English value, valid, prevail
Root meaning to be strong, yielding Latin valēre and English value, valid, prevail, avail.
Discussion
The Proto-Indo-European root *h₂welh₂- meant "to be strong, to rule, to have power" and produced derivatives across several branches relating to strength, dominion, and the exercise of authority. The double laryngeal structure (*h₂...h₂) is reflected in the vowel quality and length of its reflexes. The root occupies an important place in the Indo-European vocabulary of power and governance.
In Germanic, the root produced Old English wealdan "to rule, to control, to wield", the ancestor of modern English wield. The initial laryngeal was lost, and the *w- was preserved. To wield a sword or wield power both preserve the original sense of exercising control and strength. The German cognate walten "to rule, to govern" maintains the same meaning.
Latin valēre "to be strong, to be worth" is the principal learned reflex and has been extremely productive in English: valor (strength, courage), valid (strong, sound), value (worth, strength), prevail (to prove stronger), equivalent (of equal strength), valiant, and convalescent (becoming strong again). The personal name Valentine derives from valens "strong, healthy". The common farewell vale ("be well, be strong") is an imperative of the same verb.
In Celtic, the root appears in Welsh gwlad "country, domain" (that which is ruled) and in the name of the legendary British king Vortigern (from *wor-tigernos "over-lord"). Slavic vlast' "power, authority" (Russian) is a further cognate.
The root *h₂welh₂- thus provides vocabulary for both physical strength (wield, valor) and abstract authority (valid, value, prevail). This dual nature reflects the Proto-Indo-European understanding of power as inseparable from physical capability — to rule was to be strong, and to be strong was to have the right to govern. The modern separation of political authority from personal might would have been alien to the speakers of the proto-language.