early 15c., from Old French vehement, veement "impetuous, ardent" (12c.), from Latin vehementem (nominative vehemens) "impetuous, eager, violent, furious, ardent, carried away," perhaps [Barnhart] from a lost present middle participle of vehere "to carry" (from PIE root *wegh- "to go, move, transport in a vehicle"). The other theory is that it represents vehe- "lacking, wanting" + mens "mind." Related: Vehemently.
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."
"an emphatic assertion," 1550s, from Latin asseverationem (nominative asseveratio) "vehement assertion, protestation," noun of action from past-participle stem of asseverare/adseverare "affirm, insist on," from ad "to" (see ad-) + severus "serious, grave, strict, austere," which is probably from PIE root *segh- "to have, hold," on the notion of "steadfastness, toughness."