Etymology
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Words related to deviate

de- 

active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.

As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.

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via (prep.)

1779, from Latin via "by way of," ablative form of via "way, road, path, highway, channel, course" (from PIE root *wegh- "to go, move, transport in a vehicle," which is also the source of English way (n.)).

deviant (adj.)

c. 1400, deviaunt, "different, deviating, straying, wandering," from Late Latin deviantem (nominative devians), present participle of deviare "turn aside," from Latin phrase de via, from de "off" (see de-) + via "way" (see via). The noun meaning "one that deviates, one who goes astray" is from 1540s. It is attested by 1927 as "something that deviates from normal." In the sexual sense "person whose sexuality deviates from what is held to be normal," from 1952. Also compare deviate (n.), recorded in that sense since 1912.

devious (adj.)

1590s, "out of the common or direct way," from Latin devius "out of the way, remote, off the main road," from de via; from de "off" (see de-) + via "way, road" (see via). Compare deviate. Originally in the Latin literal sense; the figurative sense of "deceitful" is first recorded 1630s. Related: Deviously; deviousness. Figurative senses of the Latin word were "retired, sequestered, wandering in the byways, foolish, inconsistent."

undeviating (adj.)

1732, from un- (1) "not" + present participle of deviate (v.).

*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."