Etymology
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wroth (adj.)

Old English wrað "angry" (literally "tormented, twisted"), from Proto-Germanic *wraith- (source also of Old Frisian wreth "evil," Old Saxon wred, Middle Dutch wret, Dutch wreed "cruel," Old High German reid, Old Norse reiðr "angry, offended"), from *wreit-, from PIE root *wer- (2) "to turn, bend." Rare or obsolete from early 16c. to mid-19c., but somewhat revived since, especially in dignified writing, or this:

Secretary: "The Dean is furious. He's waxing wroth."
Quincy Adams Wagstaf [Groucho]: "Is Roth out there too? Tell Roth to wax the Dean for a while."
["Horse Feathers," 1932]
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wrath (n.)
Old English wræððu "anger," from wrað "angry" (see wroth) + -þu, from Proto-Germanic -itho (as in strength, width etc.; see -th (2)).
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*wer- (2)

Proto-Indo-European root forming words meaning "to turn, bend."

It forms all or part of: adverse; anniversary; avert; awry; controversy; converge; converse (adj.) "exact opposite;" convert; diverge; divert; evert; extroversion; extrovert; gaiter; introrse; introvert; invert; inward; malversation; obverse; peevish; pervert; prose; raphe; reverberate; revert; rhabdomancy; rhapsody; rhombus; ribald; sinistrorse; stalwart; subvert; tergiversate; transverse; universe; verbena; verge (v.1) "tend, incline;" vermeil; vermicelli; vermicular; vermiform; vermin; versatile; verse (n.) "poetry;" version; verst; versus; vertebra; vertex; vertigo; vervain; vortex; -ward; warp; weird; worm; worry; worth (adj.) "significant, valuable, of value;" worth (v.) "to come to be;" wrangle; wrap; wrath; wreath; wrench; wrest; wrestle; wriggle; wring; wrinkle; wrist; writhe; wrong; wroth; wry.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vartate "turns round, rolls;" Avestan varet- "to turn;" Hittite hurki- "wheel;" Greek rhatane "stirrer, ladle;" Latin vertere (frequentative versare) "to turn, turn back, be turned; convert, transform, translate; be changed," versus "turned toward or against;" Old Church Slavonic vrŭteti "to turn, roll," Russian vreteno "spindle, distaff;" Lithuanian verčiu, versti "to turn;" German werden, Old English weorðan "to become;" Old English -weard "toward," originally "turned toward," weorthan "to befall," wyrd "fate, destiny," literally "what befalls one;" Welsh gwerthyd "spindle, distaff;" Old Irish frith "against."

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