Etymology
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vermin (n.)
c. 1300, "noxious animals," from Anglo-French and Old French vermin "moth, worm, mite," in plural "troublesome creatures" (12c.), from Vulgar Latin *verminum "vermin," possibly including bothersome insects, collective noun formed from Latin vermis "worm" (from PIE root *wer- (2) "to turn, bend"). Extended to "low, obnoxious people" by 1560s.
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verminous (adj.)
1610s, from vermin + -ous or else from Latin verminosus.
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varmint (n.)
1530s, varment; the chiefly American English dialectal form varmint is attested from 1829; colloquial variant of vermin. Meaning "objectionable or troublesome person" is recorded from 1773.
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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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varsity (adj.)
1825, "university," variant of earlier versity (1670s), shortened form of university. Compare varsal (1690s), short for universal; varmint from vermin; and Grose's "Dictionary of the Vulgar Tongue" (1788) has vardy as slang for verdict. "Used in English universities, and affected to some extent in American colleges" [Century Dictionary].
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puce (n.)

"brownish-purple," literally "flea-color," 1787, from French puce "flea-color; flea," from Latin pucilem (nominative pulex) "flea," from PIE *plou- "flea" (source also of Sanskrit plusih, Greek psylla, Old Church Slavonic blucha, Lithuanian blusa, Armenian lu "flea").

[T]he couleur de Puce, or flea colour, and the couleur de Noix, or nut colour, are the reigning winter taste. [Westminster Magazine, January 1777]

Perhaps so called as the color of the scab or stain that marked a flea-bite; flea-bitten was a color word in English to describe whiter or gray spotted over with dark-reddish spots (by 1620s, often of the skins of horses, dogs, etc.). That it could be generally recognized as a color seems a testimony to our ancestors' intimacy with vermin.

OED sees no connection between this word and obsolete puke (16c.-18c.; hence Shakespeare's puke-stocking) as the name of a dark color of now-uncertain shade (Century Dictionary says perhaps reddish-brown, OED says bluish-black or inky; others suggest grey).

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