Etymology
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dowdy 

1580s (n.), "an aukward, ill-dressed, inelegant woman" [Johnson]; as an adjective, 1670s, "slovenly, shabby in dress" (of women). Perhaps a diminutive of Middle English doude "unattractive woman" (mid-14c.), which is of uncertain origin. Compare Scottish dow "to fade, wither, become dull or flat." In modern use it tends more toward "unfashionable, without style." 

If plaine or homely, wee saie she is a doudie or a slut [Barnabe Riche, "Riche his Farewell to Militarie profession," 1581]
You don't have to be dowdy to be a Christian. [Tammy Faye Bakker, Newsweek, June 8, 1987]

Modern use of dowdy (adj.) is likely a back-formation from the noun. Related: Dowdily; dowdiness.

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mare (n.1)

"female of the horse or any other equine animal," Old English meare, also mere (Mercian), myre (West Saxon), fem. of mearh "horse," from Proto-Germanic *marhijo- "female horse" (source also of Old Saxon meriha, Old Norse merr, Old Frisian merrie, Dutch merrie, Old High German meriha, German Mähre "mare"), said to be of Gaulish origin (compare Irish and Gaelic marc, Welsh march, Breton marh "horse").

The fem. form is not recorded in Gothic, and there are no known cognates beyond Germanic and Celtic, so perhaps it is a word from a substrate language. The masc. forms have disappeared in English and German except as disguised in marshal (n.). In 14c. also "a bad woman, a slut," and, apparently, also "a rabbit." As the name of a throw in wrestling, it is attested from c. 1600. Mare's nest "illusory discovery, something of apparent importance causing excitement but which turns out to be a delusion or a hoax" is from 1610s.

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