Etymology
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arse (n.)

"buttocks, hinder part of an animal," Old English ærs "tail, rump," from Proto-Germanic *arsoz (source also of Old Saxon, Old High German, Old Norse ars, Middle Dutch ærs, German Arsch "buttock"), from PIE root *ors- "buttock, backside" (source also of Greek orros "tail, rump, base of the spine," Hittite arrash, Armenian or "buttock," Old Irish err "tail").

To hang the arse "be reluctant or tardy" is from 1630s. Middle English had arse-winning "money obtained by prostitution" (late 14c.). To turn arse over tip is attested by 1884, along with the alternative arse over tit.

Every scrap of Latin Lord Edgecumbe heard at the Encaenia at Oxford he translated ridiculously; one of the themes was Ars Musica : he Englished it Bumfiddle. [Horace Walpole to the Countess of Upper Ossory, Aug. 9, 1773]
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arsy-versy (adv.)
"backside foremost," 1530s, probably a reduplication of arse, perhaps with suggestions of reverse.
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arsehole (n.)

c. 1400, arce-hoole; see arse + hole (n.). In Old English, Latin anus was glossed with earsðerl, literally "arse-thrill," with thrill (n.) in its original sense of "hole" (compare nostril).

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wheatear (n.)
type of bird, 1590s, back-formation from white-ears, literally "white-arse" (see white + arse). So called for its color markings; compare French name for the bird, cul-blanc, literally "white rump."
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cynosure (n.)

"something that strongly attracts attention," 1590s, from French cynosure (16c.), from Latin Cynosura, literally "dog's tail," an old name of the constellation (now Ursa Minor) containing what is now (but was not in ancient times) the North Star, the focus of navigation, at the tip of its tail; from Greek kynosoura, literally "dog's tail," from kyōn (genitive kynos; from PIE root *kwon- "dog") + oura "tail" (see arse). Apparently in ancient times the whole constellation was used as a rough indicator of the celestial north pole. Related: Cynosural.

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squirrel (n.)

early 14c., from Anglo-French esquirel, Old French escurueil "squirrel; squirrel fur" (Modern French écureuil), from Vulgar Latin *scuriolus, diminutive of *scurius "squirrel," variant of Latin sciurus, from Greek skiouros "a squirrel," literally "shadow-tailed," from skia "shadow" (see Ascians) + oura "tail," from PIE root *ors- "buttocks, backside" (see arse). Perhaps the original notion is "that which makes a shade with its tail," but Beekes writes that this "looks like a folk etymology rather than a serious explanation." The Old English word was acweorna, which survived into Middle English as aquerne.

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ass (n.2)
Origin and meaning of ass

slang for "backside," first attested 1860 in nautical slang, in popular use from 1930; chiefly U.S.; from dialectal variant pronunciation of arse (q.v.). The loss of -r- before -s- is attested in other words (burst/bust, curse/cuss, horse/hoss, barse/bass, garsh/gash, parcel/passel).

Indirect evidence of the change from arse to ass can be traced to 17c. By 1680s arse was being pronounced to rhyme with "-ass" words, as in "Sodom or the Quintessence of Debauchery": "I would advise you, sir, to make a pass/Once more at Pockenello's loyal arse." It is perhaps as early as Shakespeare's day, if Nick Bottom transformed into a donkey in "A Midsummer Night's Dream" (1594) is the word-play some think it is.

I must to the barber's, mounsieur; for me thinks I am marvellous hairy about the face; and I am such a tender ass, if my hair do but tickle me, I must scratch. [Bottom]

By 1785 polite speakers were avoiding ass in the "donkey" sense. 

Meaning "woman regarded as a sexual object" is by early 1940s (piece of ass seems to be implied in 1930s Tijuana Bibles), but the image is older (compare buttock "a common strumpet," 1670s). To have (one's) head up (one's) ass "not know what one is doing" is attested by 1969. Colloquial (one's) ass "one's self, one's person" attested by 1958. To work (one's) ass off "work very much" is by 1946; to laugh (one's) ass off "laugh very much" is by 1972 (implied from 1965). The (stick it) up your ass oath is attested by 1953; apparent euphemisms suggest earlier use:

He snoighed up his nose as if th' cheese stunk, eyed me wi an air o contempt fro my shoon to my yed, un deawn ogen fro my yed to my shoon ; un then pushin th' brade un cheese into my hont ogen, he says "Take your vile bread and cheese and stick it up your coat sleeve, and be demmed to you. Do you think I want your paltry grub?" Un then, turnin on his heel, he hurried into th' perk. ["Bobby Shuttle un His Woife Sayroh's Visit to Manchester," 1857] 
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defecation (n.)

1640s, "purification of the mind or soul" (figurative); 1650s, "act or process of separating from lees or dregs, a cleansing from impurities," from Late Latin defecationem (nominative deficatio), noun of action from past-participle stem of Latin defaecare "cleanse from dregs, purify," from the phrase de faece "from dregs" (see de- + feces). Meaning "act of evacuating the bowels" is from 1830. An Old English word for "bowel movement" was arse-gang literally "arse-going."

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