ass (n.1)

solid ungulate quadruped beast of burden of the horse kind, but smaller and with long ears and a short mane, native to southwest Asia, Old English assa (Old Northumbrian assal, assald) "he-ass." The English word is cognate with Old Saxon esil, Dutch ezel, Old High German esil, German Esel, Gothic asilus, and, beyond Germanic, Lithuanian asilas, Old Church Slavonic osl, Russian oselŭ, etc. All probably are ultimately from Latin asinus. De Vaan says the form of asinus suggests it was a loan-word into Latin, and adds, "Most IE words for 'ass' are loanwords."

Together with Greek onos it is conjectured to be from a language of Asia Minor (compare Sumerian ansu). The initial vowel of the English word might be by influence of Celtic forms (Irish and Gaelic asal), from Old Celtic *as(s)in "donkey." In Romanic tongues the Latin word has become Italian asino, Spanish asno, Old French asne, French âne.

In familiar use, the name ass is now to a great extent superseded by donkey (in Scotland cuddie); but ass is always used in the language of Scripture, Natural History, proverb, and fable; also, in ordinary use, in Ireland. [OED]

Sure-footed and patient in domestication, since ancient Greek times, in fables and parables, the animal has typified clumsiness and stupidity (hence ass-head, late 15c., etc.). To make an ass of oneself is from "A Midsummer Night's Dream" (1590). Asses' Bridge (c. 1780), from Latin Pons Asinorum, is fifth proposition of first book of Euclid's "Elements." In Middle English, someone uncomprehending or unappreciative would be lik an asse that listeth on a harpe. In 15c., an ass man was a donkey-driver.

For al schal deie and al schal passe, Als wel a Leoun as an asse. [John Gower, "Confessio Amantis," 1393]

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).