ass (n.1) Look up ass at Dictionary.com
beast of burden, Old English assa (Old Northumbrian assal, assald) "he-ass," probably from Old Celtic *as(s)in "donkey," which (with German esel, Gothic asilus, Lithuanian asilas, Old Church Slavonic osl) ultimately is from Latin asinus, which is probably of Middle Eastern origin (compare Sumerian ansu).
For al schal deie and al schal passe, Als wel a Leoun as an asse. [John Gower, "Confessio Amantis," 1393]
Since ancient Greek times, in fables and parables, the animal typified clumsiness and stupidity (hence asshead, late 15c., etc.). To make an ass of oneself is from 1580s. 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.
ass (n.2) Look up ass at Dictionary.com
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- attested in several other words (such as burst/bust, curse/cuss, horse/hoss, barse/bass). Indirect evidence of the change from arse to ass can be traced to 1785 (in euphemistic avoidance of ass "donkey" by polite speakers) and perhaps to Shakespeare, if Nick Bottom transformed into a donkey in "A Midsummer Night's Dream" (1594) is the word-play some think it is. Meaning "woman regarded as a sexual object" is from 1942. Colloquial (one's) ass "one's self, one's person" attested by 1958.