Etymology
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billy (n.)
"club," 1848, American English, originally burglars' slang for "crowbar;" meaning "policeman's club" first recorded 1856, probably from nickname of William, applied to various objects (compare jack, jimmy, jenny). But compare French bille "a short, stout stick" (see billet (n.1)). Billy-goat as a familiar name for a male goat is from 1826.
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heebie-jeebies (n.)
1923, said to have been coined by U.S. cartoonist Billy De Beck (1890-1942), creator of "Barney Google."
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horsefeathers (n.)
"nonsense," 1927, said to have been coined by U.S. cartoonist Billy De Beck; perhaps a variant of horseshit "nonsense," though the latter is attested in print only from 1940s.
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hillbilly (n.)

"southern Appalachian person," by 1892, from hill (n.) + Billy/Billie, popular or pet form of William. In reference to a type of U.S. folk music, first attested 1924.

I would hate to see some old railroad man come here and take my job, and then, I don't think it is right to hire some Hill Billy and give him the same right as I just because he was hired the same time I was. [The Railroad Trainmen's Journal, vol. ix, July 1892]
In short, a Hill-Billie is a free and untrammelled white citizen of Alabama, who lives in the hills, has no means to speak of, dresses as he can, talks as he pleases, drinks whiskey when he gets it, and fires of his revolver as the fancy takes him. [New York Journal, April 23, 1900]

In Scott's collection of Border ballads, billie is a frequent term of address or intimacy, "comrade, companion, a brother in arms," "a term expressive of affection and familiarity" also "a brother; a wooer of a woman," and generally "a young man" [Jamieson, 2nd edition]. It is said to be a variant of bully (n.) in its old sense of  "sweetheart," also "fine fellow."

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nanny (n.)

"children's nurse," 1795, from the widespread child's word for "female adult other than mother" (compare Greek nanna "aunt," and see nana). The word also is a nickname form of the fem. proper name Ann, which probably is the sense in nanny-goat "female goat" (1706, compare billy-goat). Nanny-house "brothel" is slang from c. 1700. Nanny state, in reference to overintrusive government policies is attested by 1987, the term is associated with British political leader Margaret Thatcher, who criticized the tendency. Nannyism in reference to actions or policies considered unduly protective is by 1959; also compare the verb.

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patsy (n.)

"fall guy, victim of a deception," by 1903, of uncertain origin, possibly an alteration of Italian pazzo "madman" (see patch (n.2)), or south Italian dialectal paccio "fool." Another theory traces it to Patsy Bolivar, character created by Billy B. Van in an 1890s vaudeville skit who was blamed whenever anything went wrong.

"Poor Rogers," Vincent said, still smiling, "he is always the 'Patsy Bolivar' of the school."
"Yes," Frank answered, "if there are any mistakes to be made or trouble to fall into, Rogers seems to be always the victim."
["Anthony Yorke," "A College Boy," 1899]
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distingue (adj.)

"having an air of distinction," 1813 (in Byron), from French distingué, literally "distinguished," past participle of distinguer "to separate between, keep separate, mark off" (see distinguish).

The girls I knew had sad and sullen gray faces
With distingué traces
That used to be there — You could see where they'd been washed away
By too many through the day
Twelve o'clock tales.
["Lush Life," Billy Strayhorn, age 17]

There was a verb distingue (Middle English distinguen, mid-14c., "to divide or subdivide, discern, perceive"), from Old French distinguer, but it has not survived.

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eccentric (n.)

early 15c., "eccentric circle or orbit," originally a term in Ptolemaic astronomy, "circle or orbit not having the Earth precisely at its center," from French eccentrique and directly from Medieval Latin eccentricus (noun and adjective), from Greek ekkentros "out of the center" (as opposed to concentric), from ek "out" (see ex-) + kentron "center" (see center (n.)). Meaning "odd or whimsical person" is attested by 1817 (S.W. Ryley, "The Itinerant, or Memoirs of an Actor").

June 4 [1800].—Died in the streets in Newcastle, William Barron, an eccentric, well known for many years by the name of Billy Pea-pudding. [John Sykes, "Local Records, or Historical Register of Remarkable Events which have Occurred Exclusively in the Counties of Durham and Northumberland, Town and County of Newcastle Upon Tyne, and Berwick Upon Tweed," Newcastle, 1824]
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goat (n.)

Old English gat "she-goat," from Proto-Germanic *gaito (source also of Old Saxon get, Old Norse geit, Danish gjed, Middle Dutch gheet, Dutch geit, Old High German geiz, German Geiß, Gothic gaits "goat"), from PIE *ghaid-o- "young goat," also forming words for "to play" (source also of Latin hædus "kid").

They are sprightly, capricious, and wanton, and their strong odor (technically called hircine) is proverbial. [Century Dictionary]

The word for "male goat" in Old English was bucca or gatbucca (see buck (n.)) until late 1300s shift to he-goat, she-goat (Nanny goat is 18c., billy goat 19c.). Meaning "licentious man" is attested from 1670s (hence goat-milker, name of a bird formerly believed to suck the milk from goats at night, but also old slang for "a prostitute," also "the female pudendum"). To get (someone's) goat is by 1908, American English, the source of many fanciful explanation stories; perhaps from French prendre sa chèvre "take one's source of milk," or more likely it is "to steal a goat mascot" from a racehorse, warship, fire company, military unit, etc.

... to become separated from your goat is a thing no soldierman is willing to contemplate. ["Letitia, Nursery Corps, U.S.A.," in American Magazine, vol. lxiv, June 1907]
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hat trick (n.)

in the sports sense, 1879, originally in cricket, "taking three wickets on three consecutive deliveries;" extended to other sports c. 1909, especially ice hockey ("In an earlier contest we had handed Army a 6-2 defeat at West Point as Billy Sloane performed hockey's spectacular 'hat trick' by scoring three goals" ["Princeton Alumni Weekly," Feb. 10, 1941]). So called allegedly because it entitled the bowler to receive a hat from his club commemorating the feat (or entitled him to pass the hat for a cash collection), but the term probably has been influenced by the image of a conjurer pulling objects from his hat (an act attested by 1876). The term was used earlier for a different sort of magic trick:

Place a glass of liquor on the table, put a hat over it, and say, "I will engage to drink every drop of that liquor, and yet I'll not touch the hat." You then get under the table; and after giving three knocks, you make a noise with your mouth, as if you were swallowing the liquor. Then, getting from under the table, say "Now, gentlemen, be pleased to look." Some one, eager to see if you have drunk the liquor, will raise the hat; when you instantly take the glass and swallow the contents, saying, "Gentlemen I have fulfilled my promise: you are all witnesses that I did not touch the hat." ["Wit and Wisdom," London, 1860]
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