Etymology
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hard hat (n.)

also hardhat, hard-hat, late 14c., "helmet," from hard (adj.) + hat (n.). From 1935 as "derby hat;" meaning "safety helmet" is from 1953; used figuratively for "construction worker" from 1970.

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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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beat up (v.)

"thrash, strike repeatedly," c. 1900 (v.), from beat (v.) + up (adv.). Earlier it meant "summon (recruits, etc.) by the beating of a drum" (1690s). Beat-up as an adjectival phrase meaning "worn-out, used hard" dates to 1946.

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dura mater (n.)

"tough outer membrane surrounding the brain and the spinal cord," c. 1400, from Medieval Latin dura mater cerebri, literally "hard mother of the brain," a loan-translation of Arabic umm al-dimagh as-safiqa, literally "thick mother of the brain." "In Arabic, the words 'father,' 'mother,' and 'son' are often used to denote relationships between things" [Klein].

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hot dog (n.)

also hotdog, "sausage on a split roll," c. 1890, American English, from hot (adj.) + dog (n.). Many early references are in college student publications; later popularized, but probably not coined, by cartoonist T.A. "Tad" Dorgan (1877-1929). It is said in early explanations to echo a suspicion (occasionally justified) that sausages contained dog meat.

Meaning "someone particularly skilled or excellent" (with overtones of showing off) is from 1896. Connection between the two senses, if any, is unclear. Hot dog! as an exclamation of approval was in use by 1906.

hot-dog, n. 1. One very proficient in certain things. 2. A hot sausage. 3. A hard student. 4. A conceited person. ["College Words and Phrases," in Dialect Notes, 1900]

Related: Hot-dogger; hot-dogging.

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