Etymology
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noli me tangere 
late 14c., "type of facial ulcer, lupus," Latin, literally "touch me not," from noli, imperative of nolle "to be unwilling" + me (see me) + tangere "to touch" (from PIE root *tag- "to touch, handle"). Used over the years of various persons or things that must not be touched, especially "picture of Jesus as he appeared to Mary Magdalene" (1670s, see John xx.17) and "plant of the genus Impatiens" (1560s, so called because the ripe seed pods burst when touched).
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tit for tat 
1550s, possibly an alteration of tip for tap "blow for blow," from tip (v.3) "tap" + tap "touch lightly." Perhaps influenced by tit (n.2).
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dim sum (n.)

"Chinese cuisine prepared as bite-sized portions served in small steamer baskets or on small plates," 1948, from Cantonese tim sam (Chinese dianxin) "appetizer," said to mean literally "touch the heart." Ayto ("Diner's Dictionary") gives the elements as tim "dot" + sam "heart."

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king's evil (n.)
"scrofula," late 14c.; it translates Medieval Latin regius morbus. The name came about because the kings of England and France claimed and were reputed to be able to cure it by their touch. In England, the custom dates from Edward the Confessor and was continued through the Stuarts (Charles II touched 90,798 sufferers) but was ended by the Hanoverians (1714).
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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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