Etymology
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mite (n.1)

"tiny animal, minute arachnid," Old English mite "minute, parasitic insect or arachnid," from Proto-Germanic *miton (source also of Middle Dutch mite, Dutch mijt, Old High German miza, Danish mide) meaning originally perhaps "the cutter," in reference to its bite, from Proto-Germanic *mait- (source also of Gothic maitan, Old High German meizen "to cut"), from PIE root *mai- (1) "to cut" (see maim). Compare ant. Or else its original sense is "something small," and it is from PIE root *mei- (2) "small," in reference to size.

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mite (n.2)

"little bit," mid-14c., from Middle Dutch or Middle Low German mite "tiny animal," from Proto-Germanic *miton-, from PIE root *mei- (2) "small," and thus probably identical with mite (n.1).

Also the name of a medieval Flemish copper coin of very small value, proverbial in English for "a very small unit of money," hence used since Wyclif to translate Latin minutum (Vulgate) in Mark xii.42, itself a translation of Greek lepton. French mite (14c.) is a loan-word from Dutch.

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mitrailleuse (n.)

kind of machine gun designed to discharge a concentrated rapid fire of small projectiles from a group of rifled barrels, 1870, from French mitrailleuse (19c.), from French mitraille "small missile," especially grape, canister, etc., fired at close quarters (14c.), originally "small coins," hence "old iron, scrap iron," then "grapeshot;" a diminutive of mite "a small coin" (see mite (n.2)). "For sense development it should be borne in mind that orig. guns used to be loaded with scrap iron" [Klein]. Especially of a type of gun introduced in the French army in 1868 and first used in the Franco-Prussian War.

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*mei- (2)

Proto-Indo-European root meaning "small."

It forms all or part of: administer; administration; comminute; diminish; meiosis; Menshevik; menu; metier; mince; minestrone; minim; minimum; minister; ministration; ministry; minor; minuend; minuet; minus; minuscule; minute; minutia; Miocene; mis- (2); mite (n.2) "little bit;" mystery (n.2) "handicraft, trade, art;" nimiety.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit miyate "diminishes, declines;" Greek meion "less, smaller;" Latin minus, minor "smaller," minuere "to diminish, reduce, lessen;" Old English minsian "to diminish;" Russian men'she "less."

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jigger (n.2)

"tiny mite or flea," a variant spelling of chigger (q.v.).

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vermin (n.)
c. 1300, "noxious animals," from Anglo-French and Old French vermin "moth, worm, mite," in plural "troublesome creatures" (12c.), from Vulgar Latin *verminum "vermin," possibly including bothersome insects, collective noun formed from Latin vermis "worm" (from PIE root *wer- (2) "to turn, bend"). Extended to "low, obnoxious people" by 1560s.
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itch (n.)
"irritating tingling sensation in the skin," also "skin inflammation caused by a burrowing mite," Old English gicce, from giccan (v.) "to itch" (see itch (v.)). Sense of "restless desire" is first attested 1530s; itching in this sense is from mid-14c.
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jigger (n.1)

"1.5-ounce shot glass," 1836, American English, in early use also of the drink itself, probably from jigger "illicit distillery" (1824), a word of unknown origin. Or else perhaps from jigger (n.2) "tiny mite or flea." As a name for various appliances the word is attested by 1726, from jig. In telegraphy it was a small transformer used for regulating and maintaining the difference of potential between terminals.

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eeny 
a word from a popular children's counting-out rhyme, recorded in the form eeny, meeny, miny, mo by 1888, when it was listed among 862 "Rhymes and doggerels for counting out" in Henry Carrington Bolton's book "The Counting-Out Rhymes of Children" [New York]. Bolton describes it as "the favorite with American children, actually reported from nearly every State in the Union." He notes similar forms in notes similar forms in German (Ene, meni, mino), Dutch, and and Platt-Deutsch (Ene, mine, mike, maken), and, from Cornwall, Eena, meena, moina, mite. The form eeny meeny mony mi is recorded in U.S. from 1873, and Hanna, mana, mona, mike is said to have been used in New York in 1815.
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miter (n.2)

in carpentry, "a joint at a 45 degree angle," 1670s, of uncertain origin, perhaps from mitre, via notion of joining of the two peaks of the folded cap. As a verb, to make or join with a miter-joint," from 1731. Related: Mitered. Miter-box is attested from 1670s.

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