Etymology
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up- 
prefix with various senses, from Old English up (adv.), corresponding to similar prefixes in other Germanic languages.
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ana- 

before vowels an-, word-forming element meaning: 1. "upward, up in place or time," 2. "back, backward, against," 3. "again, anew," from Greek ana (prep.) "up, on, upon; up to, toward; throughout; back, backwards; again, anew," from an extended form of PIE root *an- (1) "on, upon, above" (see on, which is the English cognate). In old medical prescriptions, ana by itself meant "an equal quantity of each."

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hypo- 
word-forming element meaning "under, beneath; less, less than" (in chemistry, indicating a lesser oxidation), from Greek hypo (prep. and adverb) "under, beneath; up from under; toward and under (i.e. into)," from PIE root *upo "under."
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hypso- 
word-forming element meaning "height," from Greek hypsos "height, top," from PIE *upso-, from root *upo "under," also "up from under," hence also "over" The Greek word is cognate with Sanskrit os "above, over," Old Church Slavonic vysoku "high."
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mixo- 

word-forming element of Greek origin meaning "mixed," from Greek mixo-, from mixis "a mixing, mingling, intercourse," from root of mignynai "to mix, mix up, mingle" (from PIE root *meik- "to mix"). As in mixolydian in reference to a half-Lydian mode in ancient Greek music.

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sub- 
word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c. 1800, as in subcontinent).
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ur- 
prefix meaning "original, earliest, primitive," from German ur- "out of, original," from Proto-Germanic *uz- "out," from PIE *ud- "up, out" (see out (adv.)) At first only in words borrowed from German (such as ursprache "hypothetical primitive language"); since mid-20c. a living prefix in English. Compare also Urschleim under protoplasm and Urquell under Pilsner.
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dys- 

word-forming element meaning "bad, ill; hard, difficult; abnormal, imperfect," from Greek dys-, inseparable prefix "destroying the good sense of a word or increasing its bad sense" [Liddell & Scott], hence "bad, hard, unlucky," from PIE root (and prefix) *dus- "bad, ill, evil" (source also of Sanskrit dus-, Old Persian duš- "ill," Old English to-, Old High German zur-, Gothic tuz- "un-"), a derivative of the root *deu- (1) "to lack, be wanting" (source of Greek dein "to lack, want").

Very productive in ancient Greek, where it could attach even to proper names (such as dysparis "unhappy Paris"); its entries take up nine columns in Liddell & Scott. Among the words formed from it were some English might covet: dysouristos "fatally favorable, driven by a too-favorable wind;" dysadelphos "unhappy in one's brothers;" dysagres "unlucky in fishing;" dysantiblepos "hard to look in the face."

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sh- 
sound represented in Old English by -sc- (fisc "fish"), which originally was pronounced "-sk-" but which by late Old English had softened to "-sh-." Modern English words with -sc- mostly are imports (generally Scandinavian).

The "sh" sound did not exist in Old French, therefore French scribes after the Norman conquest often represented it with -ssh- in medial and final positions, and sch- in initial positions (schape, schamful, schaft for shape, shameful, shaft). But the spelling -sh- has been standard since Caxton, probably as a worn-down form of Middle English -sch-.

In some East Anglian texts from 14c.-15c., x- is used (xal, xulde for shall, should), which would have given the language a very different look had it prevailed, but the London-based sh- ended up as the standard form. The same Germanic sound has become, by natural evolution, modern German and Dutch sch-, Scandinavian sk-.
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un- (1)

prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.

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