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- 

a 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 in England 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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ad- 

word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."

Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).

In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but French refashioned its written forms on the Latin model in 14c., and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift.

Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France (where the vernacular sometimes resisted the pedantic), resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.

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