Etymology
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retro- 

word-forming element of Latin origin meaning "backwards; behind," from Latin retro (prep.) "backward, back, behind," usually in reference to place or position, rarely of time, "formerly, in the past," probably originally the ablative form of *reteros, based on re- "back" (see re-).

L. retro stands to re- as intro, "in, within"; to in, "in," and as citro, "hither," stands to cis, "on this side." [Klein]

Common in combinations in post-classical Latin (the classical equivalent was post-). Active in English as a word-forming element from mid-20c.

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cata- 

word-forming element meaning "down, downward," but also "through, on, against, concerning," etc., from Latinized form of Greek kata-, before vowels kat-, from kata "down, downward, down from, down to," from PIE *kmt- "down, with, along" (source also of Hittite kattan (adv.) "below, underneath," katta "along with"). Occasionally in Greek it had senses of "against" (catapult) or "wrongly" (catachresis), also "along, through, over, across, concerning." Also sometimes used as an intensive or with a sense of completion of action (catalogue). Very active in ancient Greek, this prefix is found in English mostly in words borrowed through Latin after c. 1500.

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pre- 

word-forming element meaning "before," from Old French pre- and Medieval Latin pre-, both from Latin prae (adverb and preposition) "before in time or place," from PIE *peri- (source also of Oscan prai, Umbrian pre, Sanskrit pare "thereupon," Greek parai "at," Gaulish are- "at, before," Lithuanian prie "at," Old Church Slavonic pri "at," Gothic faura, Old English fore "before"), extended form of root *per- (1) "forward," hence "beyond, in front of, before."

The Latin word was active in forming verbs. Also see prae-. Sometimes in Middle English muddled with words in pro- or per-.

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de- 

active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.

As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.

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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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semi- 

word-forming element of Latin origin meaning "half," also loosely, "part, partly; partial, almost; imperfect; twice," from Latin semi- "half" (before vowels often sem-, sometimes further reduced to se- before m-), from PIE *semi- "half" (source also of Sanskrit sami "half," Greek hēmi- "half," Old English sam-, Gothic sami- "half").

The Old English cognate, sam-, was used in such compounds as samhal "in poor health, weakly," literally "half-whole;" samsoden "half-cooked" ('half-sodden'), figuratively "stupid" (compare half-baked); samcucu "half-dead," etymologically "half-alive" (see quick (adj.)); and the lingering survivor, sandblind "dim-sighted" (q.v.).

The Latin element was common in formations from Late Latin, as in semi-gravis "half-drunk," semi-hora "half hour," semi-mortuus "half-dead," semi-nudus "half-naked," semi-vir "half-man, hermaphrodite."

The Latin-derived form in English has been active in forming native words since 15c. Semi-bousi "half-drunk" ('semi-boozy'), now obsolete, was among the earliest (c. 1400). As a noun, semi has variously been short for semi-detached house (by 1912), semi-trailer (by 1942), semi-final (by 1942).

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