Etymology
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brachy- 
word-forming element meaning "short," from Latinized combining form of Greek brakhys "short," from PIE root *mregh-u- "short."
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octa- 
before vowels oct-, word-forming element meaning "eight," from Greek okta-, okt-, from PIE *okto(u) "eight" (see eight). The variant form octo- often appears in words taken from Latin, but the Greek form is said to be the more common in English.
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strepto- 
word-forming element used in science to mean "twisted," from Latinized combining form of Greek streptos "twisted, easy to bend, pliant," verbal adjective of strephein "to turn, twist," from PIE root *streb(h)- "to wind, turn."
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brachio- 
before a vowel, brachi-, word-forming element meaning "arm, of the upper arm, pertaining to the upper arm and," from Greek brakhion "arm," perhaps originally "upper arm," literally "shorter," from brakhys "short" (from PIE root *mregh-u- "short"), in contrast to the longer forearm.
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gluco- 

before vowels, gluc-, word-forming element used since c. 1880s, a later form of glyco-, from Greek glykys "sweet," figuratively "delightful; dear; simple, silly," from *glku-, a dissimilation in Greek from PIE root *dlk-u- "sweet" (source also of Latin dulcis). De Vaan writes that "It is likely that we are dealing with a common borrowing from an unknown source." Now usually with reference to glucose.

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vice- 

word-forming element meaning "deputy, assistant, substitute," also "instead of, in place of," 15c., from Latin vice "in place of," ablative of vicis "a change, a turn, interchange alternation" (from PIE root *weik- (2) "to bend, to wind"). In Middle English sometimes borrowed in Old French form vis-, vi-.

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gu- 
because g- followed by some vowels in English usually has a "soft" pronunciation, a silent -u- sometimes was inserted between the g- and the vowel in Middle English to signal hardness, especially in words from French; but this was not done with many Scandinavian words where hard "g" precedes a vowel (gear, get, give, etc.). Germanic -w- generally became -gu- in words borrowed into Romance languages, but Old North French preserved the Frankish -w-, and English sometimes borrowed both forms, hence guarantee/warranty, guard/ward, etc.
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presby- 

word-forming element meaning "old," from Greek presby-, combining form of presbys "elderly, aged," as a noun, "elder, old man," which is of uncertain and much debated origin and phonetic development (some Doric forms have -g- in place of -b-). The first element is likely *pres- "before, in front" (from PIE root *per- (1) "forward," hence "in front of, before, first"). Perhaps the whole originally meant "one who leads the cattle," from the root of bous "cow." Watkins, however, has it from PIE *pres-gwu- "going before," with second element from root *gw-u- "going," a suffixed form of root *gwa- "to come."

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re- 

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a "Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state; "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]
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