Etymology
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deutero- 

before vowels deuter-, word-forming element meaning "second," from Late Latin deutero-, from Greek deuteros "next, second," a word of uncertain origin. According to some sources from duo "two" (from PIE root *dwo- "two"), but according to Watkins the ground sense is "missing" and the Greek word is from PIE *deu-tero-, suffixed form of *deu- (1) "to lack, be wanting." But Beekes doubts even this. 

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prae- 
word-forming element meaning "before," from Latin prae (adv.) "before," from PIE *prai-, *prei-, from root *per- (1) "forward," hence "in front of, before" (also see pre-). Reduced to pre- in Medieval Latin. According to OED the full form prae- in Modern English appears "usually only in words that are still regarded as Latin, ... or that are terms of classical antiquity ...."
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-emia 

word-forming element in pathology meaning "condition of the blood," Modern Latin combining form of Greek haima (genitive haimatos) "blood," a word of no established etymology (replacing the usual IE word, represented in Greek by ear; possibly from uncertain PIE root *sei- "to drip" (compare Old High German seim "virgin honey," Welsh hufen), but according to Beekes this proposal "cannot explain the Greek vocalism."

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to- 
particle expressing separation, putting asunder, from West Germanic *ti- (source also of Old Frisian ti-, Old High German zi-, German zer-), from Proto-Germanic *tiz-, cognate with Latin-derived dis-. According to OED, some 125 compound verbs with this element are recorded in Old English; their number declined rapidly in Middle English and disappeared by c. 1500 except as conscious archaisms (such as to-shiver "break to pieces;" all to-brast).
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nano- 

introduced 1947 (at 14th conference of the Union Internationale de Chimie) as a prefix for units of one thousand-millionth part (now "one-billionth"), from Greek nanos "a dwarf." According to Watkins, this is originally "little old man," from nannos "uncle," masc. of nanna "aunt" (see nana), but Beekes calls it "An onomatopoeic word of unknown origin." Earlier nano- was used as a prefix to mean "dwarf, dwarfish," and still it is used in a non-scientific sense of "very small."

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ex- 
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
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