Etymology
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pyo- 

word-forming element used from mid-19c. and meaning "pus," from Greek puon "pus" (see pus).

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petro- (2)
word-forming element used from mid-20c. to mean "of or having to do with petroleum products," from petroleum.
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branchio- 
word-forming element used in scientific compounds since mid-18c., meaning "of or pertaining to "gills," from Latinized form of Greek brankhia "gills," plural of brankhion "fin."
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pyelo- 

before vowels pyel-, medical word-forming element used from mid-19c. in forming medical terms, from Greek pyelos "oblong trough, bathing-tub," a word of uncertain etymology, taken in modern scientific use for "pelvis."

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exo- 

word-forming element in words of Greek origin meaning "outer, outside, outer part," used from mid-19c. in scientific words (such as exoskeleton), from Greek exō (adv.) "outside," related to ex (prep.) "out of" (see ex-).

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dermat- 

word-forming element meaning "of or pertaining to skin," from Greek dermat-, from derma "(flayed) skin, leather," from PIE root *der- "to split, flay, peel," with derivatives referring to skin and leather. The shortened form derm- was used from mid-19c. but is considered incorrect.

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eo- 

word-forming element, used from mid-19c. (first in Eocene) in compound words formed by earth-scientists, and meaning "characterized by the earliest appearance of," from Greek ēōs "dawn, morning, daybreak," also the name of the goddess of the morning, from PIE root *aus- (1) "to shine," especially of the dawn. Piltdown Man, before exposed as a fraud, was known as Eoanthropus.

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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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demi- 

word-forming element meaning "half, half-sized, partial," used in English from mid-14c., especially in technical terms from French, from Old French demi "half" (12c.), from Late Latin dimedius, from Latin dimidius "half, one-half," which contains the elements dis- "apart" (see dis-) + medius "in the middle, between; from the middle," as a noun "the middle;" from PIE root *medhyo- "middle." Formerly also demy-, and in early use often written as a separate word.

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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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