Etymology
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Graeco- 
also Greco-, modern word-forming element, from Latin Graecus "Greek" (see Greek (n.)) on model of Anglo-, Franco-, etc.
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sur- (1)
word-forming element meaning "over, above, beyond, in addition," especially in words from Anglo-French and Old French, from Old French sour-, sor-, sur-, from Latin super "above, over," from PIE root *uper "over."
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pur- 

Middle English and Anglo-French perfective prefix, corresponding to Old French por-, pur- (Modern French pour), from Vulgar Latin *por-, a variant of Latin pro "before, for" (see pro-). This is the earliest form of the prefix in English, and it is retained in some words, but in others it has been corrected to Latinate pro-.

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counter- 

word-forming element used in English from c. 1300 and meaning "against, in opposition; in return; corresponding," from Anglo-French countre-, French contre-, from Latin contra "opposite, contrary to, against, in return," also used as a prefix (see contra (prep., adv.)). A doublet of contra-. In some cases it probably represents a purely English use of counter (adv.).

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non- 

a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].

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grand- 
a special use of grand (adj.) in genealogical compounds, originally with the sense of "a generation older than," first attested c. 1200, in Anglo-French graund dame "grandmother," also grandsire (late 13c.), from such use of Old French grand-, which perhaps is modeled on Latin avunculus magnus "great uncle." The partly-Englished grandmother, grandfather are from 15c. Other such words in European languages are formed with the adjectives for "old" or "best" (Danish bedstefar) or as diminutives or pet names (Greek pappos, Welsh taid). The French formation also is the model for such words in German and Dutch. Spanish abuelo is from Latin avus "grandfather" (from PIE *awo- "adult male relative other than the father;" see uncle), via Vulgar Latin *aviolus, a diminutive or adjective substitution for the noun.

The extension of the sense to corresponding relationships of descent, "a generation younger than" (grandson, granddaughter) is from Elizabethan times. The inherited PIE root, *nepot- "grandchild" (see nephew) has shifted to "nephew; niece" in English and other languages (Spanish nieto, nieta). Old English used suna sunu ("son's son"), dohtor sunu ("son's daughter").
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