Etymology
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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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yester- 
Old English geostran "yesterday," from Proto-Germanic *gester- (source also of Old High German gestaron, German gestern "yesterday," Old Norse gær "tomorrow, yesterday," Gothic gistradagis "tomorrow"), originally "the other day" (reckoned from "today," either backward or forward), from PIE root *dhgh(y)es- "yesterday" (source also of Sanskrit hyah, Avestan zyo, Persian di, Greek khthes, Latin heri, Old Irish indhe, Welsh doe "yesterday;" Latin hesternus "of yesterday").
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ap- (2)

patronymic element in Welsh pedigrees and names, earlier map "son," cognate with Gaelic mac. Since 17c. merged into surnames and reduced to P- or B- (Ap Rhys = Price, Ap Evan = Bevan, Bowen = Ap Owen, etc.).

It is said that a Welshman who evidently was not willing to be surpassed in length of pedigree, when making out his genealogical tree, wrote near the middle of his long array of 'aps' — "about this time Adam was born." ["Origin and Significance of our Names," The Chautauquan, Oct. 1887-July 1888]
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inter- 
word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."

A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
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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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