Etymology
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domain (n.)

c. 1600, "territory over which dominion is exerted," from French domaine "domain, estate," from Medieval Latin domanium "domain, estate," from Latin dominium "property, dominion," from dominus "lord, master, owner," from domus "house" (from PIE root *dem- "house, household"). A later borrowing from French of the word which became demesne.

Sense of "dominion, province of action" is from 1727. Meaning "range or limits of any department of knowledge or sphere of action" is from 1764. Internet domain name is attested by 1985. Via the notion of "ownership of land" comes legal eminent domain "ultimate or supreme lordship over all property in the state" is attested from 1738.

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Anno Domini 

"in the year of the Christian era," 1570s, Latin, literally "in the year of (our) Lord," from ablative of annus "year" (see annual (adj.)) + Late Latin Domini, genitive of Dominus "the Lord" (see domain). Also see A.D.

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demesne (n.)

c. 1300, demeine, demeyne (modern spelling by late 15c.), "power; dominion; control, possession," senses now obsolete, from Anglo-French demesne, demeine, Old French demaine "land held for a lord's own use," from Latin dominicus "belonging to a master," from dominus "lord, master," from domus "house" (from PIE root *dem- "house, household").

Re-spelled by Anglo-French legal scribes under influence of Old French mesnie "household" (and the concept of a demesne as "land attached to a mansion") and their fondness for inserting -s- before -n-. Essentially the same word as domain.

Meaning "a manor house and near or adjacent land," kept and occupied by the lord and his family, is from late 14c., hence "any landed estate" (late 14c.). Related: Demesnial.

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*dem- 

Proto-Indo-European root meaning "house, household." It represents the usual Indo-European word for "house" (Italian, Spanish casa are from Latin casa "cottage, hut;" Germanic *hus is of obscure origin).

It forms all or part of: Anno Domini; belladonna; condominium; dame; damsel; dan "title of address to members of religious orders;" danger; dangerous; demesne; despot; Dom Perignon; domain; dome; domestic; domesticate; domicile; dominate; domination; dominion; domino; don (n.) "Spanish, Italian, and Portuguese title of respect;" Donna; dungeon; ma'am; madam; madame; mademoiselle; madonna; major-domo; predominant; predominate; timber; toft.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit damah "house;" Avestan demana- "house;" Greek domos "house," despotēs "master, lord;" Latin domus "house," dominus "master of a household;" Armenian tanu-ter "house-lord;" Old Church Slavonic domu, Russian dom "house;" Lithuanian dimstis "enclosed court, property;" Old Norse topt "homestead."

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barony (n.)

c. 1300, "domain of a baron," from Old French baronie "assembly of barons, qualities of a baron," from Late Latin *baronia, from baro (see baron).

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rascality (n.)

1570s, "low and vulgar people collectively;" 1590s, "character or actions of a rascal;" see rascal + -ity. Middle English had rascaldry "common soldiers" (mid-15c.); Carlyle (1837) used rascaldom "the sphere or domain of rascals."

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pyroxene (n.)

type of mineral, 1800; from Greek pyr "fire" (see pyro-) + xenos "stranger" (see xeno-). According to OED, so named in 1796 by Abbé Haüy, French mineralogist, "because he thought it 'a stranger in the domain of fire' or alien to igneous rocks." Related: Pyroxenic.

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-machy 

word-forming element meaning "battle, war, contest, fighting, warfare," from Latinized form of Greek -makhia, from makhē "a battle, fight," related to makhesthai "to fight." Beekes suspects it is from an isolated root, perhaps Pre-Greek: "In the domain of fighting and battle, old inherited expressions can hardly be expected."

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Domesday book 

1178 in Anglo-Latin, the popular name of Great Inquisition or Survey (1086), a digest in Anglo-French of a survey of England undertaken at the order of William the Conqueror to inventory his new domain, from Middle English domes, genitive of dom "day of judgment" (see doom (n.)). "The booke ... to be called Domesday, bicause (as Mathew Parise saith) it spared no man, but iudged all men indifferently." [William Lambarde, "A Perambulation of Kent," 1570]

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county (n.)

mid-14c., "a shire, a definite division of a country or state for political and administrative purposes," from Anglo-French counte, from Late Latin comitatus "jurisdiction of a count," from Latin comes (see count (n.1)). It replaced Old English scir "shire."

From late 14c. as "the domain of a count or earl." County palatine, one distinguished by special privileges (Lancaster, Chester, Durham) is from mid-15c. County seat "seat of the government of a county" is by 1848, American English.

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