Etymology
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American (n.)

1570s, originally "one of the aboriginal peoples discovered in the Western Hemisphere by Europeans," from Modern Latin Americanus, from America (q.v.). The original sense is now Native Americans; the sense of "resident of North America of European (originally British) descent" is from 1765.

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Indian (adj., n.)

"inhabit of India or South Asia; pertaining to India," c. 1300 (noun and adjective), from Late Latin indianus, from India (see India). Applied to the aboriginal native inhabitants of the Americas from at least 1553 as a noun (1610s as an adjective), reflecting Spanish and Portuguese use, on the mistaken notion that America was the eastern end of Asia (it was also used occasionally 18c.-19c. of inhabitants of the Philippines and indigenous peoples of Australia and New Zealand). The Old English adjective was Indisc, and Indish (adj.) was common in 16c.

Red Indian, to distinguish the native Americans from inhabitants of India, is first attested 1831 in British English (Carlyle) but was not commonly used in North America. Hugh Rawson ("Wicked Words") writes that "Indian is unusual among ethnic terms for not having much pejorative value until comparatively recently." A few phrases, most of them U.S., impugn honesty or intelligence, such as Indian gift:

An Indian gift is a proverbial expression, signifying a present for which an equivalent return is expected. [Thomas Hutchinson, "History of Massachusetts Bay," 1765]

Hence Indian giver "one who gives a gift and then asks for it back" (1848). Also compare Indian summer. Indian elephant is from c. 1600; Indian corn is from 1620s; to walk Indian file is from 1758. Indian club is from 1824 as a weapon, 1825 as exercise equipment (clubs were noted in Lewis & Clark, etc., as characteristic weapons of native warriors in the American West). Indian-head (adj.) in reference to U.S. copper pennies with a portrait of an Indian in profile, from 1862.

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American (adj.)

1590s, "pertaining to the Western Hemisphere and its aboriginal inhabitants," from Modern Latin Americanus, from America (q.v.); the sense of "pertaining to the residents of North America of European (originally British) descent" is recorded by 1640s; later "pertaining to the United States." French Américain, Spanish and Italian Americano, German Amerikanisch. Fem. form Americaness attested from 1838. The American beauty rose so called from 1886. American English as a sub-language attested from 1806; Amerenglish is from 1974.

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Indian Ocean 

first attested 1515 in Modern Latin (Oceanus Orientalis Indicus), named for India, which projects into it; earlier it was the Eastern Ocean, as opposed to the Western Ocean (Atlantic) before the Pacific was surmised.

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Indian summer (n.)

"spell of warm, dry, hazy weather after the first frost" (happening anywhere from mid-September to nearly December, according to location), 1774, North American English (also used in eastern Canada), perhaps so called because it was first noted in regions then still inhabited by Indians, in the upper Mississippi valley west of the Appalachians, or because the Indians first described it to the Europeans. No evidence connects it with the color of fall leaves, or to a season of renewed Indian attacks on settlements due to renewed warm weather (a widespread explanation dating at least to the 1820s).

It is the American version of British All-Hallows summer, French été de la Saint-Martin (feast day Nov. 11), etc. Also colloquial was St. Luke's summer (or little summer), period of warm weather occurring about St. Luke's day (Oct. 18). An older and simpler name for it was autumn-spring (1630s).

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Nimzo-Indian (adj.)

type of defensive opening in chess, 1935, in reference to Aron Nimzowitsch (1886-1935), Latvian-born Jewish chess genius who popularized a variation of the Indian defense (1884) attributed to Indian chess player Moheschunder Bannerjee.

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un-American (adj.)

"not characteristic of American principles or methods, foreign to U.S. customs," 1818, from un- (1) "not" + American (adj.).

Everything is un-American that tends either to government by a plutocracy or government by a mob. [Theodore Roosevelt, 1917]
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Anglo-American (n.)

"English person who has settled in North America," 1738, from Anglo- + American. Originally often in contrast to German immigrants; later (1830s) in contrast to French-Canadians, Louisiana French, Spanish Mexicans. As an adjective from 1797, "pertaining to the English who have settled in America;" the meaning "pertaining to both England and the United States" is from 1812.

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American dream 

coined 1931 by James Truslow Adams (1878-1949), U.S. writer and popular historian (unrelated to the Massachusetts Adamses), in "Epic of America."

[The American Dream is] that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position. [Adams]

Others have used the term as they will.

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Anti-American (adj.)

also antiamerican, "opposed to the United States of America or its people or interests," 1773, in reference to British parliamentary policies, from anti- + American. As a noun by 1788. Related: Anti-Americanism "opposition to what is distinctly American" (1844).

The term "anti-American" is a loose one, and loosely employed. My own working definition of it, admittedly a slack one also, is that a person is anti-American if he or she is consistently contemptuous of American culture and furthermore supports any opponent of U.S. policy, whoever this may be. [Christopher Hitchens, review of "The Life of Graham Greene, Vol. II," The Atlantic, March 2005]
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