Etymology
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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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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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summer (n.2)
"horizontal bearing beam," late 13c., from Anglo-French sumer, Old French somier "main beam," originally "pack horse," from Vulgar Latin *saumarius, from Late Latin sagmarius "pack horse," from sagma "packsaddle" (see sumpter).
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summer (v.)
"to pass the summer," mid-15c., from summer (n.1). Related: Summered; summering.
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summer (n.1)

"hot season of the year," Old English sumor "summer," from Proto-Germanic *sumra- (source also of Old Saxon, Old Norse, Old High German sumar, Old Frisian sumur, Middle Dutch somer, Dutch zomer, German Sommer), from PIE root *sm- "summer" (source also of Sanskrit sama "season, half-year," Avestan hama "in summer," Armenian amarn "summer," Old Irish sam, Old Welsh ham, Welsh haf "summer").

As an adjective from c. 1300. Summer camp as an institution for youth is attested from 1886; summer resort is from 1823; summer school first recorded 1810; theatrical summer stock is attested from 1941 (see stock (n.2)). Old Norse sumarsdag, first day of summer, was the Thursday that fell between April 9 and 15.

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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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Anglo-Indian (adj.)
1814, "pertaining to the English who settled in India," from Anglo- + Indian.
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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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gossamer (n.)
c. 1300, "filmy substance (actually spider threads) found in fields of stubble in late fall," apparently from gos "goose" (see goose (n.)) + sumer "summer" (see summer (n.)). Not found in Old English. The reference might be to a fancied resemblance of the silk to goose down, or more likely it is shifted from an original sense of "late fall; Indian summer" because geese are in season then. Compare Swedish equivalent sommartrad "summer thread," Dutch zommerdraden (plural). The German equivalent mädchensommer (literally "girls' summer") also has a sense of "Indian summer," and there was a Scottish go-summer "period of summer-like weather in late autumn" (1640s, folk-etymologized as if from go). Thus the English word originally might have referred to a warm spell in autumn before being transferred to a phenomenon especially noticeable then. Compare obsolete Scottish go-summer "period of summer-like weather in late autumn." Meaning "anything light or flimsy" is from c. 1400; as a type of gauze used for veils, 1837. The adjective sense "filmy, light as gossamer" is attested from 1802.
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summerize (v.)
1797, "to spend the summer," from summer (n.1) + -ize. From 1935 as "to prepare (something) for summer." Related: Summerized; summerizing.
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