Etymology
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rug (n.)

1550s, "a coarse, heavy, woolen fabric," a word of Scandinavian origin; compare Norwegian dialectal rugga "coarse coverlet," from Old Norse rogg "shaggy tuft," from Proto-Germanic *rawwa-. Perhaps it is related to rag (n.1) and rough (adj.), and compare rugged.

The original meaning is obsolete. The sense evolved or expanded to "thick coverlet or lap-robe, heavy woolen wrap" used for various purposes (1590s), then "mat for the floor" (by 1808). The meaning "toupee" is theater slang attested by 1940.

To cut a rug "dance" is slang attested by 1942 (rug-cutter "expert dancer" is recorded by 1938). To sweep or brush something under the rug in the figurative sense of "conceal in hopes it won't be noticed or remembered" is by 1954. Figurative expression pull the rug out from under (someone) "suddenly deprive of important support" is from 1936, American English. Earlier in same sense was cut the grass under (one's) feet (1580s).

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rugrat (n.)

also rug-rat, "baby, small child," by 1968; see rug + rat (n.).

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rugged (adj.)

c. 1300, "having a rough, hairy, or shaggy surface" (originally of animals), a word probably of Scandinavian origin: compare Old Norse rogg "shaggy tuft" (see rug). "The precise relationship to ragged is not quite clear, but the stem is no doubt ultimately the same" [OED]. In Middle English ruggedy (late 14c.) also was used.

Of ground, "broken, stony," by 1650s. Of made things, "strongly constructed, able to withstand rough use," by 1921. By 1620s, especially of persons or their qualities, as "unsoftened by refinement or cultivation," thence "of a rough but strong or sturdy character" (by 1827). The specific meaning "vigorous, strong, robust, healthy," is American English, attested by 1847.

We were challenged with a peace-time choice between the American system of rugged individualism and a European philosophy of diametrically opposed doctrines — doctrines of paternalism and state socialism. [Herbert Hoover, speech in New York, Oct. 22, 1928]

Hoover said the phrase was not his own, and it is attested from 1897, though not in a patriotic context. Related: Ruggedly; ruggedness.

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rag (n.1)

"torn or worn scrap of cloth," early 14c., probably from a Scandinavian source (compare Old Norse rögg "shaggy tuft, rough hair," earlier raggw-; Old Danish rag; see rug), or else a back-formation from ragged. It also may represent an unrecorded Old English cognate of Old Norse rögg. In any case, from Proto-Germanic *rawwa-, from PIE root *reue- (2) "to smash, knock down, tear up, uproot" (see rough (adj.)).

Also in Middle English "a hard, rough piece of stone" (late 13c.). As an insulting term for "newspaper, magazine" it dates from 1734; slang for "tampon, sanitary napkin" is attested from 1930s (on the rag "menstruating" is from 1948). Rags "tattered clothing" is from mid-14c.; in the jocular sense of "personal clothing" it is attested by 1855 (singular), American English. Rags-to-riches as a description of a tale of a rise from poverty to wealth is attested by 1896. Rag-picker is from 1860; rag-shop, one selling old clothes, is from 1829.

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carpet (n.)

late 13c., "coarse cloth;" mid-14c., "tablecloth, bedspread;" from Old French carpite "heavy decorated cloth, a carpet" (Modern French carpette), from Medieval Latin or Old Italian carpita "thick woolen cloth," probably from Latin carpere "to card, pluck" and so called because it was made from unraveled, shredded, "plucked" fabric; from PIE root *kerp- "to gather, pluck, harvest." From 15c. in reference to floor coverings, which since 18c. has been the main sense. The smaller sort is a rug.

Formerly the carpet (usually in a single piece, like the Persian carpet) was also used (as it still is in the East) for covering beds, couches, tables, etc., and in hangings. [Century Dictionary]

From 16c.-19c., by association with luxury, ladies' boudoirs, and drawing rooms, it was used as an adjective, often with a tinge of contempt, in reference to men (as in carpet-knight, 1570s, one who has seen no military service in the field; carpet-monger, 1590s, a lover of ease and pleasure, i.e. one more at home on a carpet).

On the carpet "summoned for reprimand" is 1900, U.S. colloquial (but compare carpet (v.) "call (someone) to be reprimanded," 1823, British servants' slang). This may have merged with older on the carpet "up for consideration" (1726) literally "on the tablecloth," with the word's older sense, hence "a subject for investigation." To sweep or push something under the carpet in the figurative sense is first recorded 1953.

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regolith (n.)

in geology, "unconsolidated rocky material covering bedrock," 1897, from Latinized form of Greek rhēgos "rug, blanket" (from PIE *reg- (3) "to dye;" see raga) + lithos "stone" (see litho-).

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hooked (adj.)
Old English hoced, "shaped like a hook, crooked, curved;" past-participle adjective from hook (v.). From mid-14c. as "having hooks;" 1610s as "caught on a hook;" 1925 as "addicted," originally in reference to narcotics. hooked rug is recorded from 1880.
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raga (n.)

in Indian music, a melodic framework for improvised melodies, 1788, from Sanskrit raga-s "harmony, melody, mode in music," literally "color, mood," related to rajyati "it is dyed," from PIE *reg- (3) "to dye" (source also of Greek rhegos "blanket, rug").

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hearth (n.)

Old English heorð "hearth, fireplace, part of a floor on which a fire is made," also in transferred use "house, home, fireside," from Proto-Germanic *hertha- "burning place" (source also of Old Saxon and Old Frisian herth, Middle Dutch hert, Dutch haard, German Herd "floor, ground, fireplace"), from PIE *kerta-, from root *ker- (3) "heat, fire." Hearth-rug is from 1824. Hearth-stone is from early 14c.

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snug (adj.)
1590s, "compact, trim" (of a ship), especially "protected from the weather," perhaps from a Scandinavian source such as Old Norse snoggr "short-haired," Old Swedish snygg, Old Danish snøg "neat, tidy," perhaps from PIE *kes- (1) "to scratch" (see xyster). Sense of "in a state of ease or comfort" first recorded 1620s. Meaning "fit closely" is first found 1838. Expression snug as a bug in a rug attested by 1769; earlier snug as a bee in a box (1706).
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