Etymology
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hill (n.)

Old English hyll "hill," from Proto-Germanic *hulni- (source also of Middle Dutch hille, Low German hull "hill," Old Norse hallr "stone," Gothic hallus "rock," Old Norse holmr "islet in a bay," Old English holm "rising land, island"), from PIE root *kel- (2) "to be prominent; hill." Formerly including mountains.

In Great Britain heights under 2,000 feet are generally called hills; 'mountain' being confined to the greater elevations of the Lake District, of North Wales, and of the Scottish Highlands; but, in India, ranges of 5,000 and even 10,000 feet are commonly called 'hills,' in contrast with the Himalaya Mountains, many peaks of which rise beyond 20,000 feet. [OED]
The term mountain is very loosely used. It commonly means any unusual elevation. In New England and central New York, elevations of from one to two thousand feet are called hills, but on the plains of Texas, a hill of a few hundred feet is called a mountain. [Ralph S. Tarr, "Elementary Geology," Macmillan, 1903]
Despite the differences in defining mountain systems, Penck (1896), Supan (1911) and Obst (1914) agreed that the distinction between hills, mountains, and mountain systems according to areal extent or height is not a suitable classification. ["Geographic Information Science and Mountain Geomorphology," 2004]

 Figurative phrase over the hill "past one's prime" is recorded by 1950. Expression old as the hills is recorded by 1819, perhaps echoing Job xv.7. Earlier form old as the hills and the valleys is attested by 1808:

And this is no "new morality." It is morality as old as the hills and the valleys. It is a morality which must be adopted; or, we must confess that there are certain political evils greater than that of seeing one's country conquered. [Cobbett's Weekly Political Register, Feb. 6, 1808]

Cobbett's also had, on April 11, 1818:

However, thus it always is: "those whom God intends to destroy, he first makes foolish," which is a saying as old as the hills between Everly and Marlborough.
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hill (v.)
"cover with soil in the form of a hill, 1570s; "form into a hill," 1580s, from hill (n.). Related: Hilled; hilling.
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ant-hill (n.)
also anthill, "mound of dirt formed by ants in building their nest," late 13c., from ant + hill (n.).
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foot-hill (n.)

also foot-hill, "a hill that leads up to a mountain, a distinct lower part of a mountain," 1850, American English, from foot (n.) + hill (n.).

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sand-hill (n.)

"dune," Old English sondhyllas (plural); see sand (n.) + hill (n.). For sand-hiller "poor white of Georgia or South Carolina" (by 1848) see cracker (n.2). Earlier it meant "blackguard, user of foul language" (by 1813) in the dialect of Durham and Yorkshire, according to contemporary sources probably from Sandhill in Newcastle.

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hilly (adj.)
late 14c., from hill (n.) + -y (2).
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uphill (adj.)
1610s, from up + hill (n.). As an adverb from c. 1600. Grose's "Dictionary of the Vulgar Tongue" (1785) has "Uphills, false dice that run high."
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dunghill (n.)

"a heap of dung," early 14c., from dung (n.) + hill (n.).

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