Etymology
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holm (n.)

"small island in a river; river meadow," late Old English, from Old Norse holmr "small island," especially in a river or bay, or cognate Old Danish hulm, from Proto-Germanic *hul-maz, from PIE root *kel- (2) "to be prominent; hill." Obsolete, but preserved in place names, where it has various senses derived from the basic one of "island:" "'raised ground in marsh, enclosure of marginal land, land in a river-bend, river meadow, promontory'" ["Cambridge Dictionary of English Place-Names"]. Cognate Old English holm (only attested in poetic language) meant "sea, ocean, wave."

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Bornholm 
island in the southern Baltic, from Old Danish Burgundarholm, from Burgundar "the Burgundians" (see Burgundy) + holm "island" (see holm). The Burgundians migrated from there to France 5c.
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Durham 

c. 1000, Dunholm "city on a hill," a merger of Old English dun "hill" (see down (n.2)) and Scandinavian holmr (see holm). The change from -n- to -r- is a result of Norman confusion (see Shrewsbury). As a breed of short-horned cattle, by 1810, so called from being bred there.

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Stockholm 
capital city of Sweden; it arose mid-13c. from a fishing village; the second element in the name is holm "island" (see holm); the first is either stäk "bay" or stock "stake, pole." Related: Stockholmer.

Stockholm Syndrome is from 1978, a psychologists' term; the name derives from the Aug. 23, 1973, violent armed robbery of Sveriges Kreditbank in Stockholm, after which four bank employees were held hostage in a vault for more than five days. The hostages developed a dramatic attachment to their abuser, and a fear of would-be rescuers, that they could not explain.
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*kel- (2)

Proto-Indo-European root meaning "to be prominent," also "hill."

It forms all or part of: colonel; colonnade; colophon; column; culminate; culmination; excel; excellence; excellent; excelsior; hill; holm.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kutam "top, skull;" Latin collis "hill," columna "projecting object," cellere "raise;" Greek kolōnos "hill," kolophōn "summit;" Lithuanian kalnas "mountain," kalnelis "hill," kelti "raise;" Old English hyll "hill," Old Norse hallr "stone," Gothic hallus "rock."

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ilex (n.)
"evergreen oak," late 14c., from Latin ilex "holm-oak, great scarlet oak," perhaps from an extinct non-Indo-European language.
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Holmesian (adj.)
1911, in reference to fictional detective Sherlock Holmes, who debuted in 1887. Sherlock-Holmes-ian is from 1902.
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holmium (n.)

rare earth element, named by French chemist Lecoq de Boisbaudran in 1886, from holmia "holmium oxide," name of an earth identified and named in Modern Latin by the earth's discoverer, Swedish chemist Per Teodor Cleve, in 1879 from Holmia, Latin name of Stockholm. With metallic element ending -ium. Holmia was isolated from erbia, the Scandinavian earth which also yielded thulium, scandium, and ytterbium.

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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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