Etymology
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peak (n.)

1520s, "pointed top, projecting summit," a variant of pike (n.4) "sharp point." Meaning "top of a mountain, a precipitous mountain with a more or less conical summit" is recorded by 1630s, though pike was used in this sense c. 1400. Figurative sense is 1784. Of beards, 1590s; of hats, 1650s. Meaning "point formed by hair on the forehead" is from 1833. As "the highest point" in any varying quantity, or the time when this occurs, by 1902. 

The Peak, the prominent hill in Derbyshire, England, is older than the word for "mountaintop;" compare Old English Peaclond, for the district, Pecsaetan, for the people who settled there, Peaces ærs for Peak Cavern. In this case it is sometimes said to be a reference to an elf-denizen Peac "Puck."

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peak (v.)

1570s, "to rise in a peak," from peak (n.). Figurative meaning "reach the highest point" is recorded by 1958. Related: peaked; peaking.

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off-peak (adj.)

"that is not at the maximum," 1906, originally in reference to electrical systems, from off- (adj.) (see off (prep.)) + peak (n.).

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peaked (adj.)

"sickly-looking; having an unhealthy, emaciated appearance," 1835, from past participle of the obsolete or dialectal verb peak "look sickly or thin, shrink, waste away" (1540s), which is perhaps from peak on the notion of "become pointed" through emaciation. Middle English had also a verb peken "to move dejectedly, slink" (mid-15c.), but the connection is uncertain. Related: Peakedness.

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ben (n.)

"mountain peak" in Celtic place names (especially of roughly pyramidal peaks standing alone), 1788, from Gaelic beinn "peak, summit, mountain," from Old Irish *benno- "peak, horn, conical point" (from PIE *bend- "projecting point").

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Machu Picchu 

15c.  Inca citadel high in the Andes Mountains of Peru, from Quechua (Inca) machu "old man" + pikchu "peak."

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Ural 

mountain range between Europe and Asia (the river is named for the mountains), of uncertain origin. Perhaps from Vogul urala "mountain peak" or from Tatar ural "boundary."

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piton (n.)

"strong iron spike with an eye at one end through which a rope can be passed," 1898, from French piton "hook; peak of a mountain; piton, eyebolt," in Old French "nail, hook," from Vulgar Latin root *pitt- "point, peak" [Barnhart].

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Corinth 

city in Greece, from Latin Corinthus, from Greek Korinthos, from Pelasgian *kar- "point, peak." The -nthos identifies it as being from the lost pre-IE language of Greece.

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pinnacle (n.)

c. 1300, "mountain top, sharp peak, promontory," from Old French pinacle "top, gable" (13c.) and directly from Late Latin pinnaculum "peak, pinnacle, gable," extended form (via diminutive suffix, but not necessarily implying smallness) of Latin pinna "peak, point," (see pin (n.)). Figurative use is attested from c. 1400. The meaning "pointed turret on the buttress or roof of a building" is from late 14c.

Its constructive object is to give greater weight to the member which it crowns, in order that this may better resist some lateral pressure. The application of the term is generally limited to an ornamental spire-shaped structure, standing on parapets, angles, and buttresses, and often adorned with rich and varied devices. [Century Dictionary]
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