Etymology
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hyperbole (n.)

"obvious exaggeration in rhetoric," early 15c., from Latin hyperbole, from Greek hyperbole "exaggeration, extravagance," literally "a throwing beyond," from hyper- "beyond" (see hyper-) + bole "a throwing, a casting, the stroke of a missile, bolt, beam," from bol-, nominative stem of ballein "to throw" (from PIE root *gwele- "to throw, reach"). Rhetorical sense is found in Aristotle and Isocrates. Greek had a verb, hyperballein, "to throw over or beyond."

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hyperbola (n.)

curve formed by the intersection of a plane with a double cone, 1660s, from Latinized form of Greek hyperbole "extravagance," literally "a throwing beyond (others);" see hyperbole, which in English is the same word in its Greek garb. Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.

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hyperbolic (adj.)

1640s in rhetoric (iperbolical is from early 15c.), from Latin hyperbolic, from Greek hyperbolikos "extravagant," from hyperbole "extravagance," literally "a throwing beyond" (see hyperbole). Geometric sense is from 1670s, from hyperbola + -ic. Related: Hyperbolically.

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hype (n.)

"excessive or misleading publicity or advertising," 1967, American English (the verb is attested from 1937), probably in part a back-formation of hyperbole, but also from underworld slang verb hype "to swindle by overcharging or short-changing" (1926), itself a back-formation from hyper "short-change con man" (1914), from the prefix hyper- meaning "over, to excess."

Also possibly influenced by drug addicts' slang hype, shortening of hypodermic needle (1913). Related: Hyped; hyping. In early 18c., hyp "morbid depression of the spirits" was colloquial for hypochondria (usually as the hyp or the hyps).

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*gwele- 

*gwelə-, also *gwel-, Proto-Indo-European root meaning "to throw, reach," with extended sense "to pierce."

It forms all or part of: anabolic; arbalest; astrobleme; ball (n.2) "dancing party;" ballad; ballet; ballista; ballistic; ballistics; belemnite; catabolism; devil; diabolical; discobolus; emblem; embolism; hyperbola; hyperbole; kill (v.); metabolism; palaver; parable; parabola; parley; parliament; parlor; parol; parole; problem; quell; quail (v.) "lose heart, shrink, cower;" symbol.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit apa-gurya "swinging," balbaliti "whirls, twirls;" Greek ballein "to throw, to throw so as to hit," also in a looser sense, "to put, place, lay," bole "a throw, beam, ray," belemnon "dart, javelin," belone "needle," ballizein "to dance;" Armenian kelem "I torture;" Old Church Slavonic zali "pain;" Lithuanian galas "end," gėla "agony," gelti "to sting."

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literally (adv.)

1530s, "in a literal sense, according to the exact meaning of the word or words used," from literal + -ly (2). Since late 17c. it has been used in metaphors, hyperbole, etc., to indicate what follows must be taken in the strongest admissible sense. But this is irreconcilable with the word's etymological sense and has led to this much-lamented modern use of it.

We have come to such a pass with this emphasizer that where the truth would require us to insert with a strong expression 'not literally, of course, but in a manner of speaking', we do not hesitate to insert the very word we ought to be at pains to repudiate; ... such false coin makes honest traffic in words impossible. [Fowler, 1924]
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