Etymology
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beat (n.)

c. 1300, "a beating, whipping; the beating of a drum," from beat (v.). As "throb of the heart" from 1755. Meaning "regular route travelled by someone" is attested from 1731, also "a track made by animals" (1736), from the sense of the "beat" of the feet on the ground (late Old English), or perhaps that in beat the bushes to flush game (c. 1400), or beat the bounds (1560s). Extended to journalism by 1875. Musical sense is by 1842, perhaps from the hand motion of the conductor and the notion of "beating the time":

It is usual, in beating the time of a piece of music, to mark or signalize the commencement of every measure by a downward movement or beat of the hand, or of any other article that may be used for the purpose .... ["Godfrey Weber's General Music Teacher," 1842]

Earlier in music it meant a sort of grace note:

BEAT, in music, a transient grace note, struck immediately before the note it is intended to ornament. The beat always lies half a note beneath its principal, and should be heard so closely upon it, that they may almost seem to be struck together. ["The British Encyclopedia," London, 1809]
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beat (v.)

Old English beatan "inflict blows on, strike repeatedly, thrash" (class VII strong verb; past tense beot, past participle beaten), from Proto-Germanic *bautan (source also of Old Norse bauta, Old High German bozan "to beat"), from PIE root *bhau- "to strike."

Past tense beat is from c. 1500, probably not from Old English but a shortening of Middle English beted. Of the heart, c. 1200, from notion of it striking against the breast.

Meaning "to overcome in a contest" is from 1610s (hence the sense of "legally avoid, escape" in beat the charges, etc., attested from c. 1920 in underworld slang). Meaning "be too difficult for" intellectually or physically (by 1870) is behind the shrug-phrase beats me.

Meaning "strike cover to rouse or drive game" (c. 1400) is source of beat around (or about) the bush (1570s), the metaphoric sense of which has shifted from "make preliminary motions" to "avoid, evade." Nautical sense of "make progress against the wind by means of alternate tacks" is from 1670s. Command beat it "go away" first recorded 1906 (though "action of feet upon the ground" was a sense of Old English betan); it is attested in 1903 as newsboy slang for "travel without paying by riding on the outside of a train."

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beat (adj.)
"defeated, overcome by effort," c. 1400, from past tense of beat (v.). Meaning "tired, exhausted by exertion," is by 1905, American English. For beat generation see beatnik.
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out-and-out 

c. 1300 as an adverbial phrase, "completely, thoroughly, to the utmost degree," from out (adv.). Adjective usage is attested by 1813.

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out- 

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]
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out (n.)

late 15c., "egress," from out (adj). From 1620s, "a being out" (of something), from out (adv.). From 1764 in politics as "the party which is out of office." From 1860 in the baseball sense "act of getting an opposing player out of active play." From 1919 as "means of escape; alibi."

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out (v.)

Old English utian "expel, put out," from the source of out (adv.). It has been used in many specific senses over the years; the meaning "disclose to public view, reveal, make known" is by mid-14c.

Eufrosyne preyde Þat god schulde not outen hire to nowiht. ["Legendary of St. Euphrosyne," c. 1350]

Meaning "to expose as a closet homosexual" is first by 1990 (as an adjective meaning "openly avowing one's homosexuality" it dates from 1970s; see closet). To come out "declare oneself publicly as homosexual" is from 1968 and probably short for come out of the closet. Related: Outed; outing. Compare outen.

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out (adj.)

late Old English, "outer," from out (adv.). From mid-13c. as "that is or lies on the outside, exterior." Of a light or candle, "extinguished, no longer burning," c. 1300.  Sense of "no longer secret" is by 1713. Sense in baseball (1860) was earlier in cricket (1746). Meaning "unconscious" is attested from 1898, originally in boxing from the notion of "defeated ('out') by failing to rise within a 10-count." To be out on one's feet is from 1952. From 1966 as "unfashionable, not stylish, popular, or modern."

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out (adv.)

expressing motion or direction from within or from a central point, also removal from proper place or position, Old English ut "out, without, outside," from Proto-Germanic *ūt- (Old Norse, Old Frisian, Old Saxon, Gothic ut, Middle Dutch uut, Dutch uit, Old High German uz, German aus), from PIE root *uidh- "up, out, up away, on high" (source also of Sanskrit ut "up, out," uttarah "higher, upper, later, northern;" Avestan uz- "up, out," Old Irish ud- "out," Latin usque "all the way to, continuously, without interruption," Greek hysteros "the latter," Russian vy- "out").

Sense of "to a full end, completely, to a conclusion or finish" is from c. 1300. Meaning "so as to be no longer burning or alight; into darkness" is from c. 1400. Of position or situation, "beyond the bounds of, not within," early 15c. Meaning "into public notice" is from 1540s; that of "away from one's place of residence," c. 1600. The political sense of "not in office, removed or ejected from a position" is from c. 1600. Meaning "come into sight, become visible" (of stars, etc.) is by 1610s. In radio communication, a word indicating that the speaker has finished speaking, by 1950.

As a preposition, "out of; from, away from; outside of, beyond; except; without, lacking;" mid-13c., from the adverb.

Meaning "from harmonious relations, into quarreling" (as in to fall out) is from 1520s. Meaning "from one's normal state of mind" (as in put out) is from 1580s; out to lunch "insane" is student slang from 1955. Adjectival phrase out-of-the-way "remote, secluded" is attested from late 15c. Out-of-towner "one not from a certain place" is from 1911. Out of this world "excellent" is from 1938; out of sight "excellent, superior" is from 1891. To (verb) it out "bring to a finish" is from 1580s. Expression from here on out "henceforward" is by 1942. Out upon, expressing abhorrence or reproach, is from early 15c.

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beat off (v.)
"drive (something) away by violent blows," 1640s, from beat (v.) + off (adv.). Meaning "masturbate" is recorded by 1960s.
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