c. 1300, "a beating, whipping; the beating of a drum," from beat (v.). As "throb of the heart" from 1755. The 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). It was extended to journalism by 1875.
The 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]
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 form 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.
The meaning "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). The sense of "be too difficult for" intellectually or physically (by 1870) is behind the shrug-phrase beats me.
The meaning "strike cover to rouse or drive game" (c. 1400) is the source of beat around (or about) the bush (1570s), the metaphoric sense of which has shifted from "make preliminary motions" to "avoid, evade." The nautical sense of "make progress against the wind by means of alternate tacks" is from 1670s. Command beat it "go away" is recorded by 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."
1560s, "directed downward," from down (adv.). Sense of "depressed mentally" is attested from c. 1600. Slang sense of "aware, wide awake" is attested from 1812. Computer crash sense is from 1965. Down-and-out "completely without resources" is from 1889, American English, from situation of a beaten prizefighter.
"in a descending direction, from a higher to a lower place, degree, or condition," late Old English shortened form of Old English ofdune "downwards," originally of dune "off from (the) hill," from dune "from the hill," dative of dun "hill" (see down (n.2)). The "hill" word is general in Germanic, but this sense development is peculiar to English. As a preposition, "in a descending direction upon or along," from late 14c.
To be down on "express disapproval of" is by 1851. Down home is from 1828 as "in one's home region," as an adjective phrase meaning "unpretentious" by 1931, American English. Down the hatch as a toast is from 1931. Down to the wire is 1901, from horse-racing.
Down Under "Australia and New Zealand" attested from 1886; Down East "Maine" is from 1825; Down South "in the Southern states of the U.S." is attested by 1834. Down the road "in the future" is by 1964, U.S. colloquial. Down-to-earth "everyday, ordinary, realistic" is by 1932.
1710, "a downward movement," from down (adv.). Football sense of "an attempt to advance the ball" is by 1882.
"first feathers of a baby bird; soft covering of fowls under the feathers, the under-plumage of birds," used for stuffing pillows and feather-beds, mid-14c., from Old Norse dunn, which is of uncertain origin. Extended in Modern English to the soft hair of the human face and fine soft pubescence upon plants and some fruit.
"a hill of moderate elevation and more or less rounded outline," Old English dun "height, hill, moor," from Proto-Germanic *dunaz- (source also of Middle Dutch dunen "sandy hill," Dutch duin), "probably a pre-insular loan-word from Celtic" [Cambridge Dictionary of English Place-Names], in other words, borrowed at a very early period, before the Anglo-Saxon migration, perhaps from PIE root *dheue- "to close, finish, come full circle."
The more general meaning "elevated rolling grassland; high, rolling region not covered by forest" is from c. 1400. Specifically of certain natural pastureland districts of south and southeast England (the Downs) by mid-15c.
The non-English Germanic words tend to mean "dune, sand bank" (see dune), while the Celtic cognates tend to mean "hill, citadel" (compare Old Irish dun "hill, hill fort;" Welsh din "fortress, hill fort;" and second element in place names London, Verdun, etc.). German Düne, French dune, Italian, Spanish duna are said to be loan-words from Dutch.
1560s, "cause to go down," from down (adv.). Meaning "swallow hastily" is by 1860; football sense of "bring down (an opposing player) by tackling" is attested by 1887. Figurative sense of "defeat, get the better of" is by 1898. Related: Downed; downing.