Etymology
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ball and chain (n.)

a type of prisoner's restraint, 1818; used figuratively by 1883 of foolish, wasteful habits; as "one's wife," 1920.

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chain (v.)

late 14c., "to bar with a chain; to put (someone) in chains," also "to link things together," from chain (n.). Related: Chained; chaining.

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chain (n.)

c. 1300, "connected series of links of metal or other material," from Old French chaeine "chain" (12c., Modern French chane), from Latin catena "chain" (source also of Spanish cadena, Italian catena), which is of unknown origin, perhaps from a PIE root *kat- "to twist, twine" (source also of Latin cassis "hunting net, snare").

As a type of ornament worn about the neck, from late 14c. As a linear measure ("a chain's length") from 1660s. From 1590s as "any series of things linked together." The meaning "series of stores controlled by one owner or firm" is American English, 1846. The figurative use "that which binds or confines" is from c. 1600.

Chain-reaction is from 1916 in physics; the specific nuclear physics sense is from 1938. Chain-mail armor is from 1795, from mail (n.2). Before that, mail alone sufficed. Chain letter is recorded from 1892; at first usually to raise money; decried from the start as a nuisance.

Nine out of every ten givers are reluctant and unwilling, and are coerced into giving through the awful fear of "breaking the chain," so that the spirit of charity is woefully absent. [St. Nicholas magazine, vol. xxvi, April 1899] 

Chain of command is from 1915. Chain-lightning, visible as jagged or broken lines, is from 1834. Chain-smoker, one who smokes one after another, lighting the next from the stump of the last, is attested from 1885, originally of Bismarck (who smoked cigars), thus probably a loan-translation of German Kettenraucher. Chain-smoking (n.) is from 1895.

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ball (n.1)

"round object, compact spherical body," also "a ball used in a game," c. 1200, probably from an unrecorded Old English *beal, *beall (evidenced by the diminutive bealluc "testicle"), or from cognate Old Norse bollr "ball," from Proto-Germanic *balluz (source also of Dutch bal, Flemish bal, Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, swell."

The meaning "testicle" is from early 14c. (compare ballocks). Ball of the foot is from mid-14c. The meaning "rounded missile used in warfare" is from late 14c.

The meaning "a game played with a ball" is from mid-14c. The baseball sense of "pitch that does not cross the plate within the strike zone" is by 1889, probably short for high ball, low ball, etc.

Ball-point pen is by 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is attested from c. 1900. Many phrases are from sports: To have the ball "hold the advantage" is from c. 1400. To be on the ball is from 1912; to keep (one's) eye on the ball in the figurative sense is by 1907, probably ultimately on golf, where it was oft-repeated advice. Figurative use of ball in (someone's) court is by 1956, from tennis.

The head must necessarily be steady, for it is most important that you should keep your eye fixedly on the ball from the moment that the club-head is lifted from the ground until the ball is actually struck. "Keep your eye on the ball," should be your companion text to "Slow back." [Horace G. Hutchinson, "Hints on the Game of Golf," 1886]
Once a meeting is over, someone will be expected to do something. Make sure it is someone else. This is known as keeping the ball in their court. [Shepherd Mead, "How to Get Rich in TV Without Really Trying," 1956]
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ball (n.2)

"dancing party, social assembly for dancing," 1630s, from French, from Old French baller "to dance," from Late Latin ballare "to dance," from Greek ballizein "to dance, jump about," literally "to throw one's body" (ancient Greek dancing being highly athletic), from PIE root *gwele- "to throw, reach." The extended meaning "very enjoyable time" is American English slang from 1945, perhaps 1930s in African-American vernacular.

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ball (v.)

1650s, "make into a ball," from ball (n.1). Intransitive sense of "become like a ball, form a compact cluster" is from 1713; that of "to copulate" is first recorded 1940s in jazz slang, either from the noun sense of "testicle" or "enjoyable time" (from ball (n.2)). Related: Balled; balling.

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chain-saw (n.)

also chain saw, chainsaw; 1818 as a surgical apparatus (for amputations) consisting of a chain, the links of which have serated edges; 1835 in the saw mill sense, "power-driven saw consisting of a chain with cutting points attached to the links;" from chain (n.) + saw (n.).

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ball-boy (n.)

"boy who retrieves balls that go out of play during a game or match," 1896, in tennis, from ball (n.1) + boy. By 1955 in baseball. Ball-girl in tennis is by 1953.

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Minie ball (n.)

kind of conical rifle bullet with a hollow base, 1853, named for its inventor, French army officer Claude-Étienne Minié (1814-1879), who designed it 1847-8.

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stool-ball (n.)

outdoor game similar to cricket, in 16c. and 17c. generally played by women alone, late 15c., from stool (n.) + ball (n.1). "The 'stool' was the wicket ... perhaps it was originally an ordinary stool" [OED].

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