Etymology
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bill (v.2)
"to stroke beaks," as doves do, hence, of lovers, "caress fondly," 1590s, from bill (n.2)). Paired with coo at least since 1764; Century Dictionary [1902] defines bill and coo (by 1768) as "to kiss and caress and talk nonsense, as lovers." Related: Billed; billing.
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bill (n.2)
"bird's beak," Old English bill "bill, bird's beak," related to bill, a poetic word for a kind of sword (especially one with a hooked blade), from Proto-Germanic *bili-, a word for cutting or chopping weapons (see bill (n.3)). Used also in Middle English of beak-like projections of land (such as Portland Bill).
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dollar (n.)

"monetary unit or standard of value in the U.S. and Canada," 1550s, daler, originally in English the name of a large, silver coin of varying value in the German states, from Low German daler, from German taler (1530s, later thaler), abbreviation of Joachimstaler, literally "(gulden) of Joachimstal," coin minted 1519 from silver from mine opened 1516 near Sankt Joachimsthal, town in Erzgebirge Mountains in northwest Bohemia. German Tal is cognate with English dale. The spelling had been modified to dollar by 1600.

The thaler was from 17c. the more-or-less standardized coin of northern Germany (as opposed to the southern gulden). It also served as a currency unit in Denmark and Sweden (and later was a unit of the German monetary union of 1857-73 equal to three marks).

English colonists in America used the word dollar from 1580s in reference to Spanish peso or "piece of eight," also a large silver coin of about the same fineness as the thaler. Due to extensive trade with the Spanish Indies and the proximity of Spanish colonies along the Gulf Coast, the Spanish dollar probably was the coin most familiar in the American colonies and the closest thing to a standard in all of them.

When the Revolution came, it had the added advantage of not being British. It was used in the government's records of public debt and expenditures, and the Continental Congress in 1786 adopted dollar as a unit when it set up the modern U.S. currency system, which was based on the suggestion of Gouverneur Morris (1782) as modified by Thomas Jefferson. None were circulated until 1794.

When William M. Evarts was Secretary of State he accompanied Lord Coleridge on an excursion to Mount Vernon. Coleridge remarked that he had heard it said that Washington, standing on the lawn, could throw a dollar clear across the Potomac. Mr. Evarts explained that a dollar would go further in those days than now. [Walsh]

Phrase dollars to doughnuts "an assured thing, a certainty" (such that one would bet a dollar against a doughnut on it) is attested by 1884; dollar diplomacy "financial imperialism, foreign policy based on financial and commercial interests" is from 1910.

The dollar sign ($) is said to derive from the image of the Pillars of Hercules, stamped with a scroll, on the Spanish piece of eight. However, according to the Bureau of Engraving and Printing of the U.S. Department of the Treasury:

[T]he most widely accepted explanation is that the symbol is the result of evolution, independently in different places, of the Mexican or Spanish "P's" for pesos, or piastres, or pieces of eight. The theory, derived from a study of old manuscripts, is that the "S" gradually came to be written over the "P," developing a close equivalent of the "$" mark. It was widely used before the adoption of the United States dollar in 1785.
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bill (v.1)
"to send someone a bill of charge," 1864, from bill (n.1). Related: Billed; billing.
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bill (n.3)
ancient weapon, Old English bill "sword (especially one with a hooked blade), chopping tool," from Proto-Germanic *bili-, a word for cutting or chopping weapons (compare Old Saxon bil "sword," Middle Dutch bile, Dutch bijl, Old High German bihal, German Beil, Old Norse bilda "hatchet"), possibly from PIE root *bheie- "to cut, to strike" (source also of Armenian bir "cudgel," Greek phitos "block of wood," Old Church Slavonic biti "to strike," Old Irish biail "ax").
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bill (n.1)
"written statement," late 14c., "formal document; formal plea or charge (in a court of law); personal letter," from Anglo-French bille, Anglo-Latin billa "a writing, a list, a seal," from Medieval Latin bulla "decree, seal, sealed document," in classical Latin "bubble, boss, stud, amulet for the neck" (hence "seal"); see bull (n.2).

Sense of "written statement detailing articles sold or services rendered by one person to another" is from c. 1400; that of "order addressed to one person to pay another" is from 1570s. Meaning "paper intended to give public notice of something, exhibited in a public place" is from late 15c. Sense of "paper money, bank-note" is from 1660s. Meaning "draft of a proposed statute presented to a legislature" is from 1510s.
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sand-dollar (n.)

type of flat sea-urchin, 1884, so called for its shape; see sand (n.) + dollar (n.). Cake-urchin (1853) and sand cake were other old names for it.

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play-bill (n.)

also playbill, 1670s, "placard displayed as an advertisement of a play," giving more or less information about it, from play (n.) in the theatrical sense + bill (n.1).

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greenback (n.)
"U.S. dollar bill," 1862, so called from the time of their introduction, from green (adj.) + back (n.); bank paper money printed in green ink had been called this since 1778 (as opposed to redbacks, etc.).
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sawbuck (n.)

"ten-dollar bill or note," also saw-buck, American English slang, 1850 (implied in double-sawbuck), so called from the resemblance of X (the Roman numeral 10, prominent in the design of many mid-19c. U.S. bank notes) to the ends of a sawhorse. Sawbuck in the sense of "sawhorse" is attested by 1837 (see saw (n.1) + buck (n.3)).

At the foot of the flag staff four saplings were erected, somewhat after the form of the two ends of a "saw-buck," and not very unlike the characters that denote the value of a ten dollar bill .... [Maumee Express, Maumee City, Ohio, Oct. 21, 1837]
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