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Many suggestions have been made about the origin of the dollar symbol $, one of the commonest being that it derives from the figure 8, representing the Spanish 'piece of eight'. However, it actually derives from a handwritten 'ps', an abbreviation for 'peso' in old Spanish-American books. The $ symbol first occurs in the 1770s, in manuscript documents of English-Americans who had business dealing with Spanish-Americans, and it starts to appear in print after 1800.
Here is another version of the theory, which covers your source and the one above:
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The Dollar Sign $ - Theories of its Origins
Since the symbol is more recent than the name, and the origins of the latter are well understood, one might expect that the origins of the sign would also be known for certain particularly when the origin of the British pound sign, £, which is far older, is well-established. However that is not the case with regard to the dollar.
Perhaps this is less surprising when there has been controversy over the origin of the sign for the European euro, €, a currency that did not come into existence until 1999. (It has been claimed that the euro sign was invented by Arthur Eisenmenger more than a quarter of a century before the currency was introduced). Nevertheless a number of theories about the origin of the dollar symbol have been proposed.
The United States Abbreviation Theory
One of the most popular theories is that the dollar sign is derived from the initials of the United States. If you superimpose a capital "U" on a capital "S" then drop the lower part of the "U", what you end up with is a version of the dollar symbol with two strokes. This theory was endorsed by the American libertarian philosopher and staunch defender of capitalism, Ayn Rand, in her novel Atlas Shrugged. Chapter 10 is entitled the Sign of the Dollar. Rand claimed the dollar sign was the symbol not only of the currency, but also the nation, a free economy, and a free mind.
The Peso Abbreviation and Piece of Eight Theories
However, a more widely accepted theory nowadays is that the sign owes its origins to the Spanish peso.
One version of this theory is that the standard abbreviation of "peso" was simply "P", but the plural form was a large "P" with a small "s" above it and to its right. This was simplified by retaining only the upward stroke of the "P" and superimposing the "S" upon it. Hence the symbol of the dollar.
See:
Dreyfuss, Henry Symbol source book : an authoritative guide to international graphic symbols. New York : McGraw-Hill, 1972.
If the peso abbreviation theory is the correct one why is the US dollar sign sometimes written with two vertical strokes? A possible explanation is that the best known Spanish Peso coin had two pillars engraved on the reverse side to symbolise the "Pillars of Hercules" at Gibraltar and the words "Plus Ultra" indicating that beyond the Pillars of Hercules there were other lands. That coin was called the Pillar Dollar in the British colonies in North America and the two pillars may have become the two strokes in the Dollar sign.