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century BC) tells us the story in his treatise De Architectura. (See Vitruvius 1st century BC.) He says that Archimedes immersed in water a piece of gold and a piece of silver, both having the same weight as the wreath. He thus found that the wreath displaced more water than the gold but less than the silver. It is easy to show that from the different volumes of water displaced one can calculate the ratio of the weights of the gold and the silver in the wreath. Therefore, contrary to some popular accounts, Archimedes did not need to use the laws of hydrostatics to solve the problem of the wreath.

has been cited by: In a letter from Thomas Jefferson to M. Correa de Serra in 1814, he wrote: “The good opinion of mankind, like the lever of Archimedes, with the given fulcrum, moves the world.” Lord Byron mentions Archimedes’ statement in Don Juan. JFK used the phrase in a campaign speech, cited in The New York Times, on November 3, 1960. Mark Twain used it in an article entitled “Archimedes” in 1887.

Archimedes used an assembly of mirrors: A group of MIT students attempted to reproduce the burning of a ship with mirrors in October 2005. Some of them also repeated the experiment for the TV show Myth Busters. The results were somewhat inconclusive in that while the students were able to achieve a burning area that was self-sustaining, they did not produce a large ignition. A similar experiment performed in Germany in September 2002 did manage to ignite the sail of a ship by using 500 mirrors. A discussion of the burning mirrors can be found on a website by Michael Lahanas.

According to some accounts: Those precise words from Archimedes are mentioned in the Chiliades by Tzetzes; see Dijksterhuis 1957. Plutarch says simply that Archimedes refused to follow the soldier to Marcellus until he had solved the problem in which he was absorbed (Plutarch ca. 75 AD).

As the British mathematician and philosopher: Whitehead 1911.

Archimedes’ opus covers an astonishing range: A superb book on Archimedes’ work is The Works of Archimedes (Heath 1897). Other excellent expositions can be found in Dijksterhuis 1957 and Hawking 2005.

“There are some, king Gelon”: Heath 1897.

The story of this discovery: For a wonderful description of the history of the Palimpsest Project, see Netz and Noel 2007.

Sometime in the tenth century: Probably in 975 AD.

The scribe Ioannes Myronas: Netz and Noel 2007.

I was fortunate enough to meet: Will Noel, who is the director of the project, arranged for a meeting with William Christens-Barry, Roger Easton, and Keith Knox. This team designed the narrow-band imaging system and invented the algorithm used to reveal some of the text. Image-processing techniques have also been developed by researchers Anna Tonazzini, Luigi Bedini, and Emanuele Salerno.

“I will send you the proofs”: Dijksterhuis 1957.

his anticipation of integral and differential calculus: For a beautiful description of the history and meaning of calculus see Berlinski 1996.

The Greek mathematician Geminus: Heath 1921.

he requested it be engraved: Plutarch ca. 75 AD.

Here is Cicero’s rather moving description: Cicero 1st century BC. For a scholarly analysis of Cicero’s text in terms of structure, rhetoric, and symbolic function, see Jaeger 2002.

Galileo Galilei was born in Pisa: An authoritative modern biography is S. Drake’s Galileo at Work (Drake 1978). A more popular account is J. Reston’s Galileo: A Life (Reston 1994). See also Van Helden and Burr 1995. The complete works of Galileo appear (in Italian) in Favaro 1890–1909.

“Those who read his works”: In The Little Balance, Galilei 1586.

“wood moves more swiftly”: Galileo 1589–92 (Galilei 1600a and Galilei 1600b). C. B. Schmitt suggests (Schmitt 1969, after D. A. Maklich) that Galileo’s statement may be the result of the hand holding a lead ball being more tired than the hand holding a wooden ball, and consequently that the release of the wooden ball is more prompt. An excellent presentation of Galileo’s correct ideas on falling bodies can be found in Frova and Marenzana 1998 (McManus