The Method of Archimedes
1. The Archimedes palimpsest
Ilan Vardi at the IHES has an excellent page on The Legacy of Archimedes. The sale of the palimpsest was covered - Archimedes Unbound - in the American Scientist. The Walters Art Gallery in Baltimore exhibited the palimpsest last year, and produced the explanatory web-page Eureka!.
On October 29,1998 a manuscript was sold at Christie's, in New York, for $2,000,000. The manuscript, bound as a book, seems at first glance to be a religious text: a Euchologion, written in Constantinople sometime between the 12th and the 14th century. But there is an exceedingly valuable subtext. The monastic scribe who made this book used second-hand parchment, scrubbing out the original text and inking in the new. A book like this is called a palimpsest. In this case the original text was a 10th century copy of several works by Archimedes (died in 212 BC), one of the greatest mathematicians of all time.
The new book, sacred and precious in its own right, was treasured over the years in various monasteries. When the mathematical subtext was discovered by J. L. Heiberg in 1906, it created a scholarly sensation: one of the works had only been known to the modern world in translation, and another, the ``Method,'' had never been seen at all in modern times and and had been considered lost.
In this column we will see what was so particular about the ``Method'' and we will follow Archimedes in using this method to work out one of his most famous discoveries, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder. Archimedes was so proud of this achievement that he wanted his tombstone to bear only the picture of the nested volumes and the equation relating their sizes; Cicero reports having seen such a monument when he visited Sicily in 75 BC.
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