Keith Devlin
For about R5-million you can buy the earliest known account of the idea that inspired Archimedes to run naked down the street shouting “Eureka”.
On October 29, Christie’s New York auction house will sell the manuscript that is the only source for Archimedes’s treatise, On the Method of Mechanical Theorems, and the only known copy of the original Greek text of his work, On Floating Bodies (the apocryphal Eureka story relates to this last work).
The manuscript also contains the texts of his works, On the Measurement of the Circle, On the Sphere and the Cylinder, On Spiral Lines and On the Equilibrium of Planes.
Christie’s expects the manuscript to sell for between $800 000 and $1 200 000 (R4,7- million to R7-million), making it one of the most expensive mathematics textbooks ever. The 174 parchment pages are an example of a palimpsest – a manuscript whose leaves have been written on twice (the word comes from the Greek term meaning “scraped again”).
When parchment was costly and hard to come by, it was common practice to take an existing manuscript, thought to be of little or no value, and wash away the first writing so that it could be used again. However, traces of the original ink often remained in the fibres of the parchment and it has been possible to read the earlier writing.
The original text of the Archi- medes manuscript, which had been copied in Constantinople in the mid-10th century, was replaced with Greek religious texts in the 12th century.
Adding insult to injury as far as Archimedes was concerned, the vellum leaves, originally 300mm by 200mm, were also folded in half to make a book half the size, with the lines of the second script running perpendicular to those of the first.
Archimedes, who lived and worked in Sicily in the 3rd century BC, is generally regarded as the greatest scientist of antiquity. His main discoveries were in physics, optics and astronomy. He was also an accomplished engineer.
Among the many inventions credited to him are a planetarium that demonstrated the movement of the stars and planets, the compound pulley, the endless screw, a device for raising water and a variety of military machines used to defend Syracuse against the Roman army between 214BC and 212BC, a siege in which Archimedes perished.
He studied geometrical figures such as spheres, cylinders, circles, spirals and conic sections. His method of proof by exhaustion and his use of infinitesimals, which he used to compute areas and volumes, anticipated the development of calculus almost 2 000 years before its invention by Sir Isaac Newton and Gottfried Leibniz.
The transmission of Archimedes’s work depends on just three manuscripts, two of which are now lost. In the 1920s, this last manuscript came into the possession of a French private collector, who kept it from scholars.
Until recently it had never been systematically examined by techniques such as ultraviolet light or high-resolution digital scanning.
Recent experiments have already shown that ultraviolet light brings up new details, and digital images can be manipulated to bring out the original script while suppressing the later text.