Archimedes redux

In 1998, an anonymous buyer paid $2 million for a battered and stained prayer book of a medieval priest from a Christie's auction. The buyer was not indulging in a fit of eccentric extravagance. Faintly visible under the prayer verses lay excerpts of a treatise worth more than a king's ransom to the world of science. It was a copy of "Codex C," by Archimedes of Syracuse, long thought to have vanished in the early 13th century.

Archimedes has been immortalised in folklore "" almost certainly incorrectly "" as the man who cried "Eureka" in the bath after a key discovery on floating bodies. For mathematicians and physicists, however, he is one of the world's greatest mathematicians. Both Galileo and Newton owe him a debt of gratitude "" which they acknowledge "" for their breakthroughs in knowledge of the movement of the planets. Indeed, space technology of the 20th century owes much to Archimedes's thought experiments in the third century BC. Codex C suggests that his legacy was, in fact, much more significant.

This book is about a massive project, bankrolled by the owner of the manuscript, who remains anonymous throughout the book, by the Walters Art Museum in Baltimore for preservation and scholarly study "" a work that is still in progress. It has been co-authored by William Noel, curator of manuscripts and rare books at the Walters, who directed the project, and Reviel Netz, professor of Ancient Science at Stanford University and a leading authority on Archimedes.

Little is known about Archimedes's life, except that he was a Syracusian engineer who organised the defences of his city against the Roman Empire in 212 BCE. Those defences "" based on giant, amazingly accurate catapults "" proved impregnable in battle and the city only succumbed to the treachery of its allies. Archimedes also died in that year. His tombstone had a simple engraving of a sphere and a cylinder exactly enclosing it, a schematic representation of his proof that a sphere was always two-thirds of a cylinder that enclosed it.

Much of the Archimedes legacy is known to the modern world from Latin translations of his works from the Greek. Before that, the original works were transcribed in Greek in a massive information upgrade from the original papyrus, or reed, scrolls to more durable parchment, which is treated animal skin, mostly in the ninth and tenth centuries. Codex A and B vanished in the fourteenth and sixteenth centuries but translated versions of both were preserved in the Vatican library.

Codex C vanished when Crusaders sacked Constantinople in 1204. It surfaced intermittently in a monastery in Jordan and the Metochion church in Constantinople, from where a German scholar and leading Archimedean authority, John Ludwig Heiberg, transcribed a significant part of the underlying text in the early 20th century using, ultimately damaging, ultra-violet light.

Finally "" no one knows how "" it appeared in the private collection of a Frenchman in the 19th century and then resurfaced as a charred and unprepossessing palimpsest in New York in 1998.

Codex C was special for two reasons. First, it was the only copy of Archimedes's treatise in Greek, the language in which he wrote. Second, it is the only copy, in any language, of "The Method of Mechanical Theorems", which shows for the first time that Archimedes anticipated the invention of calculus, and Stomachion, a theorem he playfully set for fellow mathematician Eratosthenes, so named because solving it would give the person a belly-ache. Rediscovering it, therefore, was certainly a Eureka moment.

A palimpsest refers to an overwritten text. It is a kind of medieval economy drive in which the original text is scraped off ""who had any need to understand revolutionary math in the Dark Ages, after all! "" the pages rotated, folded, trimmed and the prayers inscribed at right angles to the original text. This meant that much of the underlying Archimedes texts were visible only in the gutter spaces and disappeared into the spine. This apart, four forged paintings had been added in the mid-20th century, possibly to add "value" to the book. Preserving and preparing it for research was a challenge all its own.

Noel and Netz take turns narrating the story, interspersing the history of the manuscript with an account of the efforts at preserving and reading the underlying text and explaining the significance of Archimedes's geometry.

Despite the complexities of the subject "" whether it is Archemidean geometry or preservation and imaging technology "" the book is a page-turner. It is written with a light touch, in which the authors leverage their scholarly knowledge to make an arcane subject accessible to both the math enthusiast and the layman.

THE ARCHIMEDES CODEX

Reviel Netz and William Noel
Weidenfield & Nicholson
£12.50; 288 pages