LONDON — After a millennium in obscurity, the last unreadable pages of the works of Archimedes are being deciphered with the help of one of the brightest sources of X-rays on the planet.

Thanks to the X-ray vision of an instrument at the Stanford Linear Accelerator Center in California, scholars now have the most complete record of Archimedes’s works to emerge since the Middle Ages, perhaps explaining for the first time why he really shouted, “Eureka!”

A team using a special X-ray imaging technique, called X-ray fluorescence imaging, has studied a goatskin parchment manuscript that records several works by one of the founders of modern mathematics, who lived during the third century before the common era. Archimedes is famous for supposedly shouting, “Eureka! I have found it,” upon discovering how to measure the volume of a solid while sitting in his bath.

Of all the new discoveries, one of the most remarkable is a previously indecipherable page of Archimedes’s treatise “On Floating Bodies,” written in Greek, which has significant differences from the known Latin translation and is thought to be much closer to the original. The Eureka moment is probably a myth, a member of the team, Dr. Uwe Bergmann, said. But “On Floating Bodies,” which discusses how various shapes of bodies float, was a tour de force that could well have merited running naked down the street.

The director of the Archimedes Palimpsest collaboration at the Walters Art Museum in Baltimore, William Noel, said Archimedes extended the boundaries of Greek mathematics. His place in the history of the related conceptual fields of calculus and of infinity is currently being re-evaluated, Mr. Noel said.

In the 10th century, a scribe copied Archimedes’s treatises in the original Greek onto the parchment, marking one of the earliest records of his ideas by about 400 years. But the text presented a challenge for scholars to decode because, three centuries later, a monk made the parchment into a palimpsest, a manuscript on which two or more scripts have been written. The monk scraped away the text, cut the pages in half, turned them sideways, and copied Greek Orthodox prayers onto the recycled pages. These writings have been hidden since the 13th century.