In 1906, Danish classicist Johan Ludvig Heiberg opened an old book in the private library of the Metochion of the Holy Sepulcher in Istanbul and began to scrutinize it with a magnifying glass. He was the first person in almost a millennium who understood exactly what he was looking at.

Heiberg had found seven treatises in the original Greek by Archimedes, regarded as the greatest mathematician of antiquity and one of the greatest in history, perhaps without equal before Newton. One of the treatises had been lost for nearly a thousand years. Heiberg had made a discovery of staggering importance.

"It's as if no one had ever seen a copy of Shakespeare in the original English," says Will Noel, an assistant curator at the Walters Art Gallery in Baltimore. "And then you found one."

Noel is in charge of manuscripts at the Walters, and has supervised the care of the Archimedes text since an anonymous collector bought it from a private estate last October for $2 million.

The sale marked the first time that anyone had seen the manuscript in public since it was copied by a scribe in Constantinople in the 10th century. Over the years it had been moved at least five times, deliberately defaced, scorched in a fire, threatened by an earthquake and battered in political upheavals ranging in time from the Fourth Crusade to World War I.

The Walters has one of the top manuscript collections in the country, and gained custody of the Archimedes after Noel, a Briton, asked a colleague to intercede with the new owner's London purchasing agent.

The gallery intends to exhibit the manuscript from June 20 to Sept. 5, then study and restore it in a project that could last as long as five years. As far as the owner is concerned, "money is not the issue," says Abigail Quandt, the Walters senior conservator for manuscripts and rare books. This is a good thing, because the manuscript presents difficulties that will require first-ever innovations to resolve.

For starters, the parchment leaves are badly eaten by mold, but the most daunting challenges arise because the manuscript is a palimpsest, or twice-used book. The 10th-century copy of the Archimedes text was overwritten nearly 300 years later by someone, probably a monk, who needed parchment for a how-to manual on the prayers and rites of the Greek Orthodox Church.

The monk scraped the Archimedes from the goatskin parchment, tore the pages in half, turned them 90 degrees and rebound them in a different order. The resulting book, half the original dimensions of the Archimedes, offers instructions on holding a marriage ceremony, performing an exorcism and getting rid of impurities when "something unclean falls into a vessel of wine, oil or honey."

While the prayer book is rare and valuable, the Archimedes, complete with elegantly drawn diagrams, is priceless. It can still be discerned beneath the liturgical text, but not always, and seldom clearly. An ultraviolet light can bring it into sharper focus, but the Walters will need sophisticated cameras and digital enhancement to optically suppress the prayer text and highlight the underlying script enough to make the best possible transcription.

The Walters is currently studying state-of-the-art imaging methods and asking for proposals from the tiny handful of experts in the field. Alternatives include high-resolution digital photographs manipulated on a computer screen and imaging techniques used in space photography.

Restoring the Archimedes quite likely will turn out to be a once-in-a-lifetime opportunity, Quandt says, and "I want to find the best possible equipment so we don't have to do it more than once. We haven't made a final choice."

A Man of Principle

Archimedes was born around 287 B.C. in Syracuse, Sicily, and died in 212 or 211 B.C., when the city was sacked by Roman legions. Legend holds that he was killed because he talked back to a Roman soldier who accosted him as he was working on a mathematical problem--infuriating the soldier by, in effect, telling him, "Don't bother me."

This was only one of many tales, both real and fanciful, spread about Archimedes, renowned in his lifetime for his Edison-like genius as an inventor, tinkerer, physicist and practical engineer. As a student in Alexandria, Egypt, he devised the "Archimedes' screw," still in use today as a corkscrew-like scoop cranked inside a pipe to remove water from flooded fields.

He is also credited with inventing a variety of war machines--catapults, grappling hooks and the like--that kept the Romans at bay for several years. He is said to have built a "missile thrower" able to hurl tree trunks with enough force to collapse the sides of enemy ships.

Discounted, however, is the story that Archimedes was able to burn ships with sunshine reflected from mirrors embedded in a hillside. And although he understood and developed the math associated with levers and fulcrums, he probably did not say, "Give me a place to stand, and I will move the Earth."

Also too good to be true, historians believe, is his most famous quote. Asked by King Hieron II to determine whether a new crown supposedly made of gold had been adulterated with base metal, Archimedes decided to immerse it in a pail of water and weigh the overflow. The inspiration reportedly occurred while he was taking a bath, prompting him to jump up and run naked through town shouting "Eureka!" ("I've found it!").

But the science that informed Archimedes' gimmicks was no joke. The crown trick is an application of "Archimedes' principle"--that a solid when immersed in water will appear to be lighter by the weight of the water it displaces. That mathematical proof is presented in "On Floating Bodies"--a treatise unknown in Greek until the discovery of the palimpsest.

"Archimedes discovered that through purely mathematical reasoning, you can determine how bodies behave in the physical world," says the Massachusetts Institute of Technology's Reviel Netz, serving as a consultant to the Walters. "This is something new, and no one did it comparable. It is the starting point of the scientific revolution. Galileo, Newton--they all regarded themselves as Archimedes' disciples."

Archimedes described the value of pi--the ratio of the circumference of a circle to its radius--at 22/7, by circumscribing and inscribing a circle with many-sided polygons, becoming the first person in history to realize that pi could only be approximated, never calculated.

And in "Method of Mechanical Theorems," unseen until the palimpsest, Archimedes demonstrated that two-dimensional areas can be calculated by summing up the lines on the surface, and that the volume of a solid could be determined by summing up the planes that intersect it. Scientists regard the "Method" as an antecedent of the calculus--developed by Isaac Newton and Gottfried Wilhelm Leibniz 1,900 years later.

And, by showing that a sphere is two-thirds the size of the cylinder that encloses it, Archimedes gave posterity the formula V=4/3 {pi}r{+3} --for the volume of a sphere.

"He's always trying to surprise," says Netz, who is preparing the first-ever English translation of Archimedes. "He attacks in one direction, and then in another direction, then all of a sudden it all comes together and you have the volume of a sphere."

Archimedes preserved his scientific discoveries in letters sent to colleagues in Alexandria, but the treatises were lost through much of the early Christian period.

Texts disappeared in the 6th century only to reappear in the 9th century, when they were used to make the Latin translations that served as the standard Archimedes.

By Heiberg's time, the Greek originals for "On Floating Bodies" had been lost, and the only thing known about "Method of Mechanical Theorems" was that it existed. Things "do not happen fast in the study of classics," Netz explains, and to find "two whole works," as Heiberg did, is the philological equivalent of discovering America.

Recycling a 'Useless' Book

The 10th-century Greek Archimedes, explains Noel, originally was "quite a fine book" for its time, written in Constantinople on goatskin parchment. At two pages per goat, it was expensive, stood more than a foot high and "probably was made in the emperor's palace scriptorium," he says. "It was a time of great flowering, and life was pretty rosy."

Things had changed 300 years later. In 1204, Fourth Crusaders en route to the Holy Land stopped off in Constantinople to sack the city, empty the emperor's palace and burn books. Following this debacle, Noel suggests, people probably needed prayer, but "it's hard to maintain a regular supply of parchment" when the treasury has been looted and the infrastructure is in ruins.

So 13th-century scribes made prayer books from "useless" books that no one could understand: "In the year 1000 there were maybe three or four people who knew what Archimedes had done," Noel says. "But by 1200, who cares?"

Fortunately for posterity, the treatises had been written with "iron gall," ink made from dye that comes from crushed galls--deformities on oak trees. When mixed with iron salts and water, the resulting ink is extremely high in tannic acid. It bonds with the underlying parchment and will not run. The monk could scrape it off, but he could not make the writing disappear altogether.

Sometime in the next 400 years, the prayer book was sent to the Justinian's Tower library at the Mar Saba monastery, a cliffside jumble of buildings in the Judean desert in what is now the West Bank.

There it remained until the 1830s, when a combination of political unrest and an earthquake prompted the monks to move most of their collection--more than 1,000 manuscripts--to the library of the Greek patriarch in Jerusalem, next door to the church of the Holy Sepulcher.

By mid-century, however, the palimpsest was back in Constantinople--by then Istanbul--at the Metochion, the city's Greek Orthodox religious enclave. Noel says scholars don't know why it was sent there, but the German biblical expert Constantine Tischendorf in an 1846 travel book reported visiting the Metochion library and finding nothing of interest "apart from a palimpsest dealing with mathematics."

Heiberg finally identified the palimpsest during a trip to Istanbul to examine the manuscript, whose existence had been reported in a 1899 catalogue of the Metochion collection. He found a manuscript largely undamaged by mold, but scorched around the edges from a fire sometime in the previous nine centuries. Using only a magnifying glass, Heiberg wrote down every word he could read.

"Heiberg was a genuinely great scholar, perhaps one of the greatest philologists of all time," Noel says. "Even today, if you read a Greek text that is 'translated by Heiberg,' that's pretty much the last word."

Heiberg's discovery made the New York Times front page of July 16, 1907, under the headline "Big Literary Find in Constantinople," and Heiberg published the treatises he had translated.

But the palimpsest itself disappeared, and it was only at the Oct. 29, 1998, auction at Christie's in New York that it reemerged. It was clear that a century of abuse had taken its toll.

Noel says scholars still don't know exactly who had the palimpsest between Heiberg's last visit in 1908 and the late 1920s, when it was obtained by the unnamed French family who offered it at auction. Heiberg died in 1928.

But sometime in the two decades after Heiberg saw it, the manuscript left the Metochion, perhaps sucked up in the unrest that attended World War I and the fall of the Ottoman Empire. When the French family got the book, the mold had dug deeply into the parchment, many passages read easily by Heiberg had become illegible, and the Mar Saba "ex libris" written on the inside front cover had disappeared. Worst of all, a forger had covered four pages of text with fake full-color paintings of evangelists--a transparent attempt to beautify the manuscript prior to sale. One of the forgeries covers the opening page of "Method of Mechanical Theorems," and all four cover text that Heiberg had read.

"At this stage, it's an open question" whether the new owner will want to keep the paintings, Noel says. "We will certainly do everything in our power to read the Archimedes text without removing the forgeries," he adds, "but what we really need to do is get at the Archimedes."

CAPTION: Curator Will Noel and conservator Abigail Quandt of the Walters Art Gallery plan the restoration of a rare copy of an Archimedes treatise.

CAPTION: A page of the Archimedes palimpsest shows original and later texts.