For 2,000 years, the document written by one of antiquity's greatest mathematicians was ill treated, torn apart and allowed to decay. Now, US historians have decoded the Archimedes book. But is it really new?

When the Romans advanced to Sicily in the Second Punic War and finally captured the proud city of Syracuse, one of their soldiers met an old man who, surrounded by the din of battle, was calmly drawing geometric figures in the sand. "Do not disturb my circles," the eccentric old man called out. The legionnaire killed him with his sword.

That, at least, is the legend. The truth is a different story altogether. Placed in charge of King Hieron II's artillery equipment, Archimedes later played an important military role during the siege of Syracuse.

He invented powerful catapults to defend his homeland, using cranes to hurl heavy boulders from the walls of the fortress at enemy ships. Mirrors were also used, it is said, to direct burning rays of sunlight at the Roman armada, setting the ships on fire. The Sicilians resisted the onslaught of the ambitious Roman republic for more than two years.

In short, had the legionnaire really speared the eccentric old man with his sword, he would have done the Romans a great service. In addition to being an oddball scholar, Archimedes was a skilled inventor of weapons.

How Many Grains of Sand

He was so skilled, in fact, that it almost seemed that he could stop Rome's large army single-handedly. But in the end Archimedes fell victim to brute force after all. One of the greatest inventors of all time, Archimedes was killed at the age of 73. His murder, notes British philosopher Paul Strathern, was "the Romans' only decisive contribution to mathematics."

Archimedes prepared the way for integral calculus and approximated the number Pi. He discovered the law of leverage and invented new formulas to calculate the properties of cylinders and spheres. He once yelled "Eureka" while bathing, after having dreamed up the concept of specific weight while splashing around. He even specified the number of grains of sand that could fit into the universe: 1063. Until then the Greeks had merely left it at a "myriad" (or 10,000).

"It took almost 2,000 years before anyone else could hold a candle to him," Strathern says about this extraordinary man, who lived from 285 to 212 B.C. But brilliance had its drawbacks. Archimedes was often so engrossed in thought that he would forget to eat -- and he bathed infrequently. But aside from that, researchers know little about this oddball from the early days of geometry and mechanics. Unfortunately many of his writings were lost, while the rest have been handed down in the form of Arabic and Latin copies. Vandals destroyed his famous planetarium, with its water-powered wheelworks.

But now a Greek original has been discovered after all. In "The Archimedes Codex," recently published in English, two US researchers describe the decoding of a manuscript from the early days of mathematics. It took the authors years of painstaking work to "extract the secrets from these faded letters."