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mathematics who became the head librarian in 240 BC. His greatest contribution was in geography. From at least Aristotle’s time, Greeks had known that the earth was round—otherwise, why would ships’ hulls disappear before their masts when sailing out to sea? But they had no idea how large it was. Eratosthenes concocted a formula to measure the circumference by ingeniously noting the angle of the sun simultaneously in two different spots and mathematically extracting the total distance of about twenty-five thousand miles—remarkably close to the actual figure of 24,900.
    Eratosthenes and other Greeks of his time made other contributions as well, for example, adding consistent scale and lines of latitude to maps. But it was Eratosthenes’s successor at the library a few centuries later, Claudius Ptolemaeus—known to history as simplyPtolemy—who made the greatest strides. Born around AD 100, Ptolemy’s fame rests on two books. In the first, the
Almagest,
he famously rejected the popular theory that the earth circled the sun in favor of an earth-centered universe. The Ptolemaic view survived infamously for centuries—until it was finally challenged by the likes of Copernicus and Galileo some fourteen hundred years later.
    Despite that cosmic blunder, his second book, the
Geographia,
had a more positive lasting influence. Before Ptolemy, no one had systematically gathered all geographic knowledge in one place. Ptolemy combined historical books by the likes of Herodotus, original observations, and travelers’ tales to produce twenty-seven maps showing the entire known world. Just as important, he included a list of some eight thousand place names, each with its presumed latitude and longitude. Theoretically, someone could take that list and faithfully re-create Ptolemy’s maps with parchment and a ruler.
    That is exactly what happened. Though all of Ptolemy’s maps were lost in the fall of Rome, the tables were preserved in Byzantium and the Arab world. After a dreary thousand years of flat-earth religious maps about as useful to navigation as a cartoon, a Greek monk named Maximus Planudes came upon a copy of the
Geographia
in Constantinople and translated it into Latin. In 1397, a Turkish diplomat and scholar namedManuel Chrysoloras brought a copy to Florence, where the Renaissance was just kicking off.
    Just as Alexandria had been the cultural center of the ancient world, Florence was the cultural center of fifteenth-century Europe, attracting “humanist” scholars to debate the great philosophical and scientific questions, looking back to Greece and Rome for inspiration. They seized upon the
Geographia
as a true vision of the world passed down from the ancients—using Ptolemy’s tables to faithfully reconstruct his maps. Compared to everything that had come before them, the maps were a revelation. Suddenly the contours of the Mediterranean world emerged in stunning detail, filled with continents and cities only vaguely imagined before ( Figure B ).
    Not surprisingly, Ptolemy’s maps contained some errors. He rejected Eratosthenes’s calculations of the earth’s circumference in favor of those of another Greek mathematician, who wrongly pegged it at just eighteen thousand miles. He also joined a rather indistinct Africa to a huge southern continent, and he vastly extended Asia, shrinking the distance between it and Europe to a mere twenty-five hundred miles. Those errors had profound implications later when Christopher Columbus set off from Spain with a map from the
Geographia
in hand.
    Despite them, however, it’s difficult to overstate the influence of the
Geographia,
which boldly proposed that the visible world was accessible to the human mind through mathematical precision—a heretical notion in the Middle Ages. As one Florentine described it at the time, the
Geographia
“raises us above the limits of an earth obscured by clouds,” demonstrating “how, with true discipline, we can leap up within