What If the Library of Alexandria Never Burned?

Three generations later, a mathematician named Philon stood in the same reading hall, running his finger down a scroll that Theon himself had once saved from a collapsing shelf. The text was Eratosthenes' full working notes — not just his famous estimate of the earth's circumference, but the failed drafts, the arguments with rival astronomers, the raw data from the well at Syene.

In the world Theon had almost lost, these notes would have survived only as a summary, quoted secondhand by a historian centuries later, stripped of the reasoning that made the conclusion trustworthy. Here, Philon could read the actual argument. He could disagree with it, test it, improve it. He spent four years re-measuring the angle of the sun at noon in six cities from Alexandria to Massilia, correcting Eratosthenes' figure by a fraction of a percent — a correction that would have been impossible without the original data.

It was a small thing. A number refined. But Philon's student would use that refined number to argue, successfully, that a western sea route to India was shorter than anyone assumed — an argument that reached a shipbuilder's guild in Carthage within his own lifetime, long before any Genoese captain would have needed to make the same case over a thousand years later.