How did Eratosthenes measure the whole Earth with a shadow?

Eratosthenes measured the Earth by comparing two shadows. At noon on the summer solstice, a stick in the Egyptian city of Syene, today's Aswan, cast no shadow at all, and sunlight fell straight down a well. At the same moment in Alexandria, further north, a stick did cast a shadow, tilted by about 7.2 degrees. That is one fiftieth of a full circle, so Eratosthenes reasoned that the two cities were one fiftieth of the way around the planet. Surveyors put them about 5,000 stadia apart, and 50 times 5,000 gives roughly 250,000 stadia for the whole Earth.

Nobody knows exactly how long his stadion was, so his precision is still argued over. Depending on the unit, he was off by somewhere between a few percent and about 15 percent, an astonishing result from a stick and a shadow.

He was the chief librarian of Alexandria, the man who coined the word geography. Yet some critics mocked him as Beta, 'Number 2', because he seemed to come second in everything. The rest of history disagreed. Seventeen centuries later, Christopher Columbus chose to believe the Earth was a quarter smaller than Eratosthenes had said. Had he trusted the librarian, he would have known that the land he reached was not Asia.