"But Eratosthenes knew that this wasn’t the case where he was, in Alexandria. Sure, the Sun came closer to being directly overhead at Noon on the Summer Solstice in Alexandria than at any other time during the year, but vertical objects still cast shadows.
And — like any good scientist — Eratosthenes did the experiment. By measuring the length of the shadow cast by a vertical stick during the solstice noon, he could figure out what angle the Sun made with the vertical direction at Alexandria.
And the answer he got was one-fiftieth of a circle, or 7.2 degrees. But at this time, in Syene, the angle the Sun was making with an identical vertical stick was zero degrees! What could be causing this? In perhaps a stroke of genius, Eratosthenes realized that the Sun’s rays could all be parallel, and that the Earth could be curved!
If he could then figure out the distance from Alexandria to Syene, since he knew the angular difference between the two cities, he could figure out the circumference of the Earth! If only Eratosthenes had a grad student, he could have sent one to make the trip, and measure the distance!
Instead, he was forced to rely on the reported distance between the two cities. The most “precise” measurement of his day?
Travel-by-camel. (So I can understand criticisms of his accuracy.) Nevertheless, his results were that the distance between Syene and Alexandria were 5,000 stadia. The question, of course, is how big is a stadium? The answer depends, of course, on whether Eratosthenes, a Greek living in Egypt, was using an Attic stadium or an Egyptian stadium, something still debated among historians. An Attic stadium was used more commonly, and is 185 meters in modern terms. Using this value, one gets a circumference of the Earth of 46,620 kilometers, a number that’s only about 16% bigger than the actual value.
However, an Egyptian stadium is 157.5 meters, and it’s conceivable that’s what Eratosthenes meant. In that case, we get a value of 39,375 kilometers, which is off by less than 2% from the modern value of 40,041 km!
Regardless of what the actual values were, Eratosthenes went on to become the world’s first geographer, inventing the concepts of latitude and longitude that we still use today, and constructed the first models and maps based on a spherical Earth.
Although many things were “lost” during the subsequent millenium, neither the idea of a spherical Earth nor the rough knowledge of the Earth’s circumference were one of them. In fact, anyone can perform this same experiment today with two locations at the same longitude, and with simultaneous measurements of shadow lengths, you too can measure the circumference of the Earth! Not bad, considering that the first direct, photographic evidence of the Earth’s curvature would not arrive until 1946!"
http://scienceblogs.com/startswithabang/2011/09/21/who-disco...