Eratosthenes was an ethnic ancient Greek mathematician who managed the great library of Alexandria, Egypt circa 240 BC. He was born in Cyrene, Libya in 276 BC and died in Alexandria, Egypt in 194 BC.
One day he was reading a text that told of how at midday on the summer solstice in the city of Swenett,1 Egypt, the sun’s rays would shine straight into a well to illuminate the water at the bottom. Likewise, none of the buildings cast shadows because the sun was straight overhead.
This got Eratosthenes to thinking. So on the next summer solstice, at noon, in Alexandria, he went outside expecting to see the sun straight overhead and none of the buildings casting shadows. For that would be the case if the Earth were flat.
But that was not the case. Eratosthenes witnessed shadows being cast all over the place because the sun was not directly overhead. So he embarked on an epic experiment. Between then and the next summer solstice Eratosthenes hired a man to measure the distance from Alexandria to Swenett which turned out to be 800 kilometers.
On the day of the next summer solstice, Using a plumb line to insure verticality, Eratosthenes drove a pole into to the ground and then at noon measured the length of the shadow and the angle formed by the shadow and the pole:
Now is the time for everyone’s eyes to glaze over:
A is Alexandria. S is Swenett. E, on the lower left is the center of the Earth. AT is the length of the shadow. At Alexandria, Eratosthenes measured the angle formed by the top of his pole and the end of the shadow to be, 7 degrees. By geometric theorem, the angle formed by Alexandria, the center of the earth and Swenett must also be 7 degrees.
Consequently, 800 kilometers from Alexandria to Swenett corresponds with 7 degrees. Since the circumference of a circle is 360 degrees, 360 divided by 7 is approximately 50.
Therefore, 800 kilometers multiplied by 50 equals the circumference of the earth.
800 x 50 = 40,000 kilometers. Which turned out to be the case.
Here is a video of Carl Sagan doing a great job of explaining all this mumbo jumbo:
1 Swenett was called Syene by the ancient Greeks and today is called Aswan.