Eratosthenes was the Chief Librarian of the great library of Alexandria.  One day he read a parchment that said "in Syene, on the longest day of the year, the shadows of a column grow shorter and disappear at noon.  At noon on the longest day of the year, light shines directly down to the bottom of a certain well...only on that day."

Syene was a city 800 km to the north of Alexandria.  Eratosthenes observed that columns in Alexandra do not behave this way on June 21st, the longest day of the year.  So he went to Syene and discovered that they do.  The only explanation was that the earth was round and that the difference between the angles of the shadows represented the amount of curvature in the earth.

Eratosthenes calculated that the difference between the angles of the shadows was about 7 degrees.  He hired a man to pace off the distance to Syene, which was about 800 kilometers.  7 degrees is about 1/50th of a circle.  800 x 50 = 40,000 kilometers, which is remarkably close to the actual circumference of the earth.  For the first time ever, the size of the earth was known.