Eratosthenes was Director of the Great Library at Alexandria. One day while perusing the scrolls he noticed a report that in the southern frontier outpost of Syene, at noon on June 21 (the summer solistice), vertical sticks cast no shadows, and the sun shone directly down deep wells (i.e. it was directly overhead).
Because he was a scientist Eratosthenes decide to do an experiment - would sticks cast a shadow at midday on june 21 in Alexandria ? He found out that they do. How, then, is it possible that on June 21 the sun is directly overhead at Syene, but not at Alexendria. If the world was flat there would be no shadows at either location. Eratosthenes then conluded that the only possible explanation for this effect is that the surface of the earth is curved, like a sphere. Well with a few more obsrevations you can imagine what he finally ended up with, a sphereical model of the earth. So you see he did deduce the spherical nature of the earth after all.
Then again this could all be just a nice story that Carl Sagan made up.