He didn't. Gallileo proved the earth was round. Eratosthenes of Cyrene first put the motion forward and even calculated the diameter, but Nicholas Copernicus and Galileo Galilei first put the idea into the public eye.
Well, during a lunar eclipse, you can see a shadow of the earth. The shadow is curved, so the earth must be round. If this doesn't help you, ask NASA, look in a book, or actually go up into space to...
Pictures from space for one, the laws of gravity for two and the curved horizon for three - not to mention the planes that fly and ships that sail around the world on a regular basis. Not only that,...
The earth has been proved to be round like a sphere because there are cameras and satellites to prove that the earth is round, just because the earth is round doesn't mean that it is a perfect...