The ancient Greeks knew a thing or two. Nowadays we say Copernicus discovered the earth was round, for example, but the Greeks had that figured out almost 2000 years earlier! How did they manage it?
They had several different arguments for the roundness of the earth. One of the best comes from Aristotle himself, who wrote a book called On the Heavens back in 340 B.C. The Greeks were a sea-faring culture, and sailed all over the Mediterranean. And they had noticed, Aristotle tells us, that the north star isn't always in the same spot overhead.
Now remember that all the stars seem to move in a big circle over our heads because the earth itself is spinning. The north star is the center of the circle, and stays put.
However, Aristotle noticed that when you are down south in Egypt, the north star is close to the horizon. When you are up north in Greece again, it's high in the sky. How is that possible, since the north star is supposed to stay put?
It's possible, Aristotle concluded, only if the earth is round.
Think of it this way. When you are standing at the north pole, where is the north star? Directly overhead. Now place yourself at the equator. Where is the north star? Yep, it's down on the horizon, because you have travelled along a curve. Go even farther south and you won't be able to see it at all; the earth will hide it. Go farther north and it seems to rise higher and higher.
Grab a toga, you've just shown the earth is round!