Well, it's my understanding that in our history it was long known that the world was round. People often get confused between the knowledge that the Earth went round the sun (which - in the West at least - is a relatively recent discovery that could - and did - get you persecuted by the medieval Church) and knowledge that the Earth was round (which was generally accepted by all educated people).
The song that says, "They all laughed at Christopher Columbus when he said the world was round" is wrong, wrong, wrong. Most people then (church included) thought that the world was round. They laughed at Christopher Columbus because he said that the world was much smaller than they all thought it was, so much smaller in fact that, according to him, the eastern coast of China lay only two or three thousand miles to the west of Portugal, whereas everyone else said that it was much further away - the other side of the world in fact.
And you know what? He was wrong, and they were right, and they were right to laugh at him, and it was only him getting lucky and discovering America that saved him from going down in history and as a fool.
Anyhow...
The reason why (at least, this is what I've read - I've never actually stood on the shore and tested it) people generally knew that the Earth was round was that when ships sail away, they gradually dip below the horizon, so that after a while you can only see the tops of their masts, and after a little while longer you can't even see that (which one reason is why you have a crows nest - because you can see further over the horizon). And since we know that water is always flat then it holds that if the sea is curved, then the surface of the Earth is also curved.
I'm sure someone has got a lot more detail on this subject than my highly sketchy recall, but the general gist is that knowing that the world was round wasn't as a big a secret (at least among educated people) as we tend to think.