Actually in ancient times they knew the world was spherical. It's debatable how many people really thought it was flat even in the darkest of the dark ages.
Turns out that you can actually measure the Earth's circumference pretty easily with some basic geometry. You can see the distance at which a ship starts to disappear on the horizon and are able to get a relation of distance to angle drop.
It's odd how they teach that the round Earth theory started with Copernicus.
Let me try another stab at figuring out why non Euclidean geometry took so long to arise: I'm under the impression that a large portion of Greek geometry was based on construction using a compass and protractor. Seeing that it is difficult to use those instruments on spherical or hyperbolic planes they never went beyond Euclidian geometry.
Source?