Perhaps somebody would have discovered hyperbolic or other non-Euclidean geometries before Lobachevsky? Through the lens of modern mathematics, non-Euclidean geometry seems like such a simple extension/modification of Euclidean geometry, yet it was only explored and developed in detail in the early 19th century.
Well it took more than a thousand years for the belief of a spherical Earth to be accepted. It's hard to imagine a new type of geometry when you believe the Earth is flat.
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.
On top of that, you don't even an ocean to measure the Earth's circumference. Eratosthenes of Cyrene (born in the 3rd century BC) calculated the circumference of the earth fairly accurately using the angle of elevation of the Sun measured from two different cities. Note that implies that a round earth was common knowledge to the Greeks even at this date.
