You know what would help me a lot is if Eratosthenes way of measuring the circumference of the earth would work as a proof that it's round. There's a slight problem tho. If you measure the angle between the stick that casts no shadow and the stick that casts a shadow, you will get the radius of the earth, but only if you previously assume that it's a sphere. If you assume that it's flat you instead get the distance to the sun.
Can you think of any way of getting around this by just using sticks and a watch?