If you were suddenly in a time portal and sucked back to long ago when it was very uncommon (?) to assume that the earth and moon were spherical, how could you PROVE (using the technology in those times) that the earth and moon weren’t flat?
They would have a good argument too: You don’t fling off the earth as an object which has momentum flings off what is on it. You can never personally visibly see curvature from the ground, or if you can it is not enough to extrapolate a completely curved earth. Also, the moon couldn’t be observed in a set rotation because one side of the moon is always facing us.
I will say that the use of telescopes is okay for this exercise.