In many ways, it's really just a matter of measurement power. An illuminating illustration of this is posed by how far away do you need to be from another perso

In many ways, it's really just a matter of measurement power. An illuminating illustration of this is posed by how far away do you need to be from another person to see them disappear over the horizon [0]. Turns out it's like 6 miles. I have terrible eyesight, so without telescopic optics, I'd never have been able to measure this. Rather, I'd have to rely on local measurements. And that'd nail me too: the Earth only curves about 12cm / km. So if I could only resolve a local rise-over-run of 1/1000, I wouldn't be able to fail the null hypothesis that the Earth is flat. (But if I could manage an order of magnitude better, I could!) And given that hills and such are all kinds of lumpy, and large bodies of water are rarely still, getting even that level of resolution without advanced optics would be difficult. (Though if you can be sure you've got a straight enough stick...) So I think it really comes down to how well you can prove or measure anything. Once we had telescopes, there really wasn't too much confusion about the spherical nature of the planet. (And people had suspected for a very long time the earth was - at least in some way - round. Eclipses give that away a bit.) But the details really give us the resolving power to be sure. That and it helps to get away from local measurements - get up really high, and it becomes easier to tell (and IIRC some early experiments measuring the size of the Earth took advantage of really large height differences). After all, Newton was right, too. But add a few extra zeroes to the solutions, and we start seeing some deviation from our relative measurements... [0] http://mathcentral.uregina.ca/QQ/database/QQ.09.02/shirley3.html http://mathcentral.uregina.ca/QQ/database/QQ.09.02/shirley3....