Non-Euclidean geometries? IIRC the questions of "what can you still/now prove with this one postulate removed" were studied for centuries before hyperbolic or elliptic geometries were really understood.

Or maybe I'm misremembering. That always did seem odd to me. I guess hyperbolic geometries can't be isometrically embedded in R^3, which makes them hard to intuitively comprehend. But the educated classes have known the Earth was a sphere for millennia; surely somebody noticed that this was an example of an otherwise well-behaved geometry where straight lines always intersect.