What is this quotient space of the torus?

Who discovered that the Earth was not shaped like a torus (doughnut)?

• Eratosthenes' measurements (and many other astronomical measurements) are consistent with a torus-shaped Earth, on which the Mediterranean is on the outer half of the torus. So is Magellan's circumnavigation. I can think of a few approaches to disproving the torus hypothesis, without going into space and looking back at us: 1) Follow geodesics in two orthogonal directions, until you come back to the start, and observe that you don't see portions of Earth looming above you in the sky at any point in your journey. 2) Observe that the Earth's curvature is the same in all directions, perhaps by measuring how far away a ship must get before in disappears under the horizon. Preferably, perform this measurement at several different locations. 3) Make an argument relating to gravity on a large torus. Maybe that the Earth is not packed together well enough to maintain its shape as a torus, or maybe that the gravitational force would not appear to point downward to an observer who was far from the Equator. So… who was the first person who either explicitly realized that the Earth was not a torus (or cylinder, etc.), or if you prefer, who was the first person who made a measurement that was actually inconsistent with the Earth being a torus?

• Answer:

  Can you name any thinkers who even considered the possibility of a toroidal Earth? I never heard of any, whereas the sphericity of the Earth was hypothesized and confirmed in ancient times.