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Pcdefender said..
What you would or should see is the line of the horizon all 360 degrees around you would be below you.
Imagine you are a tiny ant living on a soccer ball, the line of the horizon all around you would be below you.
Yep, pretty good analogy.
Now the really interesting but would be to get a theodolite or similar survey tool.
Line it up on the horizon, set your scale to Zero.
Then rotate it in the vertical plane until it lines up with the opposite horizon. Flat or ball the total angle should be a bit over 180. (Or get a an accurate reference to vertical and the angle should be a bit over 90)
On a flat earth, the angles should be less, because you're on a flat plane. The angles would increase pretty linearly as you raised the elevation.
On a ball however, the angle would be greater to start with, and then increase very differently as you increase your elevation.
But I imagine the tricky part would be figuring out just what limits your vision to the horizon on a flat earth? Is it a consistent phenomenon that you can rely on to take these measurements?