Among the easiest ways to detect that the Earth is round is that a mountain, ship, or building will slowly disappear below the horizon as you move away or go to a lower elevation, or appear in the reverse. The only way that makes sense is if you are on a round surface.
Eratosthenes (276-194 BC) realized you could measure the circumference by measuring the length of a shadow of objects of known height at noon from two points at known differing latitudes. He got a result of 252,000 stadia or about 40,000 km, which is within 2.5%.
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