If they knew the earth rotated, then they could assume that noon happened at different times at different locations. But did they have a way to prove this without being able to travel or communicate fast enough to observe the effects?
In: Mathematics
Ancient people? Probably not. In order to measure it, you’d need a clock in order to do so, and the first mechanical clock wouldn’t be invented until the 13th century.
However, the Earth was shown to be round by Eratosthenes around 200 BC because he heard about the Sun casting perfectly vertical shadows on a specific day of the year. On the same day, Eratosthenes in Syene (now called Aswan) measured the angle of a shadow, and got a shadow at a 7° angle. He then measured the distance between Alexandria and Syene, and determined that would be 7° of the circumference of the Earth, and then calculated the whole circumference.
It is reasonable that someone could make that conclusion that something similar happens when you travel East to West, rather than North to South, but again, you couldn’t calculate thay change without transporting the mechanical clock a very long distance.
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