This is similar to the phenomenon observed when one auto on the highway overtakes another. Briefly, the passing vehicle observes the passed vehicle to stand still, and then appear to recede, or move backwards, when in reality both cars are still moving in the same direction. This was a bit contrived, but managed to explain the retrograde motion, visually, not physically. The Earth casts a round shadow on the Moon during a lunar eclipse. Only a spherical object can cast a round shadow when viewed from an arbitrary angle.
Ships sailing into the distance disappear from the bottom up, leaving the mast last to disappear.
Observations of the sky are also a clue to the spherical shape. On a flat Earth, you'd see the same stars at the same time everywhere, whereas on a spherical Earth, if you change latitudes, different stars are then visible. This would not be true on a flat Earth. Similarly, at the equator, over the course of a year, you could see every possible star, because you see half of each hemisphere at a time.