Before anyone had a cell phone, a computer, a slide ruler, or even an electric light bulb ,
astronomers were smart. They had to use their brains.
"The earliest documented mention of the
spherical Earth concept dates from around the 5th century BC, when it was mentioned by ancient
Greek philosophers.
[1][2] It remained a matter of speculation until the 3rd century BC, when
Hellenistic astronomy established the
spherical shape of the Earth as a physical fact and calculated the
Earth's circumference."
"Lunar eclipses
The shadow of the Earth on the Moon during a lunar eclipse is always a dark circle that moves from one side of the Moon to the other (partially grazing it during a partial eclipse). This could be produced by a flat disc that always faces the Moon head-on during the eclipse, but this is inconsistent with the fact that the Moon is only rarely directly overhead during an eclipse. For each eclipse, the local surface of the Earth is pointed in a somewhat different direction. The shadow of a circular disc held at an angle is an oval, not a circle as is seen during the eclipse. The idea of the Earth being a flat disc is also inconsistent with the fact that a given lunar eclipse is only visible from half of the Earth at a time.
The only shape that casts a round shadow no matter which direction it is pointed is a sphere, and the ancient Greeks deduced that this must mean the Earth is spherical.[19]"
Spherical Earth - Wikipedia
