Aristotle believed that all Earthy matter was drawn to the center of the Earth, so a sphere was the natural shape. He noticed that during lunar eclipses, the Earth’s shadow was round and he also noticed that when you go North or South a long ways, the stars that you can see change.
When a ship is at the horizon, its lower part is invisible due to Earth’s curvature. This was one of the first arguments favoring a round-Earth model.
Wikipedia tells us that Eratosthenes, a Greek astronomer from Hellenistic Libya (276–194 BC), estimated Earth’s circumference around 240 BC. He had heard that in Syene the Sun was directly overhead at the summer solstice whereas in Alexandria it still cast a shadow. Using the differing angles the shadows made as the basis of his trigonometric calculations he estimated a circumference of around 250,000 stades. The length of a ‘stade’ is not precisely known, but Eratosthenes’s figure only has an error of around five to fifteen percent. Eratosthenes used rough estimates and round numbers, but depending on the length of the stadion, his result is within a margin of between 2% and 20% of the actual meridional circumference, 40,008 kilometres (24,860 mi). Note that Eratosthenes could only measure the circumference of the Earth by assuming that the distance to the Sun is so great that the rays of sunlight are essentially parallel.
That said, the earth is not a perfect sphere. It’s not even a perfect oblate spheroid (bulging at the equator). It’s more pear-shaped (with the bulge slightly south of the equator).
Scientists believe that the earth “sags” like this because of the enormous weight of all those National Geographic magazines that folks have been saving for decades