Eratosthenes used geometry to estimate the circumference of the Earth.
Eratosthenes measured the altitude of the noontime sun at Alexandria at its maximum on Jun 21st. On that date, the Sun is directly overhead at noontime at Syene, in southern Egypt (latitude = 23.5 degrees north).
The zenith distance is the angle from the zenith to the point where the Sun was at noon; it is also 90 degrees minus the altitude. At Syene, the zenith distance was 0 degrees; at Alexandria it was about 7 degrees.
He knew how far it was from Alexandria to Syene, so he used geometry and the difference in zenith angle to estimate the size of the Earth.
Eratosthenes also measured the tilt of the Earth axis by 23.5 degrees, which gives us the seasons .
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