What was one of Eratosthenes' methods for measuring the Earth's size?

Eratosthenes' method for measuring the Earth's size involved surveying the distances between cities, particularly the distance between Alexandria and Syene in ancient Egypt. He utilized the fact that at noon during the summer solstice, the Sun was directly overhead in Syene, causing no shadow to be cast by a vertical stick. However, in Alexandria, a stick did cast a shadow, indicating that the Sun was at an angle.

By measuring the angle of the shadow in Alexandria, which was about 7.2 degrees (or 1/50th of a complete circle), Eratosthenes could use the distance between the two cities to estimate the circumference of the Earth. Since he knew the distance between Alexandria and Syene, he calculated that the entire circumference of the Earth should then be 50 times that distance, thus providing a remarkably accurate estimate of the Earth's size for his time. This innovative use of geometry and observation was a significant achievement in ancient astronomy and mathematics.