Eratosthenes' measurement of the circumference of the Earth

The Ancient Greeks knew that the Earth was round. The first person to estimate the circumference of the Earth was Eratosthenes of Cyrene, who lived from 276 BC to 195 BC. Eratosthenes knew that on the summer solstice at local noon, the sun would be directly overhead in the city of Cyrene. This is because Cyrene lies on the Tropic of Cancer. He also knew that at local noon in Alexandria on the summer solstice, the sun was 7 degrees south of the zenith (the highest point in the sky). He used this information, as well as the distance between Cyrene and Alexandria, to calculate the circumference of the Earth.

You can try a similar experiment yourself, by moving the point D around the circle. The sun's rays are almost parallel lines, because the Sun is far away relative to the size of the Earth. The dotted line AD is a transversal of these parallel lines. It follows that the sun's angle at D is equal to the central angle in the figure. (Distances are shown in kilometers.)

The circumference of the Earth is calculated by solving the proportion
(distance)/(circumference) = (central angle)/(360°).