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Eratosthenes: Sun
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Much of what Eratosthenes wrote is now lost, including a geometrical treatise, On Means, and one on the mathematics behind Plato's philosophy, Platonicus. He ... wrote the fundamentals of astronomy in a poem called Hermes. His most famous calculation, in the now lost treatise On the Measurement of the Earth, explains how he compared the shadow of the sun at Summer Solstice noon in two places, Alexandria and Syrene.
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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).
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Eratosthenes stretched a string from the top of the post to the tip of its shadow. Then he measured the angle between the post (at its top) and the string. Do you see what he had done? The string represented the sun's ray that was casting the shadow.
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