On the Measurement of the Earth
Peri tes Anametreseos tes Ges
By comparing the angle of the sun's shadow at noon in two cities a known distance apart, the circumference of the entire earth can be calculated with remarkable accuracy using nothing more than geometry and careful observation.
- measuring the earth via solar angle at two cities
- geometry applied to a physically untestable question
- survival only through Cleomedes's later summary
- remarkable accuracy given the method's simplicity
- Eratosthenes as chief librarian of Alexandria
Eratosthenes, chief librarian at Alexandria, calculated the earth's circumference by comparing the sun's angle at local noon on the summer solstice in Alexandria against its angle, essentially zero, at the same moment in Syene, where the sun was known to shine directly down a deep well, then combined the angular difference with the known distance between the cities. Eratosthenes's original treatise does not survive; his method and results are known only through later authors, chiefly the astronomical writer Cleomedes, who preserved a summary of the technique.
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