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Calculating the circumference of the Earth
When Eratosthenes was informed that on the summer solstice at midday in Syene (in Aswan which was in the same meridian) that a well (or a vertical pillar) had no shadow, he observed that at the same moment in Alexandria the angle of his shadow was 7.2°. Considering the phenomenon as the result of the sphericity of the Earth, he concluded the following proportions of arcs and angles: 7.2°/360° = Distance Syene - Alexandria / Circumference of the Earth. Given the distance Syene -Alexandria that was 5 000 stadia, he calculated the circumference equal to 250 000 stadia, i.e. 39 690 km (almost equal to the accepted today value of 40 615 km).
SOURCES: "Proklos Diadochos, A Commentary on the First Book of Euclid's Elements"