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Eratosthenes' calculations were based on two assumptions. The first was that Syene lay on the Tropic of Cancer. The second assumption was that Alexandria lay due north of Syene on exactly the same line of longitude (the meridian line). At noon during the summer solstice, the rays of the sun always shine directly perpendicular to the Earth's surface, but only on the Tropic of Cancer. If Alexandria was exactly due north of Syene, then Eratosthenes could argue that the key measurements he used -- the length of the column's shadow in Alexandria and the distance between Alexandria and Syene -- were geographically sound.
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View of Earth with Alexandria and Syene marked

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