He observed that on the summer solstice in Syene, the sun was directly overhead. However, in Alexandria the sun did not rise as high. His reasoning: the curvature of the Earth.
He erected a vertical mast in Alexandria and measured its shadow at noon. The length of the shadow was observed to be equal to 1/50 of the circumference of a circle having the radius equal to the mast.
Using geometry laws (that of equal opposite angles of a line cutting parallel lines), he reasoned that the distance from Syene to Alexandria was 1/50 the radius of Earth.
He then measured the angle of the shadow in Alexandria. By taking the angle of the shadow (7.2 degrees) and dividing it into the 360 degrees of a circle (360 divided by 7.2 yields 50), Eratosthenes could then multiply the distance between Alexandria and Syene by 50 to determine the circumference.
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