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This illustration shows how Eratosthenes actually calculated the circumference of the Earth. At noon on the summer solstice, Eratosthenes measured the length of the shadow cast by a column of known height at Alexandria. With these two lengths, he could solve for the angle between them (θ). If
the length of the shadow, and height of the column
(h) were proportional to the distance between
Alexandria and Syene (s=4,400 stades), and the
radius of the Earth, then by calculating the
angle on the column (θ), he was calculating
the same angle formed at the center of the Earth
(θ).
The equation he used to determine the circumference
of the Earth [(360° ÷ θ) x (s)] reflects this theory. 
