Eratosthenes and the Circumference of the Earth

In his quintessentially captivating way, Carl Sagan describes the remarkable story of how the ancient Greek Eratosthenes calculated the circumference of the Earth by simply using his brain and a couple of sticks and shadows.

Of course, the argument rests on a fundamental assumption: that the distance between the earth and the sun is so vast as to not matter. Had the distance been smaller, it would certainly be possible to get different shadows on a flat planet, wouldn't it?

Did Eratosthenes get lucky, or did he have an independent way of estimating the distance between the sun and the earth? Does anyone know? Ok, you all have homework now...
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