The gnomon and the well form the ends of two radii pointing directly to the center of the Earth. If the angle between them is 7.2 degrees, and they form an arc whose distance is 5000 stadia, then an angle of 360 degrees must form a proportional arc of 250,000 stadia.

Today we know that Syene is really 4,530 stadia from Alexandria, and it lies three degrees longitude east of Alexandria, not on the same meridian as Eratosthenes believed. Nonetheless, Eratosthenes computed the circumference to be 250,000 stadia. Scholars differ over how long an Alexandrian stade really is, but at 10.2 Roman miles it would be 24,509 miles. The Earth is actually 24,888 miles around. Not bad for what the old philosopher called an "approximation".

A good friend of Archimedes, Eratosthenes (276BC - 196BC) invented the concept of longitude and latitude. He sketched the path of the Nile for the first time, developed a method of finding prime numbers, and compiled the first catalog of 675 stars. He drew an early map of the entire known world, compiled the first chronology of historical events, and wrote books about philosophy, history and comedy. But his measurement of the Earth, one of the great achievements of science, was suppressed. An alternate method proposed by Poseidonius led to a much smaller estimate of the earth's size (17,930 miles) that encouraged the happy illusion that a greater part of the world was known to man, and this was the standard measurement as late as 1492. Eratosthenes went blind at the age of seventy-nine and took the "philosopher's death", suicide by starvation.