Let the arc of the Earth between Alexandria and Syene be called arc *AS*, and let the full circumference of the Earth be called arc *EC*.

Let the angle at the center of the Earth be called angle a, and let the full 360° of the circle be called angle b.

By Euclid III-27, we have arc *EC*/arc *AS* = angle b/angle a.

By hypothesis, the length of arc *AS* is 5000 stades, and angle a is equal to 1/50th of a circle.

Since angle b is the angle measure of a complete circle, angle b= 1 circle.

Substituting these real number values into the previous ratio, we get

arc *EC*/arc *AS* = angle b/angle a

arc *EC* /5000 stades = 1/(1/50)

arc *EC * = 5000 stades/(1/50)

arc *EC * = 250,000 stades.

Therefore, since the length of arc *EC* is equal to the circumference of the Earth, we get that the circumference of the Earth is approximately 250,000 stades.