October 9, 2014
In the third century BCE, Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. We know something of Eratosthenes’ method, numerical assumptions, and the final result of 250,000 stades, because of a short account by an elementary astronomical writer named Cleomedes. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better measurements and revised his estimate, or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved by a number of ancient writers. I will show that Eratosthenes’ Earth circumference of 252,000 stades follows from assuming a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. I’ll discuss the consequences for our understanding of his program. He has gotten credit for something he didn’t do (devise the earliest geometrical method to measure the Earth)—and gotten no credit for something he did do (which was to carry the program to a higher level of sophistication).