I remember that I read, some time ago, that Erathostenes calculated the circumfernce of the Earth using the distance between Syene and Alexandria, calculated in turn by others starting from the circumference of the Earth.
To prove It, the author used arguments that convinced me at the time, yet I don't remember the name of the book.
So I guess the question Is: Is someone aware of this hypothesis? Is there a book you could point me toward?
This might refer to the wrong circumference hypothesis, but it concerns not Eratosthenes but Ptolemy. There were many issues with Erathostenes's measurement, but circularity was not one of them, see How did Eratosthenes determine that Alexandria and Syene were on the same meridian? Ptolemy, on the other hand, as might have been his custom (he is alleged to have done similar things with Hipparchus's data), used Roman itineraries (road distance measurements), and a (widely off) value of Earth's circumference taken from Posidonius, to determine longitudes of various locations on his maps. Then he implied that he determined the longitudes from astronomical measurements (proposed by Hipparchus), and used them to "derive" the distances. At least, so the hypothesis goes. Here is Scheglov's description from The Accuracy of Ancient Cartography Reassessed: The Longitude Error in Ptolemy’s Map:
"In recent years a number of researchers—Dennis Rawlins (Baltimore), Lucio Russo (Rome), Irina Tupikova (Dresden), and Klaus Geus (Berlin)—have independently proposed essentially the same hypothesis. They all suggest that the longitudinal stretching of Ptolemy’s map can be explained completely by a single factor: using the wrong value for the circumference of the Earth... On the basis of these observations, it has been argued that the east–west stretching of Ptolemy’s map was caused by a change in the proposed value of the Earth’s circumference. This means that all the linear distances (in stades, miles, etc.) underlying his map had initially been supposed to be measured on a sphere with Eratosthenes’ circumference, but eventually were converted to angular units (degrees) on a much smaller sphere. As a result, all the distances when expressed in angular units increased by a factor of 1.4... Ptolemy committed the same “crime” that was imputed to his astronomical works by Robert Newton: he not only appropriated the achievements of his predecessors but also perverted them completely.
The issue is controversial, and Shcheglov argues for an alternative explanation that has to do with differing lengths of the stade used in various reported values of the circumference. In that case, Eratosthenes's values were as off as Ptolemy's, but in the opposite direction, and likely because he relied on inaccurate distance measurements reported by travelers.
