Ptolemy's longitudes and Eratosthenes' measurement of the Earth's circumference
Although it has been noted that the longitudes of 6345 localities reported by Ptolemy in his \textit{Geographia} are in error, one that dilates their differences, this error has not been so far analyzed statistically. By restricting his analysis to cities with known locations, the author establishes that the dilatation in longitude differences performed by Ptolemy is by a factor of 1.428. This is then used to obtain a confirmation of Hultsch's 1882 determination, on philological grounds, of the value of the ``stadion'' used by Eratosthenes in his determation of the circumference of the Earth, as being 157.5 meters long, and to discard the possibility that Eratosthenes' stadion was the ``Attic stadion'' of 185 meters. The author also presents a plausible explanation for why all authors except Cleomedes tell us that the value Eratosthenes determined for the circumference of the Earth is \(252 000\) stadia. It came from \(48\times 5250 = 252 000\), where \(5 250\) stands for the distance in stadia between Alexandria and the Northern Tropic and \(\frac{1}{48}\) of a complete turn was the measure of the angle between the vertical and the direction of the sunbeams at noon on the day of the summer solstice in Alexandria.
scientific article; zbMATH DE number 6573029