Ptolemy's longitudes and Eratosthenes' measurement of the Earth's circumference
type: Item
instance of: scholarly article
title: Ptolemy's longitudes and Eratosthenes' measurement of the Earth's circumference
zbMATH Open document ID: 1341.01006
author: Lucio Russo
published in: Mathematics and Mechanics of Complex Systems
publication date: 2016-04-25T00:00:00Z
review text: 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.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 01A20
zbMATH DE Number: 6573029
zbMATH Keywords: Eratosthenes
zbMATH Keywords: Ptolemy
zbMATH Keywords: measure of stadion
MaRDI profile type: Publication
full work available at URL: memocs.2013.1.67
OpenAlex ID: W2023546450
Wikidata QID: Q56619231
DOI: 10.2140/MEMOCS.2013.1.67
description: scientific article; zbMATH DE number 6573029