Investigations of the coordinates in Ptolemy's Geographike Hyphegesis Book 8

TL;DR

This paper reconstructs and analyzes the original coordinate conversions in Ptolemy's Book 8, revealing differences between recensions and uncovering new methods used for calculating geographical data.

Contribution

It provides a detailed reconstruction of Ptolemy's coordinate conversion methods, including the discovery of a linear approximation for ecliptic distances and analysis of recension differences.

Findings

Differences between Ω- and Ξ-recensions documented.

Original linear conversion method for ecliptic distances uncovered.

Length of the longest day based on linear interpolation from Mathematike Syntaxis.

Abstract

In Book 8 of his Geographike Hyphegesis Ptolemy gives coordinates for ca. 360 so-called noteworthy cities. These coordinates are the time difference to Alexandria, the length of the longest day, and partly the ecliptic distance from the summer solstice. The supposable original conversions between the coordinates in Book 8 and the geographical coordinates in the location catalogue of Books 2-7 including the underlying parameters and tabulations are here reconstructed. The results document the differences between the $\Omega$- and $\Xi$-recension. The known difference in the longitude of Alexandria underlying the conversion of the longitudes is examined more closely. For the ecliptic distances from the summer solstice of the $\Omega$-recension it is revealed that they were originally computed by means of a so far undiscovered approximate, linear conversion. Further it is shown that the lengths of the longest day could be based on a linear interpolation of the data in the Mathematike Syntaxis 2.6.