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Archive for History of Exact Sciences

, Volume 66, Issue 5, pp 531–555 | Cite as

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

  • Christian MarxEmail author
Article

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.

Keywords

Ptolemaios Geographike Hyphegesis Book 8 Conversion of coordinates Longitude Latitude Length of the longest day Ecliptic distance 

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References

  1. Berggren J., Jones A. (2000) Ptolemy’s geography: An annotated translation of the theoretical chapters. Princeton University Press, Princeton, NJGoogle Scholar
  2. Cuntz O. (1923) Die Geographie des Ptolemaeus. Gallia Germania Raetia Noricum Pannoniae Illyricum Italia. Reprint 1975. Arno Press, New YorkGoogle Scholar
  3. Dielman, T., and R. Pfaffenberger 1982. LAV (least absolute value) estimation in linear regression: A review. In TMIS studies in the management sciences, eds. S.H. Zanakis and J.S. Rustagi, vol. 19, 31–52. Amsterdam: North-Holland Publishing Company.Google Scholar
  4. Dielman T., and R. Pfaffenberger. 1990. Tests of linear hypotheses and LAV estimation: A Monte Carlo comparison. Communication in Statistics: Simulation and Computation 19: 1179–1199.Google Scholar
  5. Hampel F.R. (1974) The influence curve and its role in robust estimation. Journal of the American Statistical Association 69: 383–393MathSciNetzbMATHCrossRefGoogle Scholar
  6. Honigmann E. (1929) Die sieben Klimata und die Poleis Episemoi, Eine Untersuchung zur Geschichte der Geographie und Astrologie im Altertum und Mittelalter. Carl Winter’s Universitätsbuchhandlung, HeidelbergGoogle Scholar
  7. Jäger R., Müller T., Saler H., Schwäble R. (2005) Klassische und robuste Ausgleichungsverfahren. Wichmann, HeidelbergGoogle Scholar
  8. Manitius, K. 1912. Des Claudius Ptolemäus Handbuch der Astronomie. 2 Volumes, reprint 1963. Leipzig: B. G. Teubner.Google Scholar
  9. Marx C. (2011) On the precision of Ptolemy’s geographic coordinates in his Geographike Hyphegesis. History of Geo- and Space Sciences 2(1): 29–37. doi: 10.5194/hgss-2-29-2011 CrossRefGoogle Scholar
  10. Neugebauer O. (1975) A history of ancient mathematical astronomy. Springer, BerlinzbMATHGoogle Scholar
  11. Nobbe, K.F.A. (ed.). 1843–1845. Claudii Ptolemaei Geographia. 3 Volumes, reprint 1966. Hildesheim: Georg Olms Verlagsbuchhandlung.Google Scholar
  12. Pedersen O. (2011) A survey of the Almagest, With annotation and new commentary by Alexander Jones. Springer, New YorkGoogle Scholar
  13. Rawlins D. (1982) An investigation of the ancient star catalog. Publications of the Astronomical Society of the Pacific 94: 359–373CrossRefGoogle Scholar
  14. Rawlins D. (1985) Ancient geodesy: Achievement and corruption. Vistas in Astronomy 28: 255–268MathSciNetCrossRefGoogle Scholar
  15. Rawlins D. (2008) The Ptolemy geography secrets. DIO 14: 33–58Google Scholar
  16. Rawlins D. (2009) First full GD 2–7 and GD 8 joint tabulation. DIO 5: 15–42Google Scholar
  17. Sachs L. (1992) Angewandte Statistik. Springer, BerlinzbMATHGoogle Scholar
  18. Stückelberger, A., and G. Graßhoff (eds.). 2006. Klaudios Ptolemaios Handbuch der Geographie. 2 Volumes. Basel: Schwabe Verlag.Google Scholar
  19. Stückelberger, A., and F. Mittenhuber (eds.). 2009. Klaudios Ptolemaios Handbuch der Geographie. Ergänzungsband mit einer Edition des Kanons bedeutender Städte. Basel: Schwabe Verlag.Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department for Geodesy and Geoinformation ScienceTechnische Universität BerlinBerlinGermany

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