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I'm looking for a good reference on how Ptolemy used the Euclidean geometry to calculate the planets positions.

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You can always read Ptolemy himself. His "Almagest", together with the "On the Revolutions of Heavenly Spheres" by Copernicus and some extracts from Kepler can be found in "Great Books of the Western World Vol. 16". Bookfinder.com lists used copies going at about $15.00 US.

Richard Fitzpatrick has prepared an excellent analysis entitled "A Modern Almagest: An updated version of Ptolemy's Almagest" which can be found at http://farside.ph.utexas.edu/Books/Syntaxis/Syntaxis.html.

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