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Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion - Bibliography and Further Reading

Sandra M. Caravella (New Jersey City University)

Good accounts of early astronomy can be found in [5], [11], and [19]; [11] and [19] also contain sections on early trigonometry. Presentations of the history of astronomy and trigonometry within the more general context of the history of mathematics can be found in [2] and [7]. For discussions of early astronomy focusing mainly on planetary models and the Copernican Revolution, see [3] and [10]. The various websites listed below offer Java animations of many of the geometric models of early astronomy, as well as general information pertaining to the subject. The primary source for Greek astronomy and trigonometry is Ptolemy’s Almagest; [20] is a good English translation. Finally, it should be mentioned that [8] contains classroom resource materials utilizing various ideas from the history of trigonometry and astronomy.

1. Scott R. Anderson, “Introduction to Astronomy, Lecture 5: The Motion of the Planets,” Open Course,, accessed September 5, 2008.

2. Carl B. Boyer, A History of Mathematics, 2nd edition, revised by Uta C. Merzbach, John Wiley & Sons, New York, 1991.

3. Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution, 2nd revised ed., Dover Publications, Mineola, 2001.

4. Dennis Duke, “Ancient Planetary Model Animations,”, accessed September 5, 2008.

5. James Evans, The History and Practice of Ancient Astronomy, Oxford University Press, New York, 1998.

6. Andres Vargas Idrobo, “Ptolemy’s Theory of Superior Planets,”, accessed September 5, 2008.

7. Victor J. Katz, A History of Mathematics: An Introduction, 3rd ed., Addison-Wesley, Boston, 2008.

8. Victor J. Katz and Karen Dee Michalowicz, eds., Historical Modules for the Teaching and Learning of Mathematics (on CD-ROM), Mathematical Association of America, Washington DC, 2004.

9. Rosemary Kennett, “Epicycles and Deferents,”, accessed September 5, 2008.

10. Thomas S. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Harvard University Press, Cambridge, 1957.

11. C. M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, Cambridge University Press, Cambridge, 2004.

12. Craig Sean McConnell, “Models of Planetary Motion from Antiquity to the Renaissance,”, accessed September 5, 2008.

13. Otto Neugebauer, A History of Ancient Mathematical Astronomy, Part 1, Springer-Verlag, New York, 1975.

14. Robert R. Newton, The Crime of Claudius Ptolemy, Johns Hopkins University Press, Baltimore, 1977.

15. Scott C. Smith, “Retrograde Motion,”, accessed September 5, 2008.

16. “Ptolemaic System Generator,” Nebraska Astronomy Applet Project,, accessed September 5, 2008.

17. “Ptolemy’s Epicycle,”, accessed September 5, 2008.

18. Noel M. Swerdlow, “The Empirical Foundations of Ptolemy’s Planetary Theory,” Journal for the History of Astronomy, 35 (2004), 249-271.

19. Hugh Thurston, Early Astronomy, Springer-Verlag, New York, 1994.

20. G. J. Toomer, transl., Ptolemy’s Almagest, Princeton University Press, Princeton, 1998.

21. Greg Van Brummelen, “Animations of Ptolemy’s Planetary Models,”, accessed September 5, 2008.

Sandra M. Caravella (New Jersey City University), "Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion - Bibliography and Further Reading," Convergence (August 2010), DOI:10.4169/loci003120