Comment on the origin of the equant papers by Evans, Swerdlow, and Jones

Journal for the History of Astronomy

Volumn 36, Issue 1, 2005, Pages 1-6

  Duke, Dennis W ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

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[No Author keywords available]

Indexed keywords

EID: 33744982854     PISSN: 00218286     EISSN: None     Source Type: Journal    
DOI: 10.1177/002182860503600101     Document Type: Article

References (16)

1. James Evans, "on the function and probable origin of Ptolemy's equant", American journal of physics, lii (1984), 1080-9.
2. Noel Swerdlow, "The empirical foundations of Ptolemy's planetary theory", Journal for the history of astronomy, xxxv (2004), 249-71.
3. Alexander Jones, "A route to the discovery of non-uniform planetary motion", ibid., 375-86.
4. James Evans, The history and practice of ancient astronomy (New York, 1998), 364.
5. The details of the calculation may be found in Olaf Pedersen, A survey of the Almagest (Odense, 1974), 285-6,
6. or Otto Neugebauer, A history of ancient mathematical astronomy (New York, 1975), 179-80.
7. Since the sidereal period of Mars is about 1.88 years, it will always pass perigee in just less than a year after it passes apogee, and vice versa. Thus, having analysed at least one trio, the analyst would be able to predict the dates of these apsidal line passings quite accurately.
8. This translation is by Jones, op. cit. (ref. 3).
9. B. L. van der Waerden, "Ausgleichspunkt, 'Methode der Perser, und indische Planetenrechnung", Archive for history of exact sciences, i (1961), 107-21, made the original suggestion and offered a justification based on a power series analysis. More recently Dennis Duke, "The equant in India: The basis of ancient Indian planetary models" (2004, submitted), has presented detailed numerical comparisons that remove any doubt that in fact the bisected equant underlies the Indian planetary models.
10. D. Pingree, "The Paitamahasiddhanta of the Visnudharmottapurana", Brahmavidya, xxxi-xxxii (1967-68),472-510;
11. K. S. Shukla, Aryabhatiya of Aryabhata (New Delhi, 1976);
12. B. Chatterjee, The Khandakhadyaka of Brahmagupta (Calcutta, 1972);
13. and K. S. Shukla, Mahabhaskariya of Bhaskara I (Lucknow, 1960).
14. D. Pingree, "On the Greek origin of the Indian planetary model employing a double epicycle", Journal for the history of astronomy, ii (1971), 80-85;
15. idem, "The recovery of early Greek astronomy from India", Journal for the history of astronomy, vii (1976), 109-123;
16. and idem, "History of mathematical astronomy in India", Dictionary of scientific biography, xv (1978), 533-633.