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Mean motions and longitudes in indian astronomy

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References

  1. O. Neugebauer, “The Transmission of planetary theories in ancient and medieval astronomy”, Scripta mathematica, 22 (1956), 165–192; D. Pingree, “The Recovery of Early Greek astronomy from India”, Journal for the history of astronomy, vii (1976), 109–123; D. Pingree, “History of Mathematical astronomy in India”, Dictionary of Scientific Biography, 15 (1978), 533–633.

  2. G. de Callataÿ, Annus Platonicus: A Study of World Cycles in Greek, Latin and Arabic Sources. Publications de l’Institut orientaliste de Louvain 47. Louvain-la-Neuve, 1996, reviews all the relevant source material. A. Jones, “The Keskintos Astronomical Inscription: Text and Interpretations”, SCIAMVS, 7 (2006), 3–42, is the definitive analysis of the Keskintos inscription, the clearest use of a great year in a Greco-Roman source; B. L. van der Waerden, “The Great Year in Greek, Persian and Hindu Astronomy”, Archive for history of exact sciences, 18 (1978), 359–383 is a good presentation of the evidence, but his conclusions are not solidly proven.

  3. G. J. Toomer, Ptolemy’s Almagest (1984), 423–426.

  4. O. Neugebauer, A history of ancient mathematical astronomy, (1975), 380–468.

  5. Toomer, ibid. (ref. 3), Books IV–V for the Moon and Books IX–XI for the planets.

  6. O. Neugebauer, ibid. (ref. 4), 905–908.

  7. K. S. Shukla, Aryabhatiya of Aryabhata (1976) is the sunrise system; K. S. Shukla, Mahabhaskariya of Bhaskara I (1960) is a commentary on the sunrise system; O. Neugebauer and D. Pingree, The Pancasiddhantika of Varahamihira (2 vols, Copenhagen, 1970–1971) contains the midnight system; B. Chatterjee, The Khandakhadyaka of Brahmagupta (1972) is a commentary on the midnight system; D. Pingree, “The Paitamahasiddhanta of the Visnudharmottapurana”, Brahmavidya, xxxi-xxxii (1967–1968), 472–510.

  8. S. Prakash, A Critical Study of Brahmagupta and His Works. (Dehli, 1986), 289–314.

  9. L. González–Reimann, Tiempo Cíclico y eras del Mundo en la India, (Mexico, 1988) and L. González–Reimann, The Mahabharata and the Yugas: India’s Great Epic Poem and the Hindu System of World Ages,(NewYork, 2002).

  10. The Mahabharata,translated by Kisari Mohan Ganguli, (1883–1896), Book 12: Santi Parva, Section 231 (see http://www.sacred-texts.com/hin/m12/m12b058.htm).

  11. H. H. Wilson, The Vishnu Purana, (London, 1840), Book 1 Chapter 3, Book 3 Chapters 1–3, Book 4 Chapter 1, and Book 5 Chapter 23 (see http://www.sacred-texts.com/hin/vp/index.htm).

  12. P. Olivelle, The Law Code of Manu, (Oxford, 2004), 1.61–86. An older version, G. Bühler, The Laws of Manu, Sacred Books of the East, vol. 25 (Oxford,1886), is available (at least in some countries) at http://books.google.co.. See in particular pp. lxxxii ff.

  13. D. Pingree, The Thousands of Abū Mashar, (London, 1968), 28–29.

  14. D. Pingree, ibid. (ref. 1, 1976) 117–120, and H. Thurston, “Medieval Indians and the Planets”, DIO 8.1 (1998) 18–20, give incomplete accounts of the following procedure. Pingree in particular claims that the construction of the R values uses only period relations but no mean longitudes at the modern date.

  15. Incidentally, every one of the 10,000 four digit integers between 0 and 9999 is the final four digits of one and only one multiple of the form n × 1097, with n ranging over 0 to 9999.

  16. D. Pingree, ibid (ref. 1); D. Pingree, “Aryabhata, the Paitamahasiddhanta, and Greek Astronomy”, Studies in History of Medicine & Science, XII 1–2 New Series (1993), 69–79.

  17. R. Billard, L’astronomie Indienne, (Paris, 1971); R. Billard, “Aryabhata and Indian Astronomy”, Indian Journal of History of Sciences 12 (1977) 207.

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  18. B. L. van der Waerden, “Two Treatises on Indian Astronomy”, Journal for the history of astronomy, xi (1980), 50–62.

  19. Duke D.W., (2005) “The equant in India: the mathematical basis of Indian planetary models”. Archive for History of Exact Sciences 59, 563–576

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  20. B. L. van der Waerden, ibid. (ref. 15) uses this example to argue, incorrectly as we shall see, that it would have been straightforward for Aryabhata to use a few observations to change the midnight scheme parameters into the sunrise scheme parameters.

  21. Mercier R., (2007) “The Standard Scheme of the Moon and Its Mean Quantities”. Archive for History of Exact Sciences 61, 255–272

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  1. Department of Physics, Florida State University, Tallahassee, Fl, 32306, USA

    Dennis W. Duke

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Correspondence to Dennis W. Duke.

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Communicated by A. Jones.

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Duke, D.W. Mean motions and longitudes in indian astronomy. Arch. Hist. Exact Sci. 62, 489–509 (2008). https://doi.org/10.1007/s00407-008-0022-1

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