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References on Astronomy

Ansari, S.M.R.: A comparative study of the mathematics of ,4ryabhata I and Al-Khwarizmi
— Celebrations of the 1500th Birth Anniversary of Aryabhata I, Indian National Science Academy, New Delhi, Page I, 1976.
2. Ayyangar, A.A.K.: The Mathematics of Aryabhata Quart. Journal Myth. Soc. 16. 1925-26. 158-179
Bag. AK.; Aryabhatta as he was known to later scholars  — Celebrations of the 1500th Birth Anniversary of Aryabhatta I, Indian National Science Academy, New Delhi. page 21, 1976.
4. Bhanu Murthy, IS: A modern introduction to Ancient Indian Mathematics, Wiley Eastern Limited, New Delhi. 1992.
5, Billard, P.: Aryabhatta and Indian Astronomy, Indian Journals of History of Science, Vol. 12(2), 207-224, 1977.
6. Behari. R.: Aryabhatta as a Mathematician, Indian Journals of History of Science, Vol. 12(2). 147-149, 1977.

7. Bhaskara I: Maha-Bhaskariya and LaghuBhaskariya  Anandashram Sanskrit Granthawoli,
8. Boyer, C.B.: A history of mathematics, John Willey and Sons, New York 1968. -
9. Clark WE.: The ryabhatiya of Aryabhatta, the University of Chicago Press, Illinois, 1930.
10. Datta, B.: Two Aryabhatta’s of Al-Beruni  B.C.M.S., 17, 59-74, 1926.
11. Datta, B.B. and Singh, AN.: History of Hindu Mathematics—A Source Book Peprinted. Asia Publishing House, Bombay.
12. Elfering, K.: The area of a triangle and the volume of a pyramid as well as the area of a circle and the surface of hemisphere in mathematics of Aryabhata I, Indian Journals of History of Science Vol. 12(2), 232-236, 1977.
13. Ganguly, SK.: The Aryabhatta’s value of 
    Ann. Math. 27, 16-29, 1920.
14. Ganitanand: A few remarks concerning certain values of    in ancient India, Ganita Bharati 12,
No. 1-2, 33-39, 1990.
15. Gupta, P.C.: On some mathematical rules from the ryabhatiya. Indian Journals of History of Science, Vol. 12(2), 200-2%. 1992.
16. Jha, Parmeshwar: Aryabhatta land his contributions to mathematics. The Bihar Research Society, Patna (1988).
17, Jha, 5K.; Jha, M.: A study of the value of     known to ancient Hindu and Jaina mathematicians, J. Bihar Math. Soc., 13. 38-44, 1990.
18. Kaye, G.P.: Two Aryabhatta’s, B.M., 10, 289-92, 1910.
19. Mohan, B.: History of mathematics (In Hind), Hindi Samiti, UP. Govt., Lucknow, 1965.

20. Mule Gunokar: Great mathematicians of the world  Raj Kamal Publications, New Delhi. 1992.
21. Prakash. S.: Founders of Sciences In ancient India Research Institute of Ancient Scientific Studies, New Delhi.
22. Premi. S.: A project Report on history of ancient Indian mathematics Department of Mathematics, Meerut University. Meerut.
23. Sengupta, P.C.: The ryabhatiya (English version). J. Dept. Letters. Calcutta University. 16, 1-
56. 1927.
24. Sharma, ML.  Aryabhatta’s contribution to Indian astronomy of Indian Journal of History of Science, Vol 12, 90-99. 1977.
25. Shukla KS.: Aryabhatta. Indian National Science Academy. Bahadur Shah Jafar Marg, New Delhi.
26. Shukla, KS. and Sarina Ky.: ryabhatiya of Aryabhatcz Indian National Science Academy.
New Delhi 1976.
27. Singh, AN.: On the Indian method of root extraclion. B.C.M.S... 18, 123-140, 1927.
28. Smith, D.F.:
History of Mathematics,
Dover PublicaNons, New Delhi. 1959.
29. Swarup, AK. Bag, and KS. Shukla: Proceeding of the International Astronomical Union Collogium
held in New Delhi Cambridge University Press. 1987.
30. Upadhya. B.L.: Ancient Indian Mathematics Qn Hind). Vigyan Bharati, New Delhi, 1971.
31, Voladavsky. A.: Mathematical achievements of Aryabhatta. Indian Journal of History of Science,
Vol. 12(2), 167-172. 1977,
32. Vano Mlchio: Three types of Hindu sine tables; Indian Journal of History of Science, Vol. 12(2).
83-89. 1977.

1. Dixit S B, 1989, Page number 144-145, Bharatiya Jyotisha Shastra (in

Marathi), Varda Publications, Pune

2. Bhat M R, 1995, translation of Varhamihira’s Brihat Samhita, Motilal

Banarasidas, for RSB see XLVII (14)

3. Burgess Rev. Ebenenezer, translation of Surya Siddhanta, Motilal

Banarasidas, 1860 and 1989 (Sanskrit version published by Chaukhamba

Surabharati Prakashan, Varanasi)

4. Dvivedi, Maha-mahopadhyaya Pandit Sudhakar, translation of Mahasiddhanta

by Aryabhatta – 2, 1995, (Chaukhamba Sanskrit Pratishthan, Delhi)

5. Daivajna Shri Ganesh, Graha-Laghavam, Motilal Banarasidas

6. Colebrooke H T, Essays on history, literature and religion of Ancient India

7. Shukla Shankar K, Bhaskara I, Bhaskara I and his works II. Maha-Bhaskariya

(Sanskrit) (Lucknow, 1960)

8. Chaterjee B, 1976, translation of Khandakhadyaka, Motilal Banarasidas

9. Sarama Ramaswarup, 1966 translation of Bramhasphuta Siddhanta by

Brahmagupta, Vol.: I, II, III, IV. Indian Institute of Astronomical & Sanskrit

Research - New Delhi.

10. Chaterjee B, 1981, translation of Sisyadhivriddhida tantra by Lalla, Indian

National Science Academy

11. Marriot C, SkyMap Pro, version 8.0

12. Harwit M, 1998, Astrophysical Quantities, Springer

13. Horizons, version DE-408

14. Chhatre, Kero Laxman, Grahasadhana Koshtak,

15. Kelley J T, Dickson S M, Maine's History of Sea Level Changes,

16. Barnhardt, W. A., W. R. Gehrels, et al. (1995). "Late Quaternary relative sea level change in the western Gulf of Maine: Evidence for a migrating glacial forebulge." Geology 23(4): 317-320. See:

17. Jarrige Jean-Francois, Meadow, R H, 1980, Scientific American, October,

1980 page 102

18. Koenraad Elst, Leuven, 1998, Astronomical data and the Aryan question







References on Ancient Indian



Clark, William Eugene, The ryabhatiya of ryabhata, An Ancient Indian Work on Mathematics and Astronomy, The University of Chicago Press, Chicago, Illinois. 1930.

Kay, G. R., Hindu Astronomy, Ancient Science of the Hindus, Cosmo Publications, New Dehli. India, 1981.

Pingree, David, Jyotihsastra, Astral and Mathematical Literature, Otto Harrassowitz, Weisbaden, 1981.

Sastri, Pundit Bapu Deva, and Lancelot Wilkinson, The Surya Siddhnta, or An Ancient System of Hindu Astronomy, Philo Press, Amsterdam, 1974.

Sen, S. N., and K. S. Shukla, History of Astronomy in India, Indian National Science Academy, New Dehli, 1985.


Since I first published this page several people have offered advice and encouragement. Some have asked for further information. In particular I wish to thank Dr. Vijay Bedekar and David B. Kelley for encouraging further research. This updated and expanded page has resulted. Thanks to Ramana Bhamidipati for his input and suggestions.


At this rewriting, Jan. 1, 2001, I still await some answers to the questions posed below. This may be indicative of the answers. To date I have found no indication of older accurate astronomical constants or published indications of modern writers noticing the accuracy of the data discovered in the Indian sources.

  • Do you know of any source previously noticing and publishing the accuracy of ryabhata's ratio?
  • Do you know of any older record reflecting such an accurate astronomic ratio? From India? In Sanskrit? From other parts of the world?
  • Do you know of any astronomic record reflecting such an accurate astronomic ratio prior to the last two centuries?
  • When did modern astronomers first arrive at an astronomic ratio of comparable accuracy?

Larousse Encyclopedia of astronomy, Prometheus Press, NY 1959

Amateur Astronomy , NewnessBooks, Middlesex ,UK, 1985

Indian Astronomy a source Book BV Subbarayappa and KV Sharma Nehru Center, Bombay, 1985

* A Bibliography of Sanskrit Works in Astronomy and Mathematics
S N Sen with the research assistance of A K Bag and S R Sarma (1966) 258 pp. A bibliography of source materials indispensable for the study of history of astronomy and mathematics in ancient and medieval India.
Rs.20/= US $ 5/=

    • History of Astronomy in India
      Eds. S N Sen and K S Shukla (Second revised edition 2000) 529pp.
      Rs.800/= $.250/=

  • The Sulbasutras
    S N Sen and A K Bag (1983) 293pp. The Sulbasutras are the manuals for the construction of altars for fire-sacrifices, an ancient cult fully established in the time of Samhitas. The origin of mathematics in India lies embedded in these ancient priestly practices. The book presents the critical texts and translation of four Sulbasutras.
    Rs.85/= US $.30/=

  • Aryabhatiya of Aryabhata (Critically edited with translation and notes)
    K S Shukla and K V Sarma (1976) 219 pp. The volume forms a critical edition of aryabhatiya based on original manuscripts and external testimonials 1976) 219 pp.
    Rs.21.50 US $.7/=

  • * Aryabhatiya of Aryabhata (with the commentary of Suryadeva Yajvan)
    Ed. K V Sarma (1976) 200pp. The volume comprises of critical edition of the Aryabhatiya with the elucidative commentary of Suryadeva Yajvan (b.1911) based on original palm leaf manuscripts.
    Rs.25/= US $.8/=

  • * Aryabhatiya of Aryabhata (with the commentary of Bhaskara & Somesvara)
    Ed. K S Shukla (1976) 382 pp. The volume sets out the critical text of the Aryabhatiya with the earliest available commentary on the work by Bhaskara ( A.D. 629 ) as supplemented by a later commentrator Somesvara.
    Rs.40/= US $.13/=
     Vedanga Jyotisa & Lagadha (in its R K and Yajus Recensious) (with the translational notes of Professor T S Kuppanna Sastry)
    Ed. : K V Sarma (1985) 74pp.
    Rs.25/= US $.8/=


    A Concise History of Sciences in India
    Eds. D M Bose, S N Sen and B V Subbarayappa (Reprinted 1989) 689pp.
    Rs.200/= US $.70/=

Aryabhata. The Aryabhatiya of Aryabhata - An Ancient Work on Mathematics and Astronomy. Walter E. Clark, Trans. and Ed. University of Chicago Press: Chicago, Illinois, 1930.

"Aryabhata I." Biographical Dictionary of Mathematicians: Reference Biographies from the Dictionary of Scientific Biography. Vol. 1, (150-152). Charles Scribner and Sons: New York, 1991.

Hayashi, Takao, "Aryabhata's Rule and Table for Sine-Differences," Historia Mathematica, vol. 24 (1997), pp. 396-406.

Srinivasiengar, C. N. The History of Ancient Indian Mathematics. The World Press Private LTD: Calcutta, 1967.

Suzuki, Jeff. A History of Mathematics. Prentice Hall: New Jersey, 2002.

Watson, Francis. A Concise History of India. Thames and Hudson: London, 1974.

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