Bibliography (A selection of references which I have found useful. Not all are referenced in the text.) Sources with translations and/or annotations. (No reference is given for the R. gveda; there are a large number of transla- tions and interpretations in a large number of languages. Precise references to chapter, poem and verse for questions related to number names can be found in Bhagyashree Bavare and P. P. Divakaran, “Genesis and Early Evolution of Decimal Enumeration: Evidence from Number Names in R. gveda”, Ind. J. Hist. Sci. vol. 48.4 (2013) p. 535). [AB-C] The Aryabhat¯ .¯ıya translated into English with commentary by Wal- ter Eugene Clark, University of Chicago Press, Chicago (1930). [AB-S] Aryabhat¯ .¯ıya of Aryabhat¯ .a, critically edited with English transla- tion, notes, etc. by Kripa Shankar Shukla in collaboration with K. V. Sarma, Indian National Science Academy, New Delhi (1976). [BM-H] The Bakhshali Manuscript, with translation and commentary by Takao Hayashi, Egbert Forsten, Groningen (1995). [GK-S] Gan. itakaumud¯ı of N¯ar¯ayan. aPan. d. ita, translated with notes by Parmanand Singh, published periodically in instalments in Gan. ita Bh¯arat¯ı, (1998 - 2002). [Ne-W] The Mathematical Papers of Isaac Newton (vols. I - VIII), edited with notes and translations from the Latin, where necessary, by D. T. Whiteside, The University Press, Cambridge (1967 onwards). [PS-K] Pa˜ncasiddh¯antik¯a of Var¯ahamihira with translation and notes by T. S. Kuppanna Sastry, P.P.S.T. Foundation, Madras (1993). [SiSi-P] L’Œuvre math´ematique et astronomique de Bhaskaracarya: Le Siddhantasiromani I-II, with translation and commentary in French by Fran¸cois Patte, Librairie Droz, Paris (2004). © Hindustan Book Agency 2018 423 P. P. Divakaran, The Mathematics of India, Sources and Studies in the History of Mathematics and Physical Sciences, https://doi.org/10.1007/978-981-13-1774-3 424 Bibliography [SuSi-B] The Sˆurya Siddhˆanta, translation with notes by Ebenezer Burgess, Motilal Banarsidass, Delhi (1989, reprint). [SuSu-SB] The Sulbas¯´ utras of Baudh¯ayana, Apastamba,¯ K¯aty¯ayana and M¯anava, with translations and commentary by S. N. Sen and A. K. Bag, Indian National Science Academy, New Delhi (1983). [TaiSam-K] The Veda of the Black Yajus School entitled Taittir¯ıyasam. hit¯a, translated by A. B. Keith, Harvard University Press, Cambridge (1914). [TaSa-RS] Tantrasa˙ngraha of N¯ılakan. tha Somay¯aj¯ı, with translation and com- mentary by K. Ramasubramanian and M. S. Sriram, Hindustan Book Agency, New Delhi (2011). [YB-S] Gan. ita-Yukti-Bh¯as.¯a of Jyes.t.hadeva, vol.I (Mathematics), Malay- alam text with English translation by K. V. Sarma (and explana- tory notes by K. Ramasubramanian, M. D. Srinivas and M. S. Sriram), Hindustan Book Agency, New Delhi (2008). [YB-TA] Yuktibh¯as.¯a (Part I - General Mathematics), Malayalam text with vy¯akhy¯a in Malayalam by Ramavarma (Maru) Tampuran and A. R. Akhileshvara Ayyar, Mangalodayam Ltd., Trichur (1948). To these has to be added Colebrooke’s translation with notes of L¯ıl¯avat¯ı and B¯ıjagan. ita and chapters XII and XVIII of Br¯ahmasphut.asiddh¯anta: [Co] Henry Thomas Colebrooke, Algebra with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bh´ascara, Sharada Publishing House, Delhi (2005, reprint). Sources in the original (without translation or detailed commentary). [ABB] Aryabhat¯ .¯ıya with the bh¯as.ya of Nilakantha (on the Gan. ita, K¯alakriy¯a and Gola chapters); Parts I and II, K. Sambasiva Sastri (ed.), Gov- ernment of Travancore, Trivandrum (1930, 1931); Part III, Suranad Kunjan Pillai (ed.), University of Kerala, Trivandrum (1957). [JM] Jyotirm¯ım¯am. s¯a of Nilakantha, K. V. Sarma (ed.), Vishveshvaranand Institute, Hoshiarpur (1977). [SD] Siddh¯antadarpan. a of Nilakantha with his own analytic commentary, K. V. Sarma (ed.), Vishveshvaranand Institute, Hoshiarpur (1976). [TaSa-S] Yuktid¯ıpik¯a of Shankara is part of Tantrasam. graha of Nilakantha (with Yuktid¯ıpik¯a and Laghuvivr.ti), K. V. Sarma (ed.), Vishvesh- varanand Institute, Hoshiarpur (1977). Bibliography 425 History of mathematics and related subjects Books [DS] Bibhutibhushan Datta and Avadhesh Narayan Singh, History of Hindu Mathematics vols. I and II, Bharatiya Kala Prakashan, Delhi (2004, reprint). [If] Georges Ifrah, Histoire universelle des chiffres, Robert Laffont, Paris (1994). [Jo] George Gheverghese Joseph The Crest of the Peacock (third edi- tion), Princeton University Press, Princeton and Oxford (2011). [Pl] Kim Plofker, Mathematics in India, Princeton University Press, Princeton and Oxford (2009). [SA] T. A. Sarasvati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidass, Delhi (1999). [Sa-HKSHA] K. V. Sarma, History of the Kerala School of Hindu Astronomy, Vishveshvaranand Institute, Hoshiarpur (1972). [St-RM] Frits Staal, Ritual and Mantras: Rules Without Meaning, Motilal Banarsidass, Delhi (1996, Indian edition). [St-Veda] Frits Staal, Discovering the Vedas. Origins, Mantras, Rituals, In- sights, Penguin Books, New Delhi (2008). [Th-EI] Romila Thapar, Early India from the Origins to AD 1300,Pen- guin Books India, New Delhi (2003). [Th-CP] Romila Thapar, Cultural Pasts. Essays in Early Indian History, Oxford University Press, New Delhi (2000). Collections [Agni] Frits Staal (ed.) Agni. The Vedic Ritual of the Fire Altar vol. II, Motilal Banarsidass, Delhi (2001, Indian edition). [CHIM] G´erard G. Emch, R. Sridharan and M. D. Srinivas (eds.) Con- tributions to the History of Indian Mathematics, Hindustan Book Agency, New Delhi (2005). [MEMCII] Victor J. Katz (ed.) The Mathematics of Egypt, Mesopotamia, China, India and Islam. A sourcebook, Princeton University Press, Princeton and Oxford (2007). [SHIM] C. S. Seshadri (ed.) Studies in the History of Indian Mathematics, Hindustan Book Agency, New Delhi (2010). [Sunya] A. K. Bag and S. R. Sarma (eds.) The Concept of S¯´unya, Indira Gandhi National Centre for the Arts, New Delhi (2003). 426 Bibliography Finally, there is the invaluable web-based archive of J. J. O’Connor and E. F. Robertson, unusually good on Indian mathematics. The master URL is http://www-history.mcs.st-andrews.ac.uk/index.html with links leading to various sub-indices. Index Abel resummation formula, 326, Anuyogadv¯ara S¯utra, 123 339 Apastamba, 14, 44, 47–50, 58–60, absolutely convergent, 328 63, 67, 69, 70, 78, 131, Achaemenid, 34 191, 237, 394, 395 Achyuta, 258, 267, 271–273, 275, Apollonius, 397 276, 281, 420, 421 Aramaic, 34 addition formula, 285, 292, 297, Aranyakas, 30 302 Archimedes, 178, 198, 221, 311, addition theorem, 194, 197, 295, 357, 382, 397, 398, 420 297, 299–301, 311, 353, arctangent series, 243, 262, 295, 405 296, 311, 313, 327–329 Adhikari, R., 87 arddhajy¯a, 303 ¯adyasam. khy¯a, 100 ardhajy¯a, 40, 154, 194, 400 Agni, 116 area and volume of the sphere, Ahichhatra, 278, 281 202, 205, 206, 296, 319, Ajanta, 163 329, 332, 357 ¯ak¯a´sa, 127 area theorem, 241, 246, 252, 253, Akbar, 220 298, 414 Alattiyur, 258, 265, 266, 273, 276, area-scaling transformations, 55 282, 420 Aristotle, 135, 403 Alberuni, 218, 219, 384, 387 arithmetic series, 170, 171, 180, Alexander, 32, 34, 144, 145, 149, 184 383 Arjuna, 124 Alexandria, 149–151, 153, 154, 172, Artha´s¯astra, 146, 147, 154 178, 197, 209, 245, 417 Aryabhata, 1, 3, 7, 8, 14, 17, 18, Alexandrian, 15, 151, 152, 156, 40, 54, 96, 100, 110, 123, 245, 246 125, 134, 143, 146–148, algebraic identities, 54, 60, 69, 228, 150, 151, 153, 155–162, 236, 240, 244, 247, 294, 164–167, 170, 171, 361, 402 175–189, 191–213, Almagest, 153 216–218, 220, 222, 225, Amitabha, 163, 166, 384 226, 230, 240, 242, 245, Amoghavarsha, 215, 216 246, 254, 258, 259, an. u, 146 261–263, 265, 267–269, anum¯ana, 270 271, 275, 286–290, an. upr¯ayam, 319, 347, 356 292–297, 299, 303, 311, © Hindustan Book Agency 2018 427 P. P. Divakaran, The Mathematics of India, Sources and Studies in the History of Mathematics and Physical Sciences, https://doi.org/10.1007/978-981-13-1774-3 428 Index 316, 319, 322, 331–333, astrology, 151, 153 335, 336, 340, 345, 347, asymptotic behaviour, 323, 341, 350, 353, 355, 357, 373, 361, 362 382, 384–387, 389, 393, asymptotic limit, 321, 335, 336 394, 396, 401–405, 410, asymptotically dominant, 341 412, 413, 417, 419 Atharvaveda,30 Aryabhata II, 188, 189, 208, 384 atomic numbers, 101, 104–109, Aryabhata school, 259 112, 116, 118, 120, 127, Aryabhata’s rule, 195–199, 202, 129, 130, 364, 409 204, 211, 301, 339, 403 Avanti, 214, 218, 383 Aryabhatan, 206, 208, 214–217, avyakta r¯a´si, 392 236, 245, 246, 259, 265, axioms, 97, 98, 102, 406 266, 276, 291, 293, 295, Ayyar, Akhilesvara, 186, 259, 260 300, 346, 356, 384, 391, 395, 417 Br.haspati, 389 Aryabhat¯ .¯ıya, 6, 7, 9, 11, 14, 41, 42, Babylonia, 90, 416 53, 54, 62, 110, 121, 143, Babylonian, 74, 79, 91, 94, 121, 148, 154, 156, 157, 160, 131, 132, 197, 391, 397, 161, 164, 166, 167, 398, 417, 419 170–172, 175–177, 180, Bakhshali manuscript, 10, 41, 64, 185, 190, 191, 193, 194, 123, 126, 128, 129, 133, 198, 203, 205, 206, 134, 167, 170, 171, 182, 208–210, 212, 213, 216, 184, 219, 305, 320, 365, 220, 240, 259, 263, 391, 392, 395 267–269, 276, 288, 292, Bakhshali square root, 172, 292, 394, 395, 403 307, 371, 411, 416 ¯ Aryabhat.¯ıyabh¯as.ya, 7, 14, 15, 157, bakul¯adhis..thita . vih¯ara, 285 161, 175, 178, 181, 185, Balagangadharan, K., 260 198, 216, 261, 263, base, 93, 104, 105, 111 267–271, 273, 285, 293, based numbers, 97, 104, 309 294, 297, 302, 309, 310, basic π series, 313, 328, 329, 359, 322, 377, 378, 390, 400, 372–374, 376 401 Baudhayana, 14, 44, 46, 47, 49, Ary¯¯ as..ta´sata,41 55–57, 60, 61, 63–70, 73, asam.