Foreword
It is indeed gratifying that the Kuppuswami Sastri Research Institute is publishing Dr. Sita's Ph.D. thesis, which is a pioneering study of Krsoa Daivajña's famous commentary Bijapallava on the Bijaganita of the celebrated mathematician-astronomer Bhaskaräcärya.
Krsna Daivajña belonged to a prominent jyotiși family of Varanasi and was associated with the Mughal court at Agra. In the concluding verses of the Bijapallava (see §1.6.1 of the present work), Krsna gives his genealogy where he praises the erudition of his father Ballala, grandfather Trimalla, great grandfather Rama and Rama's father Cintamani. Among his five brothers, Ranganatha is noted for his commentary Güdhärthaprakāśaka on the Süryasiddhanta. Several Jyotișa works by his nephews Munīśvara, Gadadhara and Näräyana have come down to us (see D. Pingree, Jyotihśāstra, p. 126, for their family tree). According to Muniśvara, the family originally lived at Dadhigrama on the Payoşni river in the Vidarbha region, but Krsna's father Balläla moved to Väräņasi (cf. D. Pingree, Census of the Exact Sciences in Sanskrit, CESS, A4, p. 432ab). In the opening verses of the Bijapallava, Krsna mentions his illustrious guru parampară (see §1.6.2 of the present work). Krsna's teacher Vişnu was the pupil of Nrsimha (b. 1548) who was himself the pupil and nephew of Ganesa (b. 1507), the celebrated author of the Grahalāghava, who studied under his own father Kešava (1. 1497/1507). This Visou is presumably the son of Divakara, the pupil of Ganesa, who wrote Süryapaksašarana (see D. Pingree, Jyotihšästra, p. 37). His works on mathematics are not known but his two rules for specific types of equations are cited by Krsna in the Bijapallava (see §6.3 of the present work). At the Mughal court, Krsņa received patronage from Jahangir as well as from Abd al-Rahim Khan-i Khanan. The horoscope of the latter was included by Krsna in his commentary on Sripati's Jätakapaddhati. Krsna was a member of the team entrusted with the task of rendering Ulugh Beg's astronomical tables into Sanskrit at Akbar's translation bureau. In a Mughal miniature painting depicting the birth of Jahangir, there is a picture of an astrologer drawing a horoscope. S.R. Sarma identifies this astrologer as Krsna (see his The Archaic and the Exotic, pp. 100-07). Aside from an original work Chadakanirnaya on eclipses (cf. §1.6.4 of the present work), Krsna produced commentaries on Bhāskarācārya's Lilävati and Bijaganita and on Sripati's Jātaka-karma-paddhati. The Janipaddhati on which Krşņa is said to have written a commentary (vrtti) according to Munīśvara (cf. CESS A4, p. 438b) seems to me to be Sripati's Jätakapaddhati, although Dr. Sita regards it as a separate work. David Pingree lists two manuscripts in the CESS with the comment, 'A ikä on the Lilävati of Bhaskara II (b. 1114) is ascribed to Krsna, but it is probably a confusion with the Bijänkura (CESS A2, p. 55b). However, there cannot be any doubt that Krsna wrote a commentary on the Lilavati, for he himself refers to it in the following words.
Preface
I take great pride in writing the preface to this publication of the Institute, Bijapallava of Krsna Daivajña, critically studied by Dr. Sita Sundar Ram. She was awarded the Ph.D. degree by the University of Madras for the same, prepared and submitted under my supervision, in the year 2008. The thesis was much appreciated by the examiners and Dr. T. Hayashi, one of the examiners (also has written the Foreword here) strongly recommended the publication of the thesis at the earliest. Accordingly, it was taken up for publication by the Institute. The Institute has been publishing, from its inception, critical editions of texts related to Indian mathematics and astronomy. The Journal of Oriental Research, Madras, published by the Institute also contains articles pertaining to these subjects. Savants like Prof. T.S. Kuppanna Sastri, Prof. D.D. Kosambi, Dr. David Pingree, Dr. Arka Somayaji, Dr. K.V. Sarma and Dr. George Abraham, were involved in such academic endeavours of the Institute. Presently, Dr. M.S. Rangachari, Dr. S. Kannan, Dr. S. Madhavan, Dr. Takao Hayashi, Dr. M.D. Srinivas and others are also associated with the Institute. The text Sadratnamālā of Sankaravarman, on Indian astronomy and mathematics, with English translation and notes by Dr. S. Madhavan (Former Prof. of Mathematics, University College, Thiruvananthapuram), was published by the Institute, recently in 2011. Bijapallava of Krsna Daivajña is a landmark in this continued research activity on the part of the Institute in the field of Indian mathematics and astronomy. Ir was possible for Dr. Sita to produce such a work, since she is a graduate in Mathematics and post graduate in Sanskrit. The knowledge of both the subjects helped her a lot in understanding the mathematical texts in Sanskrit. Registered for the Ph.D. in 2001 at the Institute under my supervision. Dr. Sita studied the text more than once with me In some places we met with the difficulty of presenting our understanding of the text in mathematical language Consultations with Dr. M.S. Rangachari (Former Director and Head, the Ramanujan Institute for Advanced Study in Mathematics, University of Madras), helped us a lot in synchronising the ancient mathematical methods with the modern ones. He always had the idea that Dr. Sita's thesis should definitely be published and accordingly suggested changes and modifications in the thesis to suit the publication. I am indeed grateful to him, both as Supervisor of Dr. Sita's thesis and as the Director of the Institute. I am deeply beholden to Dr. Takao Hayashi (Professor of History of Science, Doshisha University, Kyoto, Japan), who had very willingly accepted to write the Foreword to the book on our request and also for his valuable suggestions.
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