\textit{Gaṇita-Yukti-Bhāṣā} (Rationales in mathematical astronomy) of Jyeṣṭhadeva. Volume I: Mathematics. Volume II: Astronomy. A critical translation of the original Malayalam text by K. V. Sarma. With explanatory notes by K. Ramasubramanian, M. D. Srinivas and M. S. Sriram
Kerala (on the southwestern coast of India) has traditionally played an important role in the history of Indian mathematics and astronomy. Some of the most important mathematicians from the area include Mādhava (14th c.) and Nīlakaṇṭha Somayājī\ (ca.\ 1500), the author of the well-known astronomical work \textit{Tantrasaṅgraha}. The book under review contains an edition and English translation with explanatory notes of the \textit{Gaṇita-yukti-bhāṣā} (\textit{Rationales in Mathematical Astronomy}, ca.\ 1530) by a younger contemporary of Nīlakaṇṭha by the name of Jyeṣṭhadeva. This work provides unusually extensive explanations of the astronomical theories, constants, and planetary computations in the \textit{Tantrasaṅgraha}. It is also extraordinary in that it was written in the local language of Kerala, Malayalam, rather than in Sanskrit, the common scholarly language in pre-modern India. In spite of earlier partial and complete editions and scattered studies on particular topics, the \textit{Gaṇita-yukti-bhāṣā} is still relatively unknown. The only original division of Jyeṣṭhadeva's work is that into a mathematical and an astronomical part. The further division into topics and sub-topics as presented in the edition and translation in the book here abstracted was made by the editor of the text, K. V. Sarma. The 7 mathematical and 8 astronomical topics by which he divided the text are the following: fundamental operations, ten basic algebraic problems, fractions, rule of three, reduction and pulverisation, relation between circumference and diameter, sines; zodiac and planetary motions, the heavenly sphere, problems of spherical astronomy, shadows and rising and setting points of the ecliptic, eclipses and parallax, \textit{vyatīpāta}, reduction to the ecliptic, and lunar phases. Both the English translation of the \textit{Gaṇita-yukti-bhāṣā} and the critical edition on the basis of nine versions of the work (including various palm-leaf manuscripts, some late copies of such manuscripts, the earlier printed editions, and a copy of the Sanskrit translation) were carefully prepared by Sarma before his decease on January 14, 2005. The explanatory notes supplied by three of his close colleagues elucidate the theories and algorithms in the text in a very helpful way by means of modern equations and diagrams. The book comes with a number of appendixes and other additional chapters which make it even more useful. A Malayalam-English glossary of technical terms (with references to the usually detailed definitions in the text), a two-page second appendix listing the quotations from earlier works found in the \textit{Gaṇita-yukti-bhāṣā} (unfortunately only in Malayalam script), and an index of topics, terms, and names appear at the end of vol.~2. Of particular interest is an epilogue in vol.~1 dealing extensively with the topic of proofs in Indian mathematical and astronomical treatises, which is supplemented by the lists of Sanskrit works with rationales for mathematical and astronomical theories and computations in Sections 7 to 10 of the Introduction. The only things that this reviewer missed were a comprehensive bibliography of the secondary literature (not all references in the footnotes are so easy to follow) and English translations for some of the Malayalam and Sanskrit quotations in the Introduction. All in all, this is a very useful publication which makes an important, hitherto hardly known source of Indian mathematics and astronomy accessible to a wide audience.
scientific article; zbMATH DE number 5367216