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Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva (c.1530) is a seminal text of the Kerala school of astronomy. It is composed in the Malayalam language and presents detailed yuktis or explanations and demonstrations for the results and processes of mathematical astronomy. The text, comprising fifteen chapters, is naturally divided into two parts, mathematics and astronomy, and purports to give an exposition of the techniques and theories employed in the computation of planetary motions as set forth in the great treatise Tantrasangraha (c.1500) of Nilakantha Somayaji. Even though the importance of Ganita-yukti-bhasa was brought to the attention of modern scholarship by C.M Whish in the 1830s, a critical edition of the entire Malayalam text is published here for the first time along with an English translation and detailed explanatory notes.
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From the reviews:
"The book under review contains an edition and English translation with explanatory notes of the Ganita-yukti-bhasa ... . The explanatory notes supplied ... elucidate the theories and algorithms in the text in a very helpful way by means of modern equations and diagrams. ... a number of appendixes and other additional chapters which make it even more useful. ... All in all, this is a very useful publication which makes an important ... source of Indian mathematics and astronomy accessible to a wide audience." (Benno van Dalen, Zentralblatt MATH, Vol. 1160, 2009)
"In addition to Sarma's translation of the GYB, Ramasubramanian, Srinivas and Sriram provide extensive and invaluable explanatory notes on Jyesthadeva's derivations ... . Volume I (Mathematics) will be of the greatest interest to the mathematical community, and is well worth inclusion in any library ... oriented towards undergraduate teaching. ... it functions as rich and accessible collection of primary-source material for undergraduate classes in the history of mathematics. ... Volume II (Astronomy) is recommended for any collection in the history of mathematics ... ." (Homer S. White, The Mathematical Association of America, July, 2009)
"The work accomplished by the editors in issuing the mathematical and astronomical parts of the Ganitayuktibhasa must be applauded. ... one can easily understand how Jyesthadeva approximates the circumference of a circle first by constructing a polygon of an uncountable number of sides, then by using power approximations of sines. One can also learn how he computes the mean and true motions of Mercury, and the area of a cyclic quadrilateral, etc. All is thoroughly explained with comprehensive drawings and tables." (Agathe Keller, Journal for the History of Astronomy, May, 2010)
"The book under review Ganita-yukti bhasa (Rationales in mathematical astronomy) of Jyesthadeva ... rightly fulfils a longunmet need. GYB provides a systematic exposition of the contributions of the Kerala school and is published in two volumes. ... This two volume set is a rare and valuable addition to the literature on the history of mathematics." (Hansraj Joshi, Mathematical Reviews, Issue 2011 b)
"The book under review contains an edition and English translation with explanatory notes of the Ganita-yukti-bhasa ... . The explanatory notes supplied ... elucidate the theories and algorithms in the text in a very helpful way by means of modern equations and diagrams. ... a number of appendixes and other additional chapters which make it even more useful. ... All in all, this is a very useful publication which makes an important ... source of Indian mathematics and astronomy accessible to a wide audience." (Benno van Dalen, Zentralblatt MATH, Vol. 1160, 2009)
"In addition to Sarma's translation of the GYB, Ramasubramanian, Srinivas and Sriram provide extensive and invaluable explanatory notes on Jyesthadeva's derivations ... . Volume I (Mathematics) will be of the greatest interest to the mathematical community, and is well worth inclusion in any library ... oriented towards undergraduate teaching. ... it functions as rich and accessible collection of primary-source material for undergraduate classes in the history of mathematics. ... Volume II (Astronomy) is recommended for any collection in the history of mathematics ... ." (Homer S. White, The Mathematical Association of America, July, 2009)
"The work accomplished by the editors in issuing the mathematical and astronomical parts of the Ganitayuktibhasa must be applauded. ... one can easily understand how Jyesthadeva approximates the circumference of a circle first by constructing a polygon of an uncountable number of sides, then by using power approximations of sines. One can also learn how he computes the mean and true motions of Mercury, and the area of a cyclic quadrilateral, etc. All is thoroughly explained with comprehensive drawings and tables." (Agathe Keller, Journal for the History of Astronomy, May, 2010)
"The book under review Ganita-yukti bhasa (Rationales in mathematical astronomy) of Jyesthadeva ... rightly fulfils a longunmet need. GYB provides a systematic exposition of the contributions of the Kerala school and is published in two volumes. ... This two volume set is a rare and valuable addition to the literature on the history of mathematics." (Hansraj Joshi, Mathematical Reviews, Issue 2011 b)