Ganita-yukti-bhasa

Ganita-yukti-bhasa (also written as Ganita Yuktibhasa) is either the title or a part of the title of three different books:

• Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva,^[1] published by Springer,^[2] is the first critical edition with an English translation of Yuktibhasa, a seminal treatise in the Malayalam language composed in c.1530 CE by Jyeshthadeva. one of the most significant personalities of the Kerala school of astronomy and mathematics. The book is published in two volumes as Volume I and Volume II. Jyeshthadeva's Yuktibhasa discusses various topics in mathematics and astronomy and it is purported to be an enunciation of the rationales underlying the various mathematical assertions and the astronomical concepts and computations in the great treatise Tantrasamgraha of Nilakantha Somayaji (1444–1544). (An edition of the mathematical portion of Yuktibhasa with some explanatory notes in Malayalam had appeared in 1948.^[3])
• In addition to Jyshthadeva's Yuktibhasa, Kerala school of astronomy and mathematics had produced another work called Ganita Yuktibhasa.^[4] In contrast to Jyeshthadeva's Yuktibhasa, this work is in Sanskrit. The date of composition and the name of the author of this work in Sanskrit have not been determined with certainty. The book appears to be of a later period and seems to have been composed as a somewhat rough Sanskrit translation of the Malayalam original Yuktibhasa.
• Ganita Yuktibhasa (Volume III)^[5] is the title of a book published by Indian Institute of Advanced Study (IIAS), Shimla, and it is a critical edition of the Sanskrit Ganita Yuktibhasa.^[6] This is intended as the third volume of a series on Yuktibhasa, the first two volumes being Volume I and Volume II of Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyeshthadeva published by Springer.

More on Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva

This edition of Yuktibhasa has been divided into two volumes, even though the original Malayalam text has no such division. Volume I deals with mathematics and Volume II treats astronomy. Each volume is divided into three parts: First part is an English translation of the relevant Malayalam part of Yuktibhasa, second part contains detailed explanatory notes on the translation, and in the third part the text in the Malayalam original is reproduced. The English translation is by K.V. Sarma and the explanatory notes are provided by Ramasubramanian, K., Srinivas, M.D. and Sriram, M.S..

Volume I dealing with mathematics is divided into seven chapters. The topics discussed are the eight mathematical operations, a certain set of ten problems, arithmetic of fractions, rule of three, Kuttakara (linear indeterminate equations), infinite series and approximations for the ratio of the circumference and diameter of a circle and infinite series and approximations for sines.^[7]

Volume II dealing with astronomy is divided into eight chapters. The topics covered are computation of mean and true longitudes of planets, Earth and celestial spheres, fifteen problems relating to ascension, declination, longitude, etc., determination of time, place, direction, etc., from gnomonic shadow, eclipses, Vyatipata (when the sun and moon have the same declination), visibility correction for planets and phases of the moon.^[7]

References

1. Sarma, K.V.; Ramasubramanian, K.; Srinivas, M.D.; Sriram, M.S. (2008). Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva. Sources and Studies in the History of Mathematics and Physical Sciences (in English and Malayalam). I (Mathematics), II (Astronomy). Springer (Jointly with Hindustan Book Agency (HBA), New Delhi, India). pp. LXVIII, 1084. ISBN 978-1-84882-072-2.
2. See publishers's (Springer's) web page on the book: "Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva". Retrieved 29 April 2010.
3. Yuktibhâsâ, Part I (ed) with notes by Ramavarma (Maru) Thampuran and A. R. Akhileswara Aiyer, Magalodayam Ltd., Trichur, Kerala, 1123 Malayalam Era, 1948 CE.
4. K.V. Sarma; S. Hariharan (1991). "Yuktibhasa of Jyesthadeva : A book of rationales in Indian mathematics and astronomy – An analytical appraisal" (PDF). Indian Journal History of Science. 26 (2): 185–207. Retrieved 2 May 2010.
5. K.V. Sarma. Ganita Yuktibhasa (Volume III). Shimla: Indian Institute of Advanced Study. ISBN 81-7986-052-3.
6. Publisher's (Indian Institute of Advanced Study) web page on the book:"Ganita Yuktibhasa by K.V. Sarma". Retrieved 1 May 2010.
7. For more details on contents see Kinokuniya DataBase: "Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva". Retrieved 1 May 2010.

Further reading

• For a review of Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva by Mathematical Association of America see : Homer S. White (2009-07-17). "Ganita-Yukti-Bhāsā (Rationales in Mathematical Astronomy) of Jyesthadeva". The Mathematical Association of America. Retrieved 1 May 2010.
• For a discussion of the contents of the Malayalam Yuktibhasa and also of the question of the authorship and date of the Malayalam Yuktibhasa see : K.V. Sarma; S. Hariharan (1991). "Yuktibhasa of Jyesthadeva : A book of rationales in Indian mathematics and astronomy – An analytical appraisal" (PDF). Indian Journal History of Science. 26 (2): 185–207. Retrieved 2 May 2010.