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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.

The mathematics part is divided into seven chapters. The topics covered are Parikarma (logistics), Dasaprasna (ten problems), Bhinnaganita (fractions), Trairasika (rule of three), Kuttakara (linear indeterminate equations), Paridhi and Vyasa (infinite series and approximations for the ratio of the circumference and diameter of a circle) and Jyanayana (infinite series and approximations for sines). A distinguishing feature of the work is that it presents detailed demonstrations of the famous results attributed to Madhava (c.1340-1420), such as infinite series for p, the arc-tangent and the sine functions, and the estimation of correction terms and their use in the generation of faster convergent series. Demonstrations are also presented for some of the classical results of Aryabhata (c.499) on Kuttakara or the process of solution of linear indeterminate equations, of Brahmagupta (c.628) on the diagonals and the area of a cyclic quadrilateral, and of Bhaskara (c.1150) on the surface area and volume of a sphere.

The astronomy part is divided into eight chapters. The topics covered are Grahagati (computation of mean and true longitudes of planets), Bhugola and Bhagola (Earth and celestial spheres), Pancadasa-prasna (fifteen problems relating to ascension, declination, longitude, etc.), Chaya-ganita (determination of time, place, direction, etc., from gnomonic shadow), Grahana (eclipses), Vyatipata (when the sun and moon have the same declination), Darsana-samskara (visibility correction for planets) and Candra-srngonnati (phases of the moon). A distinguishing feature of this work is that it gives a detailed exposition of the revised planetary model proposed by Nilakantha which, for the first time in the history of astronomy, gives the correct formulation of the equation of centre and the latitudinal motion of the interior planets, Mercury and Venus. Another unique feature of Ganita-yukti-bhasa is that it presents systematic derivations of most of the results of spherical astronomy (pertaining to diurnal and shadow problems, parallax, eclipses, and so on) that are discussed in Indian astronomy.

The work will be of interest to historians of mathematics and astronomy and to philosophers of science.

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Matthew Parker, Joseph Ben Ephraim Karo, Heinrich Bullinger, Limahong, Jyesthadeva, Peter Carew, Rajah Sulaiman Iii, Matthias Flacius, James Hamilton, Duke of Châtellerault, Alonso de Góngora Marmolejo, Keawenuiaumi, Jacob Van Deventer, Anna Bijns, Francesco Maurolico, John Parkhurst, Robert Lauder of Popill, Federico Brandani, Girolamo Conversi, Tomás de Mercado, Richard Taverner, Costanzo Varolio, Claude of Valois, Juan de La Cerda, 4th Duke of Medinaceli, Diego Hurtado de Mendoza, Luis Fajardo, 2nd Marquis of Los Vélez, Sophia Jagiellon, Nicolas Psaume, Simon Vigor, Federico Commandino, Annibale Padovano, Marcin Bielski, Pierre Phalèse the Elder, Constantino of Braganza, Nicholas Harpsfield, Francisco de Ibarra, Peder Oxe, Yamagata Masakage, Isabel de Josa, Giuseppe Porta, Juan Ortiz de Zárate, Edmund O'donnell, Akiyama Nobutomo, Pieter Aertsen, Gaspard de Saulx, Torii Suneemon, Johannes Aurifaber, Naitō Masatoyo, Alexander Gordon, Chiappino Vitelli, Paulus Aemilius, Corneille de Lyon, William Dormer, Diego Andrada de Payva, Francisco Cervantes de Salazar, Jerzy Jazłowiecki, Cesare I Gonzaga, Giulio Claro, Sanada Nobutsuna, Baba Nobuharu, Constantio Varoli, Diogo de Paiva de Andrada, Thomas Wakefeld, Thomas Huyck, Hadrianus Junius, Andrés de Vandelvira, Anna of Oldenburg, Wen Boren, Saegusa Moritomo, Richard Lee, William Stevenson, Lodovico Lombardo, Pierino Belli, Cornelis Floris de Vriendt, Hara Masatane, Jean de Nogaret de La Valette, Jan Matsys, Kakizaki Kageie, Takeda Nobuzane, Tsuchiya Masatsugu. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Heinrich Bullinger (July 18, 1504 September 17, 1575) was a Swiss reformer, the successor of Huldrych Zwingli as head of the Zurich church and pastor at Grossmünster. A much less controversial figure than John Cal...More: http://booksllc.net/?id=162291 ... Read more

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Chapters: G. Madhavan Nair, Ajit Varki, George Sudarshan, Jyesthadeva, Pulickel Ajayan, Thanu Padmanabhan, George Varghese, K. Radhakrishnan, Mambillikalathil Govind Kumar Menon, Pisharoth Rama Pisharoty, Mathai Varghese, P. N. Vinayachandran, Thomas Zacharia, K. R. Ramanathan, Rappal Sangameswaraier Krishnan, Matthew Pothen Thekaekara, Sainudeen Pattazhy. Source: Wikipedia. Pages: 69. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: G. Madhavan Nair (Malayalam: ) (born October 31, 1943) is the former Chairman of Indian Space Research Organisation and Secretary to the Department of Space, Government of India since September 2003. He is also the Chairman, Space Commission and acts as the Chairman of Governing Body of the Antrix Corporation, Bangalore. Madhavan Nair was awarded the Padma Vibhushan, India's second highest civilian honour, on January 26, 2009. Nair was born at Neyyattinkara near Thiruvananthapuram, Kerala, India. He also studied as a youth in Kanyakumari District. He graduated with a B.Sc. in Engineering (1966) from College of Engineering, Thiruvananthapuram, Kerala University with specialization in Electrical ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Subrahmanyan Chandrasekhar, Aryabhata, Bhāskara Ii, Nilakantha Somayaji, Venkatraman Radhakrishnan, Jyesthadeva, Vasistha, Meghnad Saha, Jayant Narlikar, Thanu Padmanabhan, Parameshvara, Yajnavalkya, Varahamihira, Govind Swarup, J. J. Rawal, Utpala, Śrīpati, Vainu Bappu, Sankara Varman, Mohan Apte, Somnath Bharadwaj, Vatasseri Parameshwaran Nambudiri, Achyuta Pisharati, Agnes Giberne, Ramana Athreya, Gautama Siddha, Kelallur Neelakandhan Somayaji, P. Devadas, Lalla, Jagannatha Samrat, M K Das Gupta, Amil Kumar Das, Sankara Variar, Brahmadeva, Damodara, Kamalakara, Bapudeva Sastri, Mahendra Suri, Paarangot Jyeshtadevan Namboodiri, Radha Gobinda Chandra, Achyuta Panikkar, Aryabhata Ii, Lagadha. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Aryabhata (IAST: ; Sanskrit: ) (476550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499 CE, when he was 23 years old) and the Arya-siddhanta. While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" does not fit the metre either. Aryabhata mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476 CE. Aryabhata provides no information about his place of birth. The only information comes from Bhskara I, who describes Aryabhata as makya, "one belonging to the amaka country." While amaka was originally situated in the nort...More: http://booksllc.net/?id=297204 ... Read more

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High Quality Content by WIKIPEDIA articles! Jyestadeva (c.1500 – c.1610), was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Sangamagrama Madhava (c.1350 – c.1425) . He is best known as the author of Yuktibhasa, a commentary in Malayalam of Tantrasamgraha by Nilakantha Somayaji (1444-1544). In Yuktibhasa, Jyesthadeva had given complete proofs and rationale of the statements in Tantrasamgraha. This was unusual for traditional Indian mathematicians of the time. An analysis of the mathematics content of Yuktibhasa has prompted some scholars to call it "the first textbook of calculus". Jyesthadeva also authored Drk-karana a treatise on astronomical observations. ... Read more