K related to the Siddhānta-Tattvaviveka, one a regular Kamala¯kara commentary on the work, called Tattvavivekodāharan. a, and the other a supplement to that work, called Śes.āvasanā, in which he supplied elucidations and new K. V. SARMA material for a proper understanding of his main work. He held the Sūryasiddhānta in great esteem and also wrote a Kamalākara was one of the most erudite and forward- commentary on that work. looking Indian astronomers who flourished in Varanasi Kamalākara was a critic of Bhāskara and his during the seventeenth century. Belonging to Mahar- Siddhāntaśiroman. i, and an arch-rival of Munīśvara, a ashtrian stock, and born in about 1610, Kamalākara close follower of Bhāskara. This rivalry erupted into came from a long unbroken line of astronomers, bitter critiques on the astronomical front. Thus Ranga- originally settled at the village of Godā on the northern nātha, younger brother of Kamalākara, wrote, at the . banks of the river Godāvarī. Towards AD 1500, the insistence of the latter, a critique on Munīśvara’s Bhangī family migrated to Varanasi and came to be regarded as method (winding method) of true planets, entitled . reputed astronomers and astrologers. Kamalākara Bhangī-vibhangī (Defacement of the Bhangi), to which . studied traditional Hindu astronomy under his elder Munīśvara replied with a Khand.ana (Counter). Munīś- brother Divākara, but extended the range of his studies vara attacked the theory of precession advocated by to Islamic astronomy, particularly to the school of Kamalākara, and Ranganātha refuted the criticisms of his Ulugh Beg of Samarkand. He also studied Greek brother in his Loha-gola-khan. d.ana (Counter to the Iron astronomy in Arabic and Persian translations, particu- Sphere). That in turn was refuted by Munīśvara’scousin larly with reference to the elements of physics from Gadādhara in his Loha-gola-samarthana (Justification Aristotle, geometry from Euclid, and astronomy from of the Iron Sphere). These kinds of astronomical and Ptolemy. He wrote both original treatises and commen- intellectual battles were typical of the philosophical and taries on his own works and those of others. religious disputes which were common in ancient India. Kamalākara’s most important work is the Siddhānta- Tattvaviveka, written in AD 1658. The work which is See also: ▶Astronomy in India, ▶Ulugh Beg, divided into 15 chapters and contains over 3,000 ▶Astronomy in the Islamic World, ▶Sūryasiddhāntha, verses, faithfully follows the Sūryasiddhānta in the ▶Precession of the Equinoxes ▶Bhāskara, ▶Munīś- matter of parameters, general theories, and astronomi- vara cal computation. However, in certain matters Kamalā- kara made original contributions and offered new ideas. Though he accepted the planetary parameters of References Sūryasiddhānta, he agreed with Ptolemaic notions in Dikshit, S. B. Bhāratiya Jyotish Sastra (History of Indian the matter of the planetary system. He presented Astronomy). Trans. by R. V. Vaidya. Pt. II. History of geometrical optics, and was perhaps the only traditional Astronomy During the Scientific and Modern Periods. author to do so. He described the quadrant and its Calcutta: Positional Astronomy Centre, India Meteorologi- application. He proposed a new Prime Meridian, which cal Department, 1981. is the longitude passing through an imaginary city Dvivedi, Sudhakara. Gan. aka Tarangin. i: Lives of Hindu called Khalādātta, and provided a table of latitudes Astronomers. Benares: Jyotish Prakash Press, 1933. ā and longitudes for 20 important cities, in and outside Loha-gola-khan. d.ana of Rangan tha and Loha-gola- samarthana by Gadādhara. Ed. Mithalala Himmatarama India, on this basis. Kamalākara was an ardent advo- Ojha. Varanasi: Sañcālaka, Anusandhāna Sam. sthāna, 1963. cate of the precession of the equinoxes and argued Pingree, David. Jyotih. śāstra–Astral and Mathematical Liter- that the pole star also does not remain fixed, on account ature. Vol. VI, fasc. 4 of A History of Indian Literature. Ed. of precession. Kamalākara wrote two other works Jan Gonda. Wiesbaden: Otto Harrassowitz, 1981. 1160 Kerala school of astronomy and mathematics Siddhānta-Tattvaviveka. A Treatise on Astronomy by Bhat.t.a Venvāroha and Sphut.acandrāpti both contain an Kamalākara, with Śes.avāsanā by the same author. Ed. efficient computational procedure to calculate the true Sudhakara Dube. Benares: Benares Sanskrit Series, 5 vols. – longitude of the Moon every 36 min. Those books and 1880 1885: Revised by Muralidhara Jha, Benares: Krishna ā Das Gupta for Braj Bhusan Das & Co, 1924–1935. Agan. itagrahac ra are conceptually not major works. However all the later astronomer–mathematicians from Kerala attribute the path-breaking results in the infinite series for the inverse-tangent, sine and cosine functions Kerala School of Astronomy and many innovations in astronomical calculations to him. He is also hailed as Golavid (master of Spherics). and Mathematics Parameśvara of Vatasseri (AD 1360–1455), a student of Mādhava, was a prolific writer, authoring about 30 works. Emphasising the need for revising the M. S. SRIRAM planetary parameters through observations, he thor- oughly revised the Parahita system and introduced the After Bhāskara II (b. AD 1114), the most significant Dr. ggan. ita system. Apart from Dr. ggan. ita, the other contributions to mathematics and astronomy in India important works of Parameśvara are Goladīpikā came from Kerala, in the southwestern part of India. in three parts, Bhat.adīpika, a commentary on Kerala has had a continuous tradition of astronomy and Āryabhat.īya, Mahābhāskarīyabhasya and Siddhānta- mathematics from much earlier times. Sarma has listed dīpikā, a super-commentary on Govindaswamin’s nearly 750 independent works on astronomy, astrology Mahābhāskarīyabhās.ya, and Grahan. aman. dana on and mathematics including minor works by 110 authors eclipses. He was one of the astronomers to discuss in in the Kerala tradition. detail the geometrical model of planetary motion Vararuci (date unconfirmed), who is credited with the implied in the conventional calculational procedures authorship of 248 Candravākyas (sentences for compu- in Indian astronomy in his Siddhāntadīpikā and tation of the moon’s longitude) by the manuscript Goladīpikā. tradition, is considered to be the father figure in the No full-fledged work of Dāmodara, son and disciple astronomical tradition of Kerala. Āryabhat.īya (ca. AD of Parameśvara is known, but he is quoted at several 499) of Āryabhat.a which set the tone for all further work places by his famous pupil, Nīlakan.t.ha Somayāji or on mathematical astronomy in India, appears to have Somasutvan (AD 1445–1545) of Trkkantiyur. Nīlakan- . .. become popular in Kerala soon after its composition. In t.ha’s Tantrasangraha ranks along with Āryabhat.īya of fact, out of the 20 or so available commentaries on Āryabhat.aandSiddhāntaśiroman. i of Bhākaracārya as Āryabhatīya, as many as 12 are from Kerala. The one of the major works which significantly influenced all . astronomical parameters in Āryabhat.īya were revised by further work on astronomy in India. In Tantrasangraha, a group of astronomers who had gathered in the religio- Nīlakan.t.ha introduced a major revision of the traditional educational centre of Tirunavay in northern Kerala in AD Indian planetary model. There are also important 683–684. Haridatta in his Grahacāranibandhana enun- innovations in mathematical techniques especially ciated the revised system called Parahita-gan. ita.Many related to the series expansion of the trigonometric later works refer to the Parahita system. functions and systematic and exact treatment of spherical Laghubhāskarīya and Mahābhāskarīya of Bhāskara I, astronomy problems. which expounded the Āryabhat.an school in detail, In addition to Tantrasangraha,Nīlakan.t.ha composed were also popular in Kerala. Govindasvāmin (AD 800– many other works. Āryabhat.īyabhās.ya, composed late 850) wrote an elaborate commentary on Mahābhāskar- in his life, is perhaps the most elaborate commentary on . īya and his student Śankaranārāyan.a (AD 825–900) Āryabhat.īya. He himself calls it a Mahābhās.ya (from wrote one on Laghubhāskarīya. Udayadivākara (elev- mahā, great and bhās.ya, commentary), which is amply enth century), who wrote a detailed commentary titled justified considering the wealth of information in it. Sundarī on Laghubhāskarīya, also probably hailed Apart from the detailed explanation of mathematical from Kerala. This work contains a method for solving results and procedures, it discuses the geometrical quadratic indeterminate equations or Varga – prakr. ti model of planetary motion, eclipses, and even some and ascribes it to Jayadeva. It is in fact the same as the “physical” concepts like the planets’ being illuminated famous Cakravāla algorithm, expounded in detail later by the Sun. Some of his other major works are by Bhāskara II in his Bījagan. ita. Suryadeva Yajvan Golasāra on spherical astronomy, Siddhānta-darpan. a, (AD 1191–1250) wrote detailed commentaries on both in which he presents the planetary parameters as Āryabhat.īya and Laghumānasa of Manjulācarya. verified through his own observations, Candracchāyā- The Kerala tradition entered a new phase with ganita on ‘shadow’ problems, and Grahananirnaya on . Mādhava of Sangamagrāma (AD 1340–1425). His lunar and solar eclipses. Jyotīrmīmāmsā of Nīlakan.t.ha Kerala school of astronomy and mathematics 1161 has a unique place in the history of Indian astronomy, mayāji’s (AD 1660–1740) Karan. apaddhati provides