(b. Ālattūr, Kerala, India, ca. 1380; d. ca. 1460), astronomy.
Parameśvara was born into a learned Nampūtiri Brāhmạa family of Kerala, which belonged to the Bḥgugotra and followed the Āśvalāyanasūtra of the ̣gveda. His father remains obscure, but his grandfather studied under the astrologer Govindabhatta of Ālattūr (1236–1314). The family resided in an illam (“house”) called Vạaśśeri (Vạaśrẹi) in the village of Ālattūr (Aśvatthagrāma) on the north bank of the river Nilā at its mouth in Kerala. Parameśvara states that this place lies eighteen yojanas west of the meridian of Ujjain, and that the sine of its latitude is 647 (with R = 3,438); its latitude, then, is 10°51’N.
Parameśvara names Rudra as his teacher. Nilakạ̣ha (b. 1444), the pupil of his son Dāmodara, states that Parameśvara studied under Nārāyạa and Mādhava; the latter was a well-known astronomer of Sāgamagrāma in Kerala who lived between ca 1340 and ca. 1425. Parameśvara’s dates are fixed not only by the epochs of his several astronomical works, but also by his eclipse observations which extended from 1393 to 1432 (see D. Pingree, in Journal of the American Oriental Society, 87 , 337–339). His latest recorded observation was made in 1445, although he states in a verse cited by Nilakạ̣ha that he made observations for fifty-five years—that is, until 1448 if the observations commenced in 1393. Since Nilakạ̣ha, who was born in 1444, knew him personally, Parameśvara could not have died much before 1460.
Parameśvara’s greatest achievements were the revisions of the accepted parameters of planetary motions, the parahita that were based on the Āryabhạiya of Āryabhạa I (b. 476), and the accepted procedure of eclipse-computations on the basis of his observations. He called this new system the ḍggạita (see essay in Supplement). He was also active in the composition of commentaries on the standard astronomical texts that were in use in Kerala.
I. Original Works. Parameśvara’s works include the following. Parameśvara (ca. 1408), B. D. Apate, ed. (Poona, 1946), is a commentary on the Laghubhaskariya of Bhaskara I (ft. 629); Grahanamandana, K. V. Sarma, ed. (Hoshiarpur, 1965), is a treatise on eclipses, of which an earlier version contained 87 verses, and a later 100; the epoch is 15 July 1411. The Drgganita (1431), K. V. Sarma, ed. (Hoshiarpur, 1963), gives his new parameters, which modify those of the parahita system. The work contains new parameters of mean motions of the planets, of their mean longitudes at the beginning of the Kaliyuga, and of their two equations, and a table of their equations at intervals of 6° of argument. It also mentions the Grahanamandana. Nilakạ̣ha in the Aryabhatiyabhasya written after 1501 understood the fifty-five years of Parameśvara’s observations to antedate the Drgganita, but this would make him nearly a century old in Nilakạ̣ha’s own youth.
The Siddhantadipika, published by T. S. Kuppanna Sastri (Madras, 1957), is a commentary on the Bhasya, written by Govindasvamin (ft. ca. 800–850) on the Mahabhaskariya of Bhaskara I (ft. 629). In this work Parameśvara cites the series of eclipse observations (including one at Navaksetra in 1422 and two at Gokarna in 1425 and 1430), which extended from 1393 to 1432. The Grahananyayadipika, K. V. Sarma, ed. (Hoshiarpur, 1966), discusses eclipse theory in eighty-five verses and cites both the Grahanamandana and the Siddhantadipika. The first Goladipika (1443) contains four chapters that deal respectively with the armillary sphere, the motions of the planets, geography, and gnomon-problems. It was edited with Parameśvara’s own commentary, Vivrti, by K. V. Sarma (Madras, 1957). Grahanastaka, a short treatise in ten verses, gives the fundamental information required for the computation of eclipses. It was edited by K. V. Sarma, in Journal of Oriental Research, Madras, 28 (1958–1959), 47–60.
Other works include Vakyakarana, an unpublished treatise on the vakya system of astronomy (see essay in Supplement); Bhatadipika, H. Kern, ed. (Leiden, 1874), a commentary on the Aryabhatiya of Aryabhata I (b. 476); Vivarana, an unpublished commentary on the Lilavati of Bhaskara II (b. 1115); and Karmadipiks, B. Apate, ed. (Poona, 1945), is a commentary on the Mahabhaskariya of Bhaskara I (ft. 629), in which Parameśvara mentions his Siddhantadipika, his Vakyadipika (= Vakyakarana), his (Grahana) nyayadipika, his Goladipika, and his Bhatadipika, and also two lost works: a Muhurtastakadipika on astrology and a Bhadipika.
Vivarana is a commentary on the Suryasiddhanta, K. S. Shukla, ed. (Lucknow, 1957), in which the amount of precession is reckoned for 1432. This Vivarana refers to his Parameśvara on the Laghubhaskariya, his Siddhantadipika, his Lilavativivarana, and his Kamadipika. The Parameśvara, B. D. Apate, ed. (Poona, 1952), is a commentary on the Laghumanasa of Munjala (fl. 932). A second Goladipika, T. G. Sastri, ed. (Trivandrum, 1916), consists of 302 verses and discusses a number of problems that relate to the celestial spheres. In this work Parameśvara refers to his Siddhantadipika, to his first Goladipika, and to his Karmadipika, A Jatakapaddhati, K. S. Menon, ed. (Trivandrum, n.d.), is on horoscopes; and an unpublished commentary, Vrtti, is on the Vyatipatastaka, which is a work on the patas of the sun and moon. A number of astrological works by Parameśvara exist in MSS in South India: Acarasangraha, a commentary on the Muhurtaratna of Govindabhatta (1236–1314), the teacher of Parameśvara’s grandfather; a commentary on the Jatakapaddhati of Sripati (fl. 1040); and a commentary on the Satpancasika of Prthuyasas (fl. ca. 575).
II. Secondary Literature. The best source of information on Parameśvara is in the introductions to K. V. Sarma’s works. Unfortunately, there is as yet no study of how Parameśvara’s observations affected his astronomy. A brief summary of what was then known about him is given by K. K. Raja,“Astronomy and Mathematics in Kerala,”in Brahmavidya, 27 (1963), 118–167, esp. 136–143.