Parame?vara
PARAME?VARA
(b. ?latt?r, Kerala, India, ca. 1380; d. ca. 1460), astronomy.
Parame?vara was born into a learned Namp?tiri Br?hma?a family of Kerala, which belonged to the Bh?gugotra and followed the ??val?yanas?tra of the ?gveda. His father remains obscure, but his grandfather studied under the astrologer Govindabhatta of ?latt?r (1236–1314). The family resided in an illam (“house”) called Va?a??eri (Va?a?re?i) in the village of ?latt?r (A?vatthagr?ma) on the north bank of the river Nil? at its mouth in Kerala. Parame?vara 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.
Parame?vara names Rudra as his teacher. Nilaka??ha (b. 1444), the pupil of his son D?modara, states that Parame?vara studied under N?r?ya?a and M?dhava; the latter was a well-known astronomer of Sa?gamagr?ma in Kerala who lived between ca 1340 and ca. 1425. Parame?vara’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 [1967], 337–339). His latest recorded observation was made in 1445, although he states in a verse cited by Nilaka??ha that he made observations for fifty-five years—that is, until 1448 if the observations commenced in 1393. Since Nilaka??ha, who was born in 1444, knew him personally, Parame?vara could not have died much before 1460.
Parame?vara’s greatest achievements were the revisions of the accepted parameters of planetary motions, the parahita that were based on the ?ryabha?iya of ?ryabha?a I (b. 476), and the accepted procedure of eclipse-computations on the basis of his observations. He called this new system the d?gga?ita (see essay in Supplement). He was also active in the composition of commentaries on the standard astronomical texts that were in use in Kerala.
BIBLIOGRAPHY
I. Original Works. Parame?vara’s works include the following. Parame?vara (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. Nilaka??ha in the Aryabhatiyabhasya written after 1501 understood the fifty-five years of Parame?vara’s observations to antedate the Drgganita, but this would make him nearly a century old in Nilaka??ha’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 Parame?vara 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 Parame?vara’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 Parame?vara 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 Parame?vara on the Laghubhaskariya, his Siddhantadipika, his Lilavativivarana, and his Kamadipika. The Parame?vara, 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 Parame?vara 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 Parame?vara exist in MSS in South India: Acarasangraha, a commentary on the Muhurtaratna of Govindabhatta (1236–1314), the teacher of Parame?vara’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 Parame?vara is in the introductions to K. V. Sarma’s works. Unfortunately, there is as yet no study of how Parame?vara’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.
David Pingree