?ryabha?a I

(b. A. D.476).

?ryabha?a I clearly states his connection with Kusumapura (P??aliputra, modern Patna in Bihar), which had been the imperial capital of the Guptas for much of the fourth and fifth centuries. The assertion of N?laka??ha Somasutvan (b. 1443) that ?ryabha?a was born in the A?makajanapada (this presumably refers to the Nizamabad district of Andhra Pradesh) is probably the result of a confusion with his predecessor. Bh?skara I, as commentator on the ?ryabha??ya, ?ryabha?a I wrote two works: the ?ryabha??ya in 499 (see Essay V), and another, lost treatise in which he expounded the ?rddhar?trika system (see Essay VI).

The ?ryabha??ya consists of three parts and a brief introduction: Da?ag?tik?, introduction with parameters (ten verses); Ga?itap?da, mathematics (thirtythree verses); K?lakriy?p?da, the reckoning of time and the planetary models (twenty-five verses); Golap?da, on the sphere, including eclipses (fifty verses). It was translated into Arabic in about 800 under the title Z?j al-Arjabhar, and it is to this translation that all the quotations in al-B?r?n? refer, including those that led Kaye to conclude—mistakenly—that the Ga?itap?da was not written by ?ryabha?a I.

The ?ryabha??ya has been commented on many times, especially by scholars of south India, where it was particularly studied. The names of those commentators who are known are as follows:

1. Prabh?kara (ca. 525). His commentary is lost.
2. Bh?skara I (629). His Bh?sya is being edited by K. S. ?ukla of Lucknow.
3. Some?vara (fl. 1040). His V?san?bh?sya is preserved in two manuscripts in the Bombay University Library.
4. S?ryadeva Yajvan of Kerala (b. 1191). There are many manuscripts of his Bha?aprak??a, in south India.
5. Parame?vara(fl. 1400–1450). His Bha?ad?pik?, based on S?ryadeva’s Bha?aprak??a, was published by H. Kern (see below).
6. N?laka??ha Somasutvan (b. 1443). His Bh?sya is published in Trivandrum Sanskrit Series (see below).
7. Yallaya (fl. 1482). His Vy?khy?na is based on S?ryadeva’s Bha?aprak??a; there is one manuscript of it in Madras and another among the Mackenzie manuscripts in the India Office Library.
8. Raghun?tha (fl. 1590). His Vy?khy?na is dealt with by K. Madhava Krishna Sarma, “The ?ryabha??yavy?khy? of Raghun?thar?ja—A Rare and Hitherto Unknown Work,” in Brahmavidy?, 6 (1942), 217–227.
9. Koda??ar?ma of the Ko?ikalap??ikula, a resident of Bobbili in the God?var? district of Andhra Pradesh (fl. 1854). Besides an ?ryabha?atantraga?ita, he wrote a Telugu commentary on the ?ryabha??ya entitled Sudh?taran?ga; it was edited by V. Lakshmi Narayana Sastri, in Madras Government Oriental Series, 139 (Madras, 1956).
10. Bh?tivi??u. There is apparently only one manuscript (in Berlin) and its apograph (in Washington, D. C.) of his commentary (Bh?sya) on the Da?ag?tik?.
11. Gha??gopa. There are two manuscripts of his Vy?khy? in Trivandrum.
12. Vir?p?k?a S?ri. There is a manuscript of his Telugu commentary in Mysore.

There also exists a Mar??h? translation of the ?ryabha??ya in a manuscript at Bombay.

There are several editions of the ?ryabha??ya That by H. Kern (Leiden, 1874) is accompanied by the commentary of Parame?vara. Kern’s text and commentary were reprinted and translated into Hindi by Udaya N?r?yana Singh (Madhurapur, Etawah, 1906). A new edition of the text, with the commentary of N?laka??ha Somasutvan (who does not include the Da?ag?tik?), was published in three volumes: Vols. I and II by K. S?mb?iva ??str? and Vol, III by Suranad Kunjan Pillai, in Trivandrum Sanskrit Series, 101, 110, and 185 (Trivandrum, 1930, 1931, 1957). The text has also been published accompanied by two new commentaries, one in Sanskrit and one in Hindi, by Baladeva Mishra (Patna, 1966). The Ga?itap?da was translated into French by Léon Rodet, in Journal Asiatique, 7, no. 13 (1879), 393–434; and into English by G. R. Kaye, in Journal of the Asiatic Society of Bengal, 4 (1908), 111– 141 . Complete English translations have been made by Baidyanath Rath Sastri (Chicago, 1925; unpub.); P. C. Sengupta, Journal of the Department of Letters of Calcutta University, 16 (1927), 1–56; and W. E. Clark (Chicago, 1930).

BIBLIOGRAPHY

It is intended here to include references only to those books and articles that are primarily concerned with ?ryabhata I and his works; the many other papers and volumes that mention and/or discuss him can be found listed in David Pingree Census of the Exact Sciences in India. Listed chronologically, the references are F.-E. Hall, “On the ?rya-siddh?nta,” in Journal of the American Oriental Society, 6 (1860), 556–559, with an “Additional Note on ?ryabha??a and his Writings” by the Committee of Publication (essentially W. D. Whitney), ibid., 560–564; H. Kern, “On Some Fragments of ?ryabha?a,” in Journal of the Royal Asiatic Society20 (1863), 371–387 repr. in Kern’s Vespreide Geschriften I (The Hague, 1913), 31–46; Bh?u D?j?, “Brief Notes on the Age and Authenticity of the Works ?ryabha?a, Var?hamihira, Brahmagupta, Bha??otpala, and Bh?skar?ch?ya,” in Journal of the Royal Asiatic Society (1865), pp. 392–418 (?yabhatya only pp. 392–406, 413–414); L. Rodet, “Sur la véritable signification de la notation numérique inventée par ?ryabha?a” in Journal Asiatiqeu, ser. 7, 16 (1880), 440–485; Sudh?kara Dvivedin Ga?akatarn?gi?? (Benares, 1933; repr. from The Pandit, 14 [1892]), 2–7; ?. B. D?k?ita, Bh?rat?ya Jyoti???stra (Poona, 1931; repr. of Poona ed., 1896), pp. 190–210; G. Thibaut, Astronomie, Astrologie und Mathematik, Grundriss der indo-arischen Philologie und Altertumskunde, III, pt. 9, (Strasbourg, 1899), 54–55; T. R. Pillai, ?rybha?a or the Newton of Indian Astronomy (Madras, 1905—not seen—reviewed in Indian Thought [1907], pp. 213–216); G. R. Kaye, “Two ?ryabha?as,” in Bibliotheca mathematica, 10 (1910), 289–292; J. F. Fleet, “?ryabha?a’s System of Expressing Numbers,” in Journal of the Royal Asiatic Society (1911), pp. 109–126; N. K. Mazumdar, “?ryyabhatta’s Rule in Relation to Indeterminate Equations of the First Degree,” in Bulletin of the Calcutta Mathematical Society, 3 (1911/1912), 11–19; J. F. Fleet, “Tables for Finding the Mean Place of Saturn,” in Journal of the Royal Asiatic Society (1915), pp. 741–756; P. C. Sengupta, “?ryabha?a’s Method of Determining the Mean Motions of Planets,” in Bulletin of the Calcutta Mathematical Society, 12 (1920/1921), 183–188.

See also R. Sewell, “The First Arya Siddhanta,” in Epigraphia Indica, 16 (1921/1922), 100–144, and 17 (1923–1924), 17–104; A. A. Krishnaswami Ayyangar, “The Mathematics of ?ryabha?a,” in Quarterly Journal of the Mythic Society, 16 (1926), 158–179; B . Datta, “Two ?ryama?as of al-Biruni,” in Bulletin of the Calcutta Mathematical Society, 17 (1926), 59–74; S. K. Ganguly, “Was ?ryabha?a Indebted to the Greeks for His Alphabetical System of Expressing Numbers?,” ibid., 195–202, and “Notes on ?rayabha?a,” in Journal of the Bihar and Orissa Research Society12 (1926), 78–91; B. Datta, “?ryabha?a, the Author of the Ga?ita,” in Bulletin of the Calcutta Mathematical Society, 18 (1927), 5–18; S. K. Ganguly, “The Elder ?ryabhata and the Modern Arithmetical Notation,” in American Mathematical Monthly, 34 (1927) 409–415; P. C. Sengupta, “?ryabha?a, the Father of Indian Epicyclic Astronomy,” in Journal of the Department of Letters of Calcutta University, 18 (1929), 1–56; S. K. Ganguly, “The Elder ?ryabha?a’s Value of ?,” in American Mathematical Monthly, 37 (1930), 16–29; P. C. Sengupta, “?ryabhata’s Lost Work,” in Bulletin of the Calcutta Mathematical Society22 (1930), 115–120; B . Datta, “Elder ?ryabha?a’s Rule for the Solution of Indeterminate Equations of the First Degree,” ibid., 24 (1932), 19–36; P. K. Gode, “Appayad?k?ita’s Criticism of ?yabha?a’s Theory of the Diurnal Motion of the Earth (Bh?bhramav?da),” in Annals of the Bhandarkar Oriental Research Institute, 19 (1938), 93–95, repr. in Gode’s Studies in Indian Literary History, II, Singhi Jain Series, 38 (Bombay, 1954), 49–52; S. N. Sen, “?ryabha?a’s Mathematics,” in Bulletin of the National Institute of Sciences of India, 21 (1963), 297–319; Satya Prakash, Founders of Sciences in Ancient India (New Delhi, 1965), pp. 419–449.

David Pingree