Gane?a

(b. Nandod, Gujarat, India, 1507)

astronomy.

Gane?a was born into a Brâhma?a family of astronomers and astrologers. He was the son of Ke?ava of the Kau?ikagotra and his wife Laksmî, and studied under his famous father, on many of whose works he eventually wrote commentaries. In his turn Gane?a trained N?si?ha (b. 1548), the son of his brother Râma, and N?si?ha both commented on Ga?eéa’s Grahalâghava and wrote, in 1603, a set of astronomical tables entitled Grahakaumudî based on that work. Ga?e?a also taught Divâkara of Golagrâma, many of whose descendants commented on various of his master’s books. Gane?a’s last dated work, the Vivâhahadîpikâ, was written in 1554; he must, however, have lived at least a decade longer in order to have been his nephew’s teacher. So far as is known, he never left his native village.

Gane?a wrote a number of works on jyoti?a?âstra (astronomy and astrology) and dharma?âstra (Hindu law). These are listed by his nephew, N?si?ha, in his commentary, Har?akaumudî, on the Grahalâghava:.

1. Grahalâghava (see essay in Supplement).

2. Laghutithicintâma?i (see essays in Supplement).

3. B?hattithicintâma?i (see essays in Supplement).

4. Siddhânta?iromaniviv?ti (see essay in Supplement).

5. Lîl?vatîvyâk?ti (see essay in Supplement).

6. V?ndâvana?îkikâ.

7. Muhûrtatattvavivgti.

8. ?râddhâdivinir?aya.

9. Chandor?avaviu?ti.

10. Sudhîran?njana..

11. Tarjanîyantraka.

12. K???â??amînir?aya.

13. Holikânir?aya.

To these the following can be added.

14. Pâtasâra?î.

15. Câbukayantra.

16. Pratodayantra.

17. Dhruvabhrama?ayantravyâkhyâ

The Grahalâghava or Siddhântarahasya, Gane?a’s main work on astronomy, was composed in 1520, when he was thirteen. It contains sixteen chapters:.

1. On the mean longitudes of the planets.

2. On the true longitudes of the sun and moon.

3. On the true longitudes of the five “starplanets.”

4. On the three problems involving diurnal motion.

5. On lunar eclipses.

6. On solar eclipses.

7. On calendrical problems.

8. On eclipses.

9. On helical risings and settings.

10. On the planets’ altitudes.

11. On the altitudes of the fixed stars.

12. On the lunar crescent.

13. On planetary conjunctions.

14. On the pâtas of the sun and moon.

15. On calculating lunar eclipses with a calendar.

16. Conclusion.

The Grahalâghava has been the most popular Sanskrit astronomical treatise in northern and western India since the sixteen century. Its popularity is reflected in the hundreds of manuscripts of it that are extant, in the several commentaries on it, and in the numerous sets of astronomical tables based on its parameters. The known commentaries are the following (for editions, see the list of editions of the Grahalâghava itself given below):

1. Tîkâ of Mallâri (fl. ca. 1600), the son of Divâkara of Golagrâma (published).

2. Har?akaumudî of N?si?ha3 (b 1548), Ga?e?a’s nephew.

3. Manoramâ of Gan?gâdhara (1586).

4. Siddhântarahasyodâhara?a of Vi?vanâtha (1612), the son of Divâkara of Golagrâma (published).

5. Manoramâ of Kamalâkara, the great-grandson of Divâkara of Golagrâma.

6. Udâh?ti of Nârâyana (1635[?]).

7. Sadvâsanâ of Sudhâkara Dvivedin (1904, published).

8. Sudhâmanjarîvâsanâ of Sîtârâma Jhâ (1932, published).

9. Mâdhurî of Yugeývara Jhâ (1946, published).

10. Tîkâ of Bâlagovinda.

The following astronomical tables are based on the Hrahalâghava:.

1. Grahalâghavasâri?î I (the initial epoch is 1520).

2. Grahakaumudî of N?si?ha3 (1603).

3. Grahasâra?î of Gañgâdhara (1630).

4. Grahalâghabasâri?î of Premami?ra (1656).

5. Grahaprabodhasâri?î of Yâdava (1663).

6. Grahalâghabasâri?î II (1754).

7. Grahalâghavîyasârinî of Gangâdhara Varman (Bombay, 1907; 2nd ed., 1923).

Most of these sets of tables are described in D. Pingree, “Sanskrit Astronomical Tables in the United States,” in Transactions of the American Philosophical Society, n.s. 58 no, 3 (1968), passim; “On the classification of Indian Planetary Tables,” in Journal of the History of Astronomy, 1 (1970), 95-108; and “Sanskrit Astronomical Tables in England,” in Journal of Oriental Research (to be published).

The Grahalâghava has often been published in India:

1. Edited with the Tîkâ of Mallâri by L. Wilkinson (Calcutta, 1848).

2. Edited with the Tîkâ of Mallâri and the Udâhara?a of Vi?vanâtha by Bhâlacandra (Benares, 1864).

3. Edited with the Udâhara?a of Vi?vanâtha and a Marâ?hî translation by K???a ?âstrî Go?abole and Vâmana K???a Jo?î Gadre (2nd ed., Bombay, 1873; 5th ed., Poona, 1914; 6th ed., Poona, 1926).

4-7. Edited with the ?îkâ of Mallâri (Bombay, 1875; Benares, 1877; Delhi, 1877; Bombay, 1883).

8. Edited with the Udâhara1E47;a of Vi?vanâtha and a Bengâlî translation by Rasikamohana Cattopâdhyâya (Calcutta, 1887).

9. Edited with the Hindî translation of Jiyârâma ?âstrî by Râme?vara Bha??a (Kalyâna-Bombay, 1899).

10. Edited with the ?îkâ of Mallâri by Hariprasâda ?arman (Bombay, 1901).

11. Edited with the ?îkâ of Mallâri, the Udâhara?a of Vi?vanâtha, and his own Sadvâsanâ by Sudhâkara Dvivedin (Benares, 1904; repr. Bombay, 1925).

12. Edited with the Tîkâ of Mallâri and the Ândhra?îkâ of Ma?gipû?i Vîrayya Siddhântigâr (Masulipatam, 1915).

13. Edited with his own Sudhâmañjarîvâsanâ and a Hindî bhâsâ by Sîtârâma Jhâ (Benares, 1932; repr. Benares, 1941).

14. Edited with the Udâhara?a of Vi?vanâtha, the Mâdhurî of Yuge?vara Jhâ, and a Hindî ?îkâ by Kapile?vara ?âstrî Kâ?î Sankrit Series 142 (Benares, 1946).

The Laghutithicintâma?i consists of table for determining tithes, nak?atras, and yogas accompanied by a short introductory text; Ga?e?a composed it in 1525. Of this work also there are hundreds of manuscripts as well as several commentaries:

1. ?îkâ of N?si?ha3 (b, 1586), the grandson of Divâkara of Golagrâma and the nephew of Mallâri, the commentator on the Grahalâghava.

2. Udâhara?a a Vi?vanâtha (1634), the commentator on the Grahalâghava. Published.

3. ?ippa?a of Vye?ka?a, alias Bâpû.

4. ?îkâ of Yajñe?vara.

The Laghutithicintâma?i has been published twice:.

1. Edited with his own Hindî commentary, Vijayalakshmî (1924), by Mât?pasâda Pâ??eya, Haridas Sanskrit Series 76 (Benares, 1938).

2. Edited with the Udâhara?a of Vi?vanâtha by V. G. Âpte, Ânandâ?rama Sanskrit Series 120 (Poona 1942), part I.

The tables of the Laghutithicitâma?i are discussed in D. Pingree, “Sanskrit Astronomical Tables in the United States,” pp. 47b-50b; and “Sanskrit Astronomical Tables in England.”

The B?hattithicintâma?i, also consisting of tables for computing tithes, nak?atras, and yogas and an introductory text, was written in 1552. It was much less popular than the Laghutithicintâma?i; there are only a dozen manuscripts, and the unique commentary is the Sùbodhinî composed by Vi??u, the son of Divâkara of Golagrâma and the brother of Mallâri. The text alone with Vi??u’s Subodhini is published By V. G. Âpte, Ânandâ?rama Sanskrit Series 120 (Poona, 1942), part 2. The tables are described in D. Pingree, “Sanskrit Astronomical Tables in the United States,” pp. 50b-51a; and “Sanskrit Astronomical Tables in England.”

The Lîlâvatîvyâk?ti or Buddhivilâsinî, a commentary on the Lîlâvatî of Bhâskara II, was composed by Ga?e?a in 1545. It was published in the edition of the Lîlâvatî produced by Dattâtreya Âpte, Ânandâsrama Sanskrit Series 107, 2 vols,. (Poons, 1937).

The V?ndâvana?îkikâ or Vivâhadîpikâ, commentary on the Vivâhav?ndâvana of Ke?avârka (a work on astrology applied to marriage), was written by Ga?esa in 1554. It was published at Benares in 1868.

The Muhûrtatattvaviv?ti or Muhûrtadîpikâ, a commentary on the Muhûrtatattva of his father, Ke?ava (a work on catarchic astrology), was written by Ga?e?a before the Vivâhadîpikâ, which refers to it. The Muhûrtadîpikâ has not yet been published.

The ?râddhâdivinir?aya is evidently a work on offerings to one’s ancestors. No manuscripts are known.

The Sudhîra?jana is a work on The astronomical instrument of the same name. It has not yet been published.

The Tarjanîyantraka is presumably a work on another astronomical instrument called the tarjanî. No manuscripts are known.

The K???â??amînir?aya is work on the festival of K???a’s birthday, which falls on the eighth tithi of the K???apak?a of the month ?râva?a. No manuscripts are known.

The Holikânir?aya is a work on the festival called Holikâ which falls on the full moon of the month Phâlguna. No manuscripts are known.

The Pâtasâri?î or Oâtasâdhana is a set of tables for computing the daters of pâtas of the sun and moon, accompanied by a brief explanatory text; Ga?e?sa wrote it in 1522. There are three commentaries:

1. Viv?ti of Divâkara (b. 1606, a great-grandson of Divâkara of Golagrâma.

2. Vivrti of Vi?vanâtha (1631), the son of Divâkara of Golagrâma.

3. Viv?ti of Dinakara (1839).

Neither the Pâtasâri?î itself nor any of its commentaries has yet been published.

The Câbukayantra and Pratodayantra are works on the astronomical instruments called by these names. A manuscript of the latter is said to be dated 1516, when Ga?e?a was only nine years old. Neither work has been published.

The Dhruvabhrama?ayantravyâkhyâ is a commentary on the second adhikâra of Padmanâbha’s Yantraratnâvalì (ca. 1360). This adhikâra describes the dhruvabhrama?ayantra, which is an instrument for observing the north pole star. Its ascription to Ga?e?a is uncertain. It has not yet been published.

BIBLIOGRAPHY

The editions of Ga?e?a’s works have already been mentioned. Very little else has been written of him or his astronomical system save my articles and books on astronomical tables, to which reference has been made. There are articles on him by Sudhâkara Dvivedin in his Ganakatarîginî (Benares, 1933; repr. from Pandit, n.s. 14 [1892], 58-63); by ?. B. Dîk?ita, in Bhâratîya Jyoti??âstra (Poona, 1931; repr. of 1896 ed.), pp. 259-267; and by G. Thibaut, in Astronomie, Astrologie und Mathematik (Strasbourg, 1899), pp. 61-62. M. G. Inamdar, “An Interesting Proof of the formula for the Area of a (Cyclic) Quadrilateral and a Triangle Given by the Sanskrit Commentator Ganesh in About 1545 A.D.,” in Nagpur University Journal, 11 (1945), 36-42, deals with a passage in the Buddhivilâinî.

David Pingree