B. C. 961. Other epochs also are calculated, the last of which is the year of our Lord 538, from which modern Hindoo astronomy is dated.

The reader will find ample information on this subject, in the papers of Mr. Bentley in the sixth and eighth numbers of the Asiatic Researches; in vol. i, x, and xii, of the Edinburgh Review: in the Westminster Review, vol. ii: and in.

An Historical View of the Hindoo Astronomy, from the earliest dawn of that science in India to the present time, by the late J. Bentley, Calcutta, 1824, 8vo; again, London, 1825, 8vo. plates.

Astronomie der Inder, in the Blättern für literar. Unterhalt, 1829, Juli, No. clxxv.

Rapport sur le Kala Sankalita, recueil de mémoires du lieutenant-colonel John Warren, publié à Madras, en 1825, 1 vol. in 4to.; Lu à la Société Asiat. dans sa séance du 3 Déc. 1827, par M. Stahl, in the Journ. Asiat. 1827, lxvi, p. 356.

Sir William Jones states, that he had seen a catalogue of seventy-nine astronomical works in the Sanscrit language. See Craufurd's Researches on India, vol. i, p. 243.

The principal and most ancient astronomical work of the Hindoos is the Surya Siddhanta, which forms one of the six supplementary works, Vedangas, to the Vedas, (see above, p. 84,) and whose author is said to have lived in the fifth century of the Christian eraa.

Part of the first chapter of the Surya Siddhanta, in the Asiatic Journal, 1817, May, p. 429, 430; June, p. 546, 547.

An English translation of the whole of the Surya

a See Asiatic Researches, tom. vi, p. 540. According to the notion of the Hindoos, this work was a divine revelation made at the close of the Satya-yug, of the twenty-eighth Maha-yug, of the seventh Manwantara : that is, about 2,164,899 years ago. See 1. c.

Siddhanta was printed at Madras in the treatises of Captain Warren, upon the chronology of the Hindoos.

This was succeeded by Vishnu Chandra and Brahmagupta in the early part of the seventh, and Munjala, towards the middle of the tenth century.

Siromani, an astronomical work, by Bháscara, surnamed Acharya, (the teacher,) dates from the middle of the twelfth century: it is translated by Taylor in the Lilavati, which will presently come under notice. It is divided into two sections; the Gola Adhyaya, or lectures on the earth, and the Ganita Adhyaya, or lectures on numbers as applied to astronomy.

Opinions of Bháscara, respecting the globe and the attraction of the earth, in the Asiatic Journal, 1817, Feb. p. 110: see also Millin's Annales Encyclop. 1818, Sept. p. 108. This is nothing more than an extract from Dr. Taylor's translation of the Lilavati.

A translation by Colebrooke, mentioned in this place by Adelung, is placed under Arithmetic, to which it properly belongs.

Tithi Tatua and Jyatisha Tatua, two treatises on Astronomy and Astrology. Manuscripts in the Royal Library at Copenhagen.

Bârah Másá, a poetical description of the year in Hindoostan, by Mirza Cázim Ali Tawun, Calcutta, 1812, 4to.

The Asiatic Society of London possesses a manuscript treatise in Sanscrit upon the Eclipses of the Sun.

B. Arithmetic.

Short Account of the present mode of teaching Arithmetic in Hindoo schools, from Taylor's translation of the Lilavati, in the Asiatic Journal, 1817, March, p. 213-217.

The principal work upon Arithmetic is the Lilavati,

which is reckoned one of the six supplements (Vedangas) to the Vedas. The author, Bháscara Acharya, gave his work the name of his daughter, in order to console her for the want of a husband".

The original Sanscrit was printed for the first time at Calcutta, with the English title, The Lilavati, or System of Hindoo Arithmetic.

Lilavati, or a Treatise on Arithmetic and Geometry, by Bháscara Acharya, translated from the original Sanscrit, by John Taylor, Bombay, 1816, 4to. A copious extract from it is given in the Journal des Savans, 1817, Sept. p. 535-545.

Translation of the Lilavati and Vidyaganita, Treatises of Arithmetic and Algebra, by Bháscara, and an Extract from the Course of Astronomy of Brahmágupta, comprising his Arithmetic and Algebra, translated from the Sanscrit by H. T. Colebrooke, esq., and published with a preliminary Dissertation on the Origin of Algebra, Calcutta, 1818, 4to. This had already been printed under the title of, Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmágupta and Bháscara, by H. T. Colebrooke, esq., London, Murray, 1817.

This work is considered of much importance in the Edinburgh Review, where it is made the subject of an article, vol. xviii, p. 141. It contains four different treatises in Sanscrit verse. Two of these, the Lilavati and Vidyaganita are the works of Bháscara Acharya; the first on Arithmetic, the second on Algebra. The others are still more ancient, and were composed by a mathematician named Brahmágupta, who is supposed to have lived in the sixth or seventh century. These, like most of the mathematical

h Respecting another Sanscrit work bearing the title of Lilavati, see Catalogue des mss. Sanscrits, p. 65, 66.

writings of the Hindoos, form systems of astronomy; the first two being the introduction to the Siddhanta Siromani, and the other two forming the twelfth and eighteenth chapters of the Brahma Siddhanta of Brahmágupta.

Mr. Taylor possesses another manuscript under the title Udaharna, which contains the proofs of rules given in the Lilavati.

y. Algebra.

A Dissertation, by Mr. Colebrooke, on the Early History of Algebra in India, Arabia, Greece, etc. will be found prefixed to his translation of the Lilavati and Vidyaganita, just mentioned under the preceding head. It is full of learned and judicious research.

Bija Ganita, or the Algebra of the Hindoos, by Edward Strachey, of the East India Company's Bengal Civil Service, with notes, by Davis, London, 1813, 4to.

The Bija Ganita, or System of Hindoo Algebra, translated into the English, Calcutta, 1827.

Algebra of the Hindoos, with Arithmetic and Mensuration, from the Sanscrit of Brahmágupta and Bháscara, translated by H. T. Colebrooke, esq., London, 1817, 4to. See notice of this work under Arithmetic.

Kala Sankalita, a complete System of Algebra, of Arithmetic, and Geometry of the Hindoos, translated from the Sanscrit, by J. Warren, Madras, 1827. See Journal Asiatique, vol. xi, p. 356.

Some account of a Sanscrit work on a game resembling Chess will be found in the Asiatic Journal, 1818, February, p. 121, by Sir William Jones. This was first printed in vol. ii of the Asiatic Researches, and will also be found in Sir William Jones's Works, vol. i,

i There is a notice of it in the Edinb. Review, Nov. 1817. It is also made the subject of an appendix to Mr. Mill's History of India, vol. i, Appendix, No. ii, and again Asiatic Journal, Dec. 1818.

Z

4to. Some particular positions at Chess from the Sanscrit, are given in the Asiatic Journal, Oct. 1819, p. 347. Sir W. Jones believed that this game was invented by the Hindoos, and the Persians are of the same opinion.

HISTORY.

Professor Wilson informs us, that the only Sanscrit composition yet discovered to which the title of historical can with any propriety be applied, is the Rája Taringini, a history of Cashmire. This work was first introduced to the knowledge of the Mahommedans by the learned minister of Acber Abufazl; but the summary which he has given of its contents was taken, as he informs us, from a Persian translation; the Hindoo original being so scarce as not to be procured. Sir William Jones sought for it without success; and it escaped the search of all Europeans, until Mr. Colebrooke fortunately procured a copy in 1805, from the heirs of a Brahman, who died in Calcutta. Since that time the late Mr. Speke procured another transcript from Lucknow; and professor Wilson procured a third, which was brought for sale to Calcutta. The latter gentleman states, that he was unable to meet with another copy either in that city or at Benares.

The Raja Taringini, as we are informed by professor Wilson, is not one entire composition, but a series of compositions written by different authors at different periods: a circumstance that gives a greater value to its contents; as, with the exception of the early periods of the history, the several authors may be regarded almost as the chroniclers of their own times.