ROMANTIC ORIGIN OF THE LILAVATI. 311 



Again, in the year 1816 John Taylor,'M.D., of the East 

 India Company's Bombay ]\Iedical Establishment, pub- 

 lished in India a translation of the Lilavati directly from the 

 Sanscrit ; and in the following year, H. T. Colebrooke, 

 Esq., published Algebra, with Arithmetic and Mensuration, 

 from the Sanscrit of Bramagupta and Bhascara. This work 

 contains translations of four different treatises WTitten in 

 Sanscrit verse on the arithmetic, algebra, and geometry of 

 Hindostan. Two of these are the LUavati (arithmetic)' and 

 Vija Ganita (algebra) of Bhascara already mentioned. The 

 other two books are still more ancient, and were composed 

 by a mathematician named Bramagupta. These, like most 

 of the mathematical treatises of the Hindoos, form part of 

 iiystems of astronomy ; the first two being the introduc- 

 tion to the Stddhanta Siromam of Bhascara, and the other 

 two forming the twelfth and eighteenth chapters of the 

 Bravia Siddkanta, an astronomical work of Bramagupta. 



The age of Bramagupta is considerably earlier than that 

 of Bhascara, and his works are very rare. Mr. Colebrooke 

 was fortunate enough to obtain a copy of them, which is 

 imperfect in some respects, but in which the chapters on 

 mathematics are complete. The age in which he lived is 

 fixed with great probability from various concurring circum- 

 stances, particularly from the position which he assigns in 

 his astronomy to the solstitial points, to the sixth or begin- 

 ning of the seventh century of the Christian era, — a period 

 earlier than the first dawn of the sciences in Arabia, al- 

 though much less ancient than all that now remains of the 

 Greek mathematics and astronomy. Ganesa, the most dis- 

 tinguished of the commentators on Bhascara, quotes a pas- 

 sage from Arya Bhatta on algebra, which contains the re- 

 fined artifice for the solution of indeterminate problems, 

 which is called in Sanscrit Cuttaca. Arya Bhatta is in- 

 deed regarded as the most ancient uninspired writer that 

 has treated of astronomy. By a variety of arguments Mr. 

 Colebrooke makes it appear that this alo-ebraist wrote as far 

 back as the fifth century of the Christian era, and perhaps 

 earlier. He was therefore almost as old as the Greek al- 

 gebraist Diophantus, who lived about the year 360. The 

 Persian translator of the Lilavati, Fyzee, gives an account 

 of the origin of that treatise, whichhas in it much of that 

 air of romance that distinguishes every thing oriental, not 



