314 HINDOO MATHEMATICS. 



must, however, be conceded to the Hindoo algebraist that 

 he had advanced farther in the science, since he appears to 

 have been able to resolve equations containing several un- 

 known quantities, which it is not clear that Diophantus 

 knew : and also had a general method of resolving indeter- 

 minate equations of at least the first degree, which it is 

 certain that Diophantus had not attained. There is yet a 

 curious question left for discussion : Was the science ot 

 algebra known long before, and by what degrees of improve- 

 ment did it advance until the time of Arya Bhatta 1 The 

 late Professor Playfair was of opinion that it was much 

 older. He observes, " It is generally acknowledged that /^w- 

 phantus cannot have been himself the inventor of a.l the 

 rules and methods which he delivers; much less is Arya 

 Bhatta to be held the sole inventor of a system that was 

 still more perfect than that of Diophantus. Indeed, before 

 an author could think of imbodying a treatise of algebra in 

 the heart of a system of astronomy, and turmng the re- 

 searches of the one science to the purposes of the other, both 

 must be in such a state of advancement as the lapse ot 

 several aaes and many repeated elibrts of invention were re- 

 quired to° produce."* Delambre, in answer to this, says, 

 when an author has created a new science among a people 

 considerably advanced in civilization, men of genius wiU 

 not be long in acquiring the new notions, in order to ex- 

 tend and multiply their application. Thus among the 

 Greeks, Archimedes succeeded to Conon, and -^poUomus 

 followed Archimedes, in less than sixty years. The Ber- 

 noullls made decided progress in modern analysis even m 

 the lifetime of Newton and Leibnitz, its inventors.! 



It appears from the Hindoo treatises on algebra that they 

 understood well the arithmetic of surd roots ; that they 

 knew the general resolution of equations of the second de- 

 gree, and had touched on those of higher denomination, re- 

 solving them in the simplest cases ; that they had attained 

 a general solution of indeterminate problems of the first de- 

 gree, and a method of deriving a multitude of answers to 

 problems of the second degree, when one solution was dis- 

 covered by trials. Now, this is as near an approach to a 



' * Edinburgh Review, vol. xxii. p. 143. , r, „ „,ii.-, 



t Delambre, Hist, de PAstronomie du Moyen Age, Dtseours preltm- 

 inaire. 



