ALGEBRA. 



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seneral solution as was made until the time of Lagrange. 

 The Hindoos had also attempted to solve equations ot higher 

 orders, but with very little success. They not only apphed 

 alcrebra both to astronomy and geometiy, but conversely 

 ap^pUed geometry to the demonstration of algebraic rules. 

 In fact, they cultivated algebra much more, and with greater 

 success, than geometry, as is manifest from their low state 

 of knowledge in the one, and high attainments m the other. 

 Mr Colebrooke has instituted a comparison between the 

 Indian algebraist and Diophantus, and has found reason to 

 conclude that, in the whole science, the latter is very far 

 behind the former. He says the points m which the Hin- 

 doo algebra appears distinguished from the Greek are, be- 

 sides a better and more convenient algorithm,— 



1st, The management of equations of more than one un- 

 known quantity. , 



'>d The resolution of equations of a higher order, m 

 which, if they achieved little, they had at lea>t the merit ot 



' 3d"Se'ral methods for the resolutions of indeterminate 

 problems of the first and second degrees, m which they 

 went far indeed beyond Diophantus, and anticipated dis- 

 coveries of modern algebraists. . , . r 

 4th The application of algebra to astronomical mvesti- 

 aations and geometrical demonstrations, in which they also 

 hit upon some matters which have been reinvented m mod- 



"o!uhe whole, when we consider that algebra made little 

 or no pro^rress among the Arabians— an ingenious people, 

 and particularly devoted to the study of the sciences, and 

 that centuries elapsed from its first introduction into Europe 

 until it reached any considerable degree of perfection-we 

 incline to the opmion of Professor Playfair rather than to 

 that of Delambre, on this branch of Indian science and^re 

 disposed to believe that algebra may have existed in one 

 shape or another, long before the time of Arja Bhatta. 



