i m 
who lived about the year 360. Mr. Colebrooke has further 
instituted a comparison between the Greek and Hindoo 
algebraists, and found reason to conclude that, in the 
whole science, the former are very far behind the latter. 
He says, the points in which the Hindoo algebra appears 
distinguished from the Greek are, besides a better and more 
convenient algorithm : 
1st. " The management of equations of more than one 
unknown quantity. 
2d. " The resolution of equations of a higher order, in 
which, if they achieved little, they had at least the merit 
of the attempt. 
3d. " General methods for the resolutions of indeter- 
minate problems of the first and second degrees, in which 
they went far indeed beyond Diophantus, and anticipated 
discoveries of modern algebraists. 
4th. " The application of algebra to astronomical inves- 
tigations and geometrical demonstrations, in which they 
also hit upon some matters which have been re-invented in 
modern times." 
Having determined the inferiority of the algebra of 
Diophantus ; the degrees of improvement by which it ad- 
vanced to its perfection, in the time of Aryabhatta, becomes 
the next question — was it known long before, or was it then 
only discovered. " The late Professor Playfair was of opinion, 
that it was much older. He observes, that it is generally 
acknowledged that Diophantus cannot, himself, have been 
the inventor of all the rules and methods which he delivers ; 
much less is Aryabhatta 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 embodying a 
treatise of algebra in the heart of a system of astronomy, 
and turning the researches of the one science to the purposes 
of the other, both must be in such a state of advancement, 
