160 ON THE EzlRLY 



tirely from a Persian translation) it is proved, that the Hindus had made 

 a wonderful progress in some parts of Algebra; that in the indeterminate 

 analysis they were in possession of a degree of knowledge, which was m 

 Europe, first communicated to the world by Bachet and Fermat, in the 

 seventeenth century, and by Euler and Ds La Grange, in the eighteenth. 

 It would be very curious to push these inquiries into the Hindu indeter- 

 minate analysis, as far as possible. They might, perhaps, shew that the 

 Indians had a knowledge of continued fractions, and possibly speculations 

 in physics and the higher geometry, that we know nothing of : for the 

 foundation of the indeterminate analysis of the Hindus is directly ex- 

 plicable on the principle of continued fractions. And there are branches 

 of natural philosophy and mathematics, where equations will arise, which 

 can be solved only by the rules of the indeterminate analysis. In the in- 

 troduction to the Bija Ganita, where the first principles are given, a 



2 



method is taught of solving problems of the form Ax-\-b=zQ. This, 

 simply considered, may be thought only a vain speculation on numbers ; 

 but, in the body of the Bija Ganita, the rule is applied to the solution of 

 equations. It is true, that these equations arise from questions purely 

 numeral ; yet it appears, nevertheless, that the application of the rule was 

 understood. But whatever may be thought of this argument, it is, at all 

 events, interesting, to ascertain the progress which has been made in the 

 sciences, by different nations, in distant times. 



A good comparison of any of the mathematical sciences of the Greeks, 

 the Arabs, and the Indians, would be exceedingly valuable ; and every 

 information, which will serve to illustrate the subject, is of importance to 

 the early history of science. 



We know but very lit.tle of Algebra, in its infancy and first progress, 



