ASTRONOMY of thi BRAHMINS. 185 



we would find it impoflible to difcover from tliem exac.'Hly, on 

 account of the fmall quantities that may have been neglected 

 in their calculations. Fortunately, we can arrive at this know- 

 ledge, which is very material when the progrefs of geo- 

 metry is to be eftimated, from a paflage in the Ayecn Ak- 

 bery, where we are told, that the Hindoos fuppofe the dia- 

 meter of a circle to be to its circumference as 1250 to 3927 *, 

 and where the author, who knew that this was more accurate 

 than the proportion of Archimedes, (7 to 22), and believed it to 

 be perfe<5lly exact, exprefles his aftonifliment, that among fo fnn- 

 ple a people, there ihould be found a truth, which, among the 

 wifeft and moft learned nations, had been fought for in vain. 



The proportion of 1250 to 3927 is indeed a near ap- 

 proach to the quadrature of the circle ; it differs little from 

 that of Metius, 113 to 355, and is the fame with one 

 equally remarkable, that of i to 3. 141 6. When found in 

 the fimpleft and moft elementary way, it requires a poly- 

 gon of 768 fides to be infcribed in a circle ; an operation 

 which cannot be arithmetically performed without the know- 

 ledge of fome very curious properties of that curve, and, at 

 leaft, nine extradlions of the fquare root, each as far as ten 

 places of decimals. All this muft have been accomplifhed in 

 India j for it is to be obferved, that the above mentioned 

 proportion cannot have been received from the mathemati- 

 cians of the weft. The Greeks left nothing on this fubje(5l more 

 accurate than the theorem of Archimedes ; and the Ara- 

 bian mathematicians, feem not to have attempted any nearer 

 approximation. The geometry of modern Europe can much 

 lefs be regarded as the fource of this knowledge. Metius and 

 ViETA were the firft, who, in the quadrature of the circle, 

 furpaflfed the accuracy of Archimedes ; and they flouriflied 

 at the very time when the Inftitutes of Akbar were colleded 

 in India. 



Vol. II. a a 60. "" 



* AyeenAkbery, Vol. III. p. 32. 



