86 . B S ERVjriONS on the 



radius, or diameter of a circle, by parts of a curve line, namely, 

 the circumference, is a refinement not at all obvious, and has 

 probably been fuggefted to them by fome very particular view, 

 vsrhich they have taken, of the nature and properties of the cir- 

 cle. As to the accuracy of the meafure here affigned to the 

 radius, viz. 3438 of the parts of which the circumference con- 

 tains 2 T 600, it is as great as can be attained, without taking in 

 fmaller divifions than minutes, or 6oths of a degree. It is true 

 to the nearefl minute, and this is all the exa(5lnefs aimed at in 

 thefe trigonometrical tables. It muft not however be fuppofed, 

 that the author of them meant to alTert, that the circumference 

 is to the radius, either accurately or even very nearly, as 21600 

 to 3438. I have fliewn, in another place*, from the Inftitutes of 

 Akbar, that the Brahmins knew the ratio of the diameter to 

 the circumference to great exatT:nefs, and fuppofed it to be that 

 of I to 3. 14 1 6, which is much nearer than the preceding. Cal- 

 culating, as we may fuppofe, by this or fome other proportion, 

 not lefs exa<5l, the authors of the tables found, that the radi- 

 us contained in truth 3437'- 44". 48'", l^c. ; and as the frac- 

 tion of a minute is here more than a half, they took, as their 

 conftant cuftom is, the integer next above, and called the radius 

 3438 minutes. The method by which they came to fuch an 

 accurate knowledge of the ratio of the diameter to the circum- 

 ference, may have been founded on the fame theorems which 

 were fubfervient to the conftrud;ion of their trigonometrical 

 tables f . 



4. These tables are two, the one of fines, and the other of 

 verfed fines. The fine of an arch they call cramajya ox jyapinda^ 

 and the verfed fine utcramajya. They alfo make ufe of the co- 

 fine or bhujajya. Thefe terms feem all to be derived from the 

 wordjjiT, which fignifies the chord of an arch, from which the 



name 



• Tranf. R. S. Edin. vol. II. p. 185. Phyf. CI. 

 + See Note, J 6. 



