TRIGONOMETRT of the BRAHMINS. 97 



by the rule jufl laid down, was fovind the fine of 15°, then of 

 7". 30', and laflly of 3°. 45', which is the fine required. Thus 

 the fine of 3°. 45' would be found equal to 224', 44", as above 

 obferved, and, the fine of 7°. 30', equal to 448'. 39", and, taking 

 the nearefl integers, the firfl was made equal to 225, and the fe- 

 cond to 449*. 



7. When, by the bifedlions that have juft been defcribed, 

 the fine of 3°. 45, or of 225', was found equal to 235', the reft 

 of the table was conflrudled by a rule, that, for its fimplicity 

 and elegance, as well as for fome other reafons, is entitled to 

 particular attention. It is as follows : " Divide the firft jya- 

 pinda, 225' by 225 ; the quotient i, dedudled from the divi- 

 dend, leaves 224', which added to the firft jyapinda, or fine, 

 gives tlie fecond, or the fine of 7°. 30', equal to 449'. Divide 

 the fecond jyapinda, which is thus found, by 225, and dedudl 2, 

 the neareft integer to the quotient, from the former remain- 

 der 224', and this new remainder 222', added to the fecond jya- 

 pinda, will give the third jyapinda equal to 671'. Divide this 

 laft by 225, and fxibtradl 3, the neareft integer to the quotient, 

 from the former remainder 222', and there will be left 219', 



M which, 



* By fuch continual bifeftions, the Hindoo mathematicians, like thofe of Europe 

 before the invention of infinite feries, may have approximated to the ratio of the 

 diameter to the circumference, and found it to be nearly that of i to 3.1416 as 

 above obferved. A much lefs degree of geometrical knowledge than they poflefl'ed, 

 would inform them, that fmall arches are nearly equal to their fines, and that the 

 fmaller they are, the nearer is this equality to the truth. If, therefore, they afTumed 

 the radius equal to I, or any number at pleafure, after carrying the bifeftion of the 

 arch of 30, two fteps farther than in the above conftrufbion, they would find the 

 iine of the 384th part of the circle, which, therefore, multiplied by 384, would 

 nearly be equal to the circumference itfelf, and would a£lual!y give the proportion 

 of I to 3.14159, as foraewhat greater than that of the diameter to the circumfe- 

 rence. By carrying the bifeflions farther, they might verify this calculation, or 

 eftimate the degree of its exaflnefs, and might afiume the ratio of i to 3.1416 as 

 more fimple than that juft mentioned, and fufiiciently near to the truth. 



