512 Mr. Wutsu on the Hindi Quadrature of the Circle. 
** If you proceed thus (as laid down in the former verse), and measure the circum- 
** ference of a great circle by 100000000000000000 parts, the circumference will be 
** equal to 314159265358979324 of such parts.” 
The approximations to the true value of the circumference with a given 
diameter, exhibited in these three works, are so wonderfully correct, that 
European mathematicians, who seek for such proportion in the doctrine of 
fluxions, or in the more tedious continual bisection of an arc, will wonder by 
what means the Hindi has been able to extend the proportion to so great 
a length. Some quotations which I shall make from these three books, will 
shew that a system of fluxions peculiar to their authors alone among Hindus, 
has been followed by them in establishing their quadratures of the circle ; 
and a few more verses, which.I shall hereafter treat of and explain, “will 
prove, that by the same mode also, the sines, cosines, &c. are found with 
the greatest accuracy. 
T proceed to quote extracts from the Téntra Sangraham. The first, of the 
measure called A nushtubvrittam, is from the chapter upon sines, &c. 
Vydsdrdham prathamannitwatatovanydt gunannayét 
Sambandhanniyamanchaivam vynéydvydsa vrittayoh. 
** Having found the radius, you may construct the sines ; but you must first know the 
‘* proportion between the diameter and the circumference.” 
The next is of the Gitivrittam measure : 
Vydsé varidhinihité ripa hrité vydsasdgarabhihate 
Trisarddhi vishama sanchyd bhactamrinamswam prithacramat curydt 
Yatsanchyaydtra harané critérnivritté hritistujamitaya 
Tasyé tirdhwa gataydssamasanchyd taddalamgunontésydt. 
Jadvargg6 ripayuté hard vydsdbdhighatacah pragwat. 
Tabhydmdptam swamriné critédhané sodhananchacarantydm 
Sticshmah paridhissasydt bahucritwoharanatoti sieshmascha. 
«« Multiply the diameter by 4, and from it subtract and add alternately the quotients 
** obtained by dividing four times the diameter by the odd numbers 3, 5, 7, 9, 11, &e., 
«* do thus to the extent required; and having fixed a limit, take half the even number 
“ next less than the last odd divisor for a multiplier, and its square plus one for a divisor, 
‘“* Multiply four times the diameter by the multiplier, and divide the product by the 
*« divisor, and add it or subtract it, according to the sign of the last quote in the series, 
** from the sum of the series: thus the circumference of the given diameter will be 
** obtained very correctly.” 
