510 Mr. Wutsu on the Hindi Quadrature of the Circle. 
Metuwvs, viz. 113 to 355, though in all three the circumference is rated at 
more than the truth. The s/éca in the Lildvati is as follows : 
Vydsé bhanandagnihaté vibhacté 
Chabdnastryath paridhissussieshmah 
Dwévimsatinighnévihritétha sailath 
Stilothavdsy ddvyavahdrayogyah.’* 
A’‘ryap’Hatta has not left behind him any record of the means by which 
he obtained so accurate a proportion. His work however shews so much 
geometrical knowledge, that there can be little doubt that he effected his 
approximation in the same manner with Arcuimepes, by a numeral calcu- 
lation of the perimeters of inscribed and circumscribed polygons with the 
circle; for in the polygon of 768 sides to a circle whose radius is one, the 
perimeter of the inscribed polygon is 628316, and of the circumscribed 
628326. The circumference of the circle will therefore be greater than 
628316, but less than 628326, or nearly half their sum, namely, 628321, 
to which the above approximation is nearly similar. 
In the Stirya Sid’dhdénta, the radius of a circle is stated at 3438, in terms 
of minutes of the circumference, being about one-quarter of a minute too 
great ; and in the following sléca, it appears that a very coarse rule is laid 
down by the author. 
Yojandndm satényashtau bhikarné dwigundnitu 
Jadvargaté dasagundt padam bhiparidhirbhavet.t 
“* Square the yojanas of the earth’s diameter 1600, and multiply the square by 10, 
«and extract the root of the product: the root is the equatorial circumference of the 
‘© earth.” 
In such a matter, the strictest accuracy need not be required ; but for a 
general rule, this would err considerably from the truth, being less correct 
than the proportion of 7 to 22; and yet we find the same in the Cdma- 
dégdhri, acommentary on the Surya Sid’dhanta, laid down in the following 
terms : 
Vritta vargdt dasa hritat padamvydsdbhavédiha 
Evam paricshitévydsah vrittastu viparitatah. 
“ The root of the square of the circumference divided by ten, is the diameter ; to 
find the circumference of a given diameter, reverse the rule.” 
* This verse is in the Upajdtivrittam measure. 
+ This verse is in the Anushtubvrittam measure. 
