Gerx509n0)9 
XXXIII. On the Hindu Quadrature of the Circle, and the infinite Series of the 
proportion ofthe circumference to the diameter exhibited in the four S'dstras, 
the Tantra Sangraham, Yucti Bhdashd, Carana Padhati, and Sadratnamila. 
By Cuartrs M. Wutsn, Esq., of the Hon. East-India Company’s Civil 
Service on the Madras Establishment. 
(Communicated by the Mapras Lirenary Socrety and Auxrirary 
Royat Astaric Socrery.) 
Read the 15th of December 1832. 
A’ryas’satta, who flourished in the beginning of the thirty-seventh 
century of the Cali Yuga,* of which four thousand nine hundred and twenty 
years have passed, has in his work, the Aryal’hatiyam, in which he 
mentions the period of his birth, exhibited the proportion of the diameter 
to the circumference of the circle as 20000 to 62832, in the following 
verse : 
Chaturadhicam satamashtagunandwashashtistatha sahasrandm 
Ayutadwaya vishcambhasydsanné vritta parindhah.t 
Which is thus translated : 
«© The product of one hundred increased by four and multiplied by eight, added to 
** sixty and two thousands, is the circumference of a circle whose diameter is twice ten 
«© thousand,” 
The author of the Lildvati, who lived six centuries after A’ryap’HaTTA, 
states the proportion as 7 to 22, which, he adds, is sufficiently exact for 
common purposes. As amore correct or precise circumference, he proposes 
that the diameter be multiplied by 3927, and the product divided by 
1250; the quotient will be a very precise circumference. ‘This proportion 
is the same with that of A’ryap’Hatra, which is less correct than that of 
* Or the sixth century of the Christian era. 
+ This verse is in the variety of the Aryavrittam measure, called Vipula. 
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