514 Mr. Wutsu on the Hindi Quadrature of the Circle. 
«© Multiply any given diameter squared by 12, and extract the root of the product ; 
this is the first quote : divide this first by 3 for the second quote ; this second, and each 
so obtained quote, divide by 3 continually, place them in order, and divide them in 
succession by the odd numbers], 3, 5, 7, 9, 11, &c. Then add together the first, 
third, fifth, &c., quotes ; and add together also the second, fourth, sixth, &c. quotes ; 
then subtract the sum of the even from that of the odd, and the remainder will be the 
circumference of the circle, whose diameter was given.” 
The series laid down in the verse is thus expressed algebraically : 
1 1 1 1 1 
al Cig Seay Se AE eR 
ppt 2x(1 3.3'3.37.979,3 rptse.) 
The next verse is of the Gitivrittam measure: 
Samapanchdhataydyé rupddyayujas chaturghna milayutah. 
Tabhisshédasa gunitadvydsat prithaga hritétu vishamayate. 
Sama phala yagé tyacté sydtishta vyasa sambhavah paridhih. 
‘«* Divide the diameter multiplied by 16 severally by the fifth power of the odd 
numbers 1, 3, 5, 7, 9, &c., adding to each fifth power four times its root ; of the 
quotes thus obtained subtract the sum of the second, fourth, sixth, &c, from that of 
the first, third, fifth, and seventh, the remainder will be the circumference of the circle 
whose diameter was taken.” 
a 
€ 
ee 
a 
€ 
a 
€ 
This is an infinite series of the following form : 
16d 16d 16d 16 d 16d 
Ge Poa. FFs. F455 FAT FF 4.9 
&e. 
Or, if the diameter be one : 
1 1 1 1 ) 
ca6x (apgq-sqastegas Fait & 
The next verse of the Gitivrittam measure is as follows: 
Vydsddwaridhi nihatat pritagdptantrydyugvimild ghanath 
Trighna vydsé swamrinam cramasah kritwapi paridhivdnéyah. 
«* Divide four times the given diameter by the cubes of the odd numbers 3, 5, 7, 9, 
«11, 13, &c., subtracting from each its respective root; the quotes thus obtained 
«* alternately add to, and subtract from three times the diameter ; this is the circumfe- 
‘© rence of the circle whose diameter was given.” 
This is an infinite series (given in the Carana Padhati in nearly the same 
words), as follows: 
ae 4d 4d 4d 
Ca8dt gry tpoetReT woot 
