516 Mr. Wursu on the Hindi Quadrature of the Circle. 
The two series thus explained are found to be of the following forms : 
o_i8¢ 8a adi eared 
= eoitenitio—_itivoitigoit 
bg’ Vai “ag hs, Be 
Radig Ge Ite 1t ie (tect ee) 
Which, if d=1, become respectively : 
1 1 1 I sii 
0=8x(s5te7teanta ti, pt 8) 
1 1 1 1 1 
GSasss & bene +o ti. Bt. atipaté) 
Now, let the former series within the brackets bea, and the latter); thenitcan 
; BOP IG l 1 1 i 1 
be easily proved that a+-J, or the series —> +33 +37+7.9 toit& = 3% 
: d : 1 1 1 1 
and it has been mentioned above that the series a eta Tete 
(when the diameter is one), the are of 90°—4=a—J; having therefore the 
values of a—b and a+4, it can be easily proved that a=the arc of 45°, 
and b =4— are of 45°; therefore, in the first of these quadratures, 8a= 
circumference, and in the second, 4—8b=circumference also, as taught 
by the author. 
The author, after laying down the above series, proceeds to shew in 
numbers a proportion of the circumference to the diameter in the verse 
which has been originally quoted and translated, and then finishes his 
chapter by rules for finding the sines and cosines, of which mention will be 
made hereafter. 
In the Carana Padhati, the sixth chapter commences thus : 
Vydsacchaturghnat bahusah prithac sthat 
Tripanja saptadyayugahritdni 
Vyasé chatuoghné cramasastwripam swam 
Curydttadasyat paridhissustieshmah. 
‘* Divide the given diameter multiplied by 4 severally and continually by the odd 
« numbers 3, 5, 7, 9, 11, &e., and the quotients thus obtained, alternately subtract 
« from, and add to, the diameter multiplied by 4. The result is the precise circum- 
“ ference.” 
This series is the same with the first laid down by the author of the 
Tantra Sangraha, namely, 
1 1 1 1 1 
Ome x(a ~34+5-7tp-Tt®) 
