520 Mr. Wuuisu on the Hindi Quadrature of the Circle. 
principles laid down in another sléca of the Vasantitilaca-orittam measure in 
the same chapter, as follows : 
Cotthrita triguna bahu vadhé chatasmé 
Tattat phalachcha bhujavarga hatdttu cotyah 
Crityd critéshucha dharagni saradi bhacte 
Shwojaicyatastyajatuyugmayutim dhanustat. 
«« The radius into the sine divided by the cosine is the first quote: this multiplied by 
*« the square of the sine, and divided by the square of the cosine, is the second quote ; 
«« this second, and those obtained continually in the same way, multiply and divide by 
«* the square of the sine and the square of the cosine respectively : divide the quotes in 
«« order by 1, 3, 5, 7, 9, 11, &c. respectively, and the difference of the sum of the Ist, 
«© 3d, 5th, &c., and of the 2d, 4th, 6th, &c., will be the arc whose sine was taken.” 
This, of which the meaning is the same with that in the Carana Padhati, is 
expressed thus : 
ree GSP! OR SOS Np GP 
cos. 3cos® Sicos® 7 cos.’ 
+ &e 
Now if the arc of 30° be taken, the first quote = the tangent of that arc 
= v4; to multiply this by the square of the sine, and divide it by the 
square of the cosine, it is sufficient to divide it simply by 3 (because the 
square of the sine of 30° is one-third of the square of the cosine of that 
angle): divide then each quote in succession by the odd numbers 1, 3, 5, 7, 
9, 11, &c., respectively ; the arc, thus obtained, multiplied by 6, will equal 
the semi-circumference when the radius = 1, or the whole circumference if 
the diameter be 1; but 6 x v}=2x y3=v12; therefore vy 12 x 
(1 ~dtye-psterc-nst &e. ) equals the whole circumference when 
the diameter is one, according to the rule laid down in the Sadratnamdlah 
in the verse “ Vyasércaghnacriteh,” &c., and in the Tantra Sangraha in 
the verse “ Vyasa Vargadravihatat,” &c. before quoted. The rule also for 
finding the sum of any arc from the tangent is thus expressed in the same 
work in four slécas of the Anushtub measure. 
Vrittanayana margindbreshta jydna dhanurnayét 
Ishta jyd trijyayorghdatat cdtyaptam prathamam phalam 
Jyd vargom gunacam critwd coti vargancha haracam 
Prathamdadi phalébhyotha néyaphalalatirmuhuh. 
Ecatryddydja sanchyabhirbhactéshwétéshwanucramat 
Ojdndm yutitastyacte yugma yogé dhanurbhavét 
Doh cétyéralpamévéshtam calpantyamihéditam 
Muhuh critépi labd hinadnnanyathdvasitirbhavet. 
