Mr. Waist on the Hindi Quadrature of the Circle. 515 
Which, if d=1, will be: 
ae 1 1 1 1 
c=sititx (5p a5eit eee eee +60.) 
The author then proceeds in the same measure : 
Dwyddiyujdm vacritays vyécd haradwinighna vishcambhe 
Dhanamrinamanténtydrdhwa gataujacritidwi sahitaharddwighni. 
** Multiply the diameter by 4, and divide the product severally by the squares of the 
“* numbers 2, 4, 6, 8, 10, &c., subtracting 1 from each square ; the quotients alternately 
add to, and subtract from, twice the diameter : rectify the sum obtained, by taking the 
** next odd number less than the last even figure squared, squaring it, adding 2 to the 
. “© square, doubling this sum, and with this thus obtained as a divisor, dividing four times 
“ the diameter: this quotient add or subtract, as is required, from the sum formerly 
obtained, for a very correct circumference.” 
a 
a 
a 
a 
The series thus obtained is : 
Ad 4d 4d 4d a2 4d 
C=2d+ 5-2 4+ a ot 8 
Zo 1-161 BI faa Nae 
Where C=circumference, d=diameter, and p=the last even number 
squared in the series, which, if the diameter be 1, becomes, 
1 1 1 1 SF 1 
CHOY nya Pectaten coe phate teal gift). ) 
VS s5. 88,7 9779 Polpeea2 
“ ° : 1 1 1 1 - 
This series, viz. EG Rata IAI TLOa &e. can easily be proved to be 
equal to the arc of 90°—1, therefore 2+-4 into the series will equal the 
whole circumference, the diameter being one, as in our authotr’s series. 
Two other series are then exhibited in lines of the Gidi measure. 
Dwyddéschaturddérva chaturadhicdndnniréca vargassyuh 
Harah cunjara gunitd vishcambhaswamati calpitobhdjyah 
Phatlayutiradyé vrittam bhdjyadalam phalavihinamanyatra. 
«« Take the squares of the terms, diminished by 1, of the two arithmetical progressions 
«« whose first terms are respectively 2 and 4, and ratio of progression 4, for divisors: in 
“* the former series, divide 8 times the diameter by the divisors severally, and the sum of 
‘* the quotients is the circumference of the circle ; in the latter, subtract from 4 times 
“ the diameter the sum of the quotients of 8 times the diameter divided by the divisors 
“« severally, and the result is the circumference in the second case.” 
Vor. III. 3 xX 
