Mr. Wursx on the Hindi Quadrature of the Circle. 517 
The next verse in the chapter is of the measure called Gitivriitam. 
Vydsddwana samgunitat prithagdptantryddyay ugvimilaghanaih 
Trigunita vydsé swamrinam Cramasah critwapi paridhiranéyah. 
‘* Divide the given diameter multiplied by 4 severally and continually by the cubes of 
the odd numbers 3, Oaigeo, lemeces subtracting from each cube its respective 
“root; the sums thus obtained alternately add to, and subtract from, 3 times the 
« 
« 
* 
a 
diameter: thus you will obtain the circumference of the circle whose diameter was 
** given,” 
This series is also the same with one of the former book, namely, 
1 1 1 1 
ag 4 if y 
e +4x (555 4.5.6°6.7.8 a=), 
The fourth verse of the chapter is of the measure called Indra Vajra- 
vrittam. 
Vargairyujémvadwigunairnnirécaih 
Vargicritairvarjita yugma vargaih 
Vydsancha shadghnam vibhajét phalam swam 
Vydsé trinighné paridhistadadsyat. 
«* Add to three times the diameter the sum of the quotes obtained by dividing six 
** times the diameter by the square of twice the square minus one of the even numbers 
= 2; 4, 6,8; 10, &e:;, subtracting from each the square of its even figure respectively. 
«© The sum is the circumference.’”’ 
This is an infinite series thus expressed algebraically : 
6d 6d 6d 
C=3d+ + @ net 8) pre, 
(2. 2-172 (2.4712 42" (2. 61) 6" 
Which, if the diameter = 1, becomes 
ae teas x ( eee i aa +S ALB att se.) 
The author proceeds with the verse originally quoted, for determining the 
diameter and radius in terms of minutes of the circumference, and then 
teaches how, by certain series, the sines, cosines, &c. are to be constructed. 
He next exhibits a stanza for finding an are of the circumference of a 
circle by means of the sum obtained by multiplying the sine of the arc into 
its radius and dividing the product by its cosine. This sum, it will be 
readily observed, is equivalent to a tangent of that arc, for cosine is to 
radius as sine is to tangent; but the tangent individually does not appear in 
the mathematics of the Hindis. 
8X 2 
