Mathematics in Ancient and Medieval India c8.s3.53

c8.s3.53

*English Translation* : Multiply the arc by the square of itself ( multiplication being repeated any number of times ) and divide the result by the product of the square of even numbers increased by that number and square of the radius (the multiplication being repeated same number of times). The arc and the results obtained from above are placed one below the other and are subtracted systematically one from its above. These together give the *jīvā* ( r sin θ ) collected here as found in the expression beginning with *vidvān* etc. Multiply the unit (i.e. radius) by the square of the arc (multiplication being repeated any number of times) and divide the result by the product of square of even number decreased by that number and square of the radius (multiplication being repeated same number of times). Place the results one below the other and subtract one from its above. These together give the *śara* ( r-r cos θ ) collected here as found in the expression beginning with *stena*.