Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 435

238
GANITASĀRASANGRAHA
In the case of the quadrilateral figure witb) three equal sides, the square root of the difference between the two area-squares above noted) is added to the approximate measure of the area. (On treating the resulting sum as the optional quantity and) on adding and subtracting (the said square root as before), the base and the top-side are obtained so as to have to be divided by the square root of (such) optional quantity. (Here also), the approximate measure of the area, on being divided by the square root of (this optional quantity, gives rise to the measure of the other sides.
An example in illustration thereof. 1663. The accurate measure of the area is 5; the approximate measure of the area is 13; and the optionally chosen quantity is 16. What are the values of the base, the top-side, and the (other) side in the case of a quadrilateral figure with two equal sides ?
An example relating to a quadrilateral figure with three
equal sides. 1671. The accurate measure of the area is 5; and the approximate measure of the area is 13. Think out and tell me, O friend, the values of the sides of the quadrilateral figure with three equal sides.
The rule for arriving, when the approximate and the accurate ineasures of an area are known, at the equilateral triangle and also at the diameter of the circle, having those same approximate and accurate measures (for their area) :
1683. That which happens to be the square root of the square root of the difference between the squares of the (approximate measure and of the accurate measure of the given) area is to be
+ d2
XN
2
); and usb+d
2
R -a (b + d)
a (b - d)2 2 The formulas given above for the base and the top-side can be easily verified by substituting these values of R, r and p therein. Similarly the rule may be seen to hold good in the case also of a quadrilateral figure with three equal sides.
168. For the approximate and accurate values of an equilateral triangle Bee rules in stanzas 7 and 50 of this chapter.