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 426

CHAPTER VII–MEASUREMENT OF AREAB.
229
229 (also) of the square. (That same) quotient, if multiplied by sid, gives rise to the required measure of the base of the (equilateral) triangle as also of the longish quadrilateral figure. Half (of this is the measure of the perpendicular-side (in the case of the longish quadrilateral figure).
An example in illustration thereof. 143-145. A king caused to be dropped an excellent carpet on the floor of (his) palace in the inner apartinents of his zenana amidst the ladies of his harem. That (carpet) was in shape) a regular circle. It was held in band) by those ladies. The fistfuls of both their arms made each of them) acquire 15 (dandas out of the total area of the carpet). How many are the ladies, and what is tbe diameter (of the circle) here? What are the sides of the square (if that same carpet be square in shape) ? and what the
magnitude. The stanza states a rule for finding out the measure of the diameter of the circle, or of the sides of the square, or the equilateral triangle or the oblong. If m represents the area of each part and n the length of a part of the total perimeter, the formulas given in the rule are
*4= diameter of the circle, or side of the square ;
and
x 6 = side of the equilateral triangle or of the oblong;
n
and half of x B= the length of the perpendicular-side in the case of the oblong.
The rationale will be clear from the following equations, where a represents the number of parts into which each figare is divided, a is the length of the radius in the case of the circle, or the length of a side in the case of the other figures, and b is the vertical side of the oblong: In the case of the Circle 2 x m_ta%
xn 2 a
ахта 2 In the case of the Square
In the case of the Equilateral Triangle =
X 1 3a In the case of the Oblong
x xm a xb
here b is taken to be equal
xn 2 ( a + b) to half of a. It has to be noted that only the approximate value of the area of the equilateral triangle, as given in stanza 7 of this chapter, is adopted here. Otherwise the formula given in the role will not hold good.
143-145. What is called fistful in this problem is equivalent to four angulas in measure.