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 386

CHAPTER VII-MEASUREMENT OF AREAS.
189
of the annulus is 45. What is the calculated measure of the area of (this) annulus ?
18. In the case of a figure resembling the crescent moon, the breadth is seen to be 2 hastas, the outer curve 68 hastas, and the inner curve 32 hastas. Say what the (resulting) area is.
The rule for arriving at the (practically approximate value of the) area of the circle :
19. The (measure of the) diameter multiplied by three is the measure of the circumference; and the number representing the square of half the diameter, if multiplied by three, gives the (resulting area in the case of a complete circle. Teachers say that, in the case of a semicircle, half (of these) give (respectively) the measure of the circumference and of the area).
Examples in illustration thereof.
20. In the case of a circle, the diameter is 18. What is the circumference, and what the (resulting) area (thereof)? In the case of a semicircle, the diameter is 18: tell me quickly what the calculated measure is (of the area as well as of the circumference).
The rule for arriving at (the value of) the area of an elliptical figure :
21. The longer diameter, increased by half of the (shorter) diameter and multiplied by two, gives the measure of the circumference of the elliptical figure. One-fourth of the shorter) diameter, multiplied by the circumference, gives rise to the (measure of the area (thereof).
19. The approximate character of the measure of the circumference as well 28 of the area as given here is due to the value of being taken as 3.
21. The formula given for the circumference of an ellipse is evidently an approximation of a different kind. The area of an ellipse is . a.b, where a and b are the semi-axes. If is taken to be equal to 3, then 7. a.b, = 3 a.b. But the formula given in the stanza makes the area equal to 2ab + b2.