Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 391

CHAPTER VIL MEASUREMENT OF ARBAS.
189
of the annulus is 45. What is the caloulated measure of the area of (this) annulus ?
18. In the case of a figure resembling the crescent moon, the broadth is seen to be 2 hastas, the outer curvo 68 hastas, and the inner onrve 82 hastas. Say what the resulting) area is.
The rule for arriving at the (pructioally approximato value of the) area of the cirole :
19. The (measure of the) diamotor multiplicd by three is the measure of the circumference; and the number representing the squaro of half the diameter, if multiplied by thrre, gives the (resulting) area in the case of a completo virolo. Tenchers say that, in the case of a semicircle, half (of those) givo (respootively) the measure (of the ciroumference and of the arca).
Examples in illustration thereof.
20. In the case of a cirolo, the diameter is 18. What is the circumference, and what the (rcsulting) area (thereof) In the case of a semicircle, the diameter is 18: toll me quickly what the calculated measuro is (of the area as well as of tho circumference).
The rule for arriving at (tho valuo of) the area of an elliptical figure :
21. The longer diameter, increasod by half of the shorter) diameter and multiplied by two, gives the measuro of the cir-( cumference of the elliptical figuro. Onc-fourth of the (shortor) diameter, multiplied by the circumference, gives riso to the (measure of tho) area (thereof).
19. The approximate character of the measure of the circamforenco aw woll w of the ares as given bere io dao to the value of being taken 6 3.
21. The formula given for the circumference of an ellipms is evidently an approximation of different kind. The area of an ollip ir r. a.b, where 4 and I are the semieres. Ils is taken to be equal to 8, tbon r. a.b, = 8 a. But the formula given in the stansa makes the area equal to 2ab + 69.