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 405

80€
CHAPTER VIMBABUREMENT OF AREAS.
The rule for arriving at the minutely accurate values relating to & figore resembling (the longitudinal section of) the yara grain, and also to a figure having the outline of a bow :
701. It should be known that the measure of the string (chord) multiplied by one-fourth of the moasure of the arrow, and then multiplied by the square root of 10, gives rise to the (800urate) value of the area in the case of a figure having the outline of a bow as also in the case of a figure resembling the (longitudinal) section of a yava grain.
Examples in illustration thereof. 711. In the case of & figure resembling (the longitudinal) section of the yara grain, the (maximum) length is 12 landas; the two ends are noodle points, and the broadth in the middle is 4 dandas. What is the area ?
721. In the case of a figure having the outline of a bow, the string is 24 in measure ; and its arrow is taken to be 4 in-moasure. What may be the minutely accurate value of the aroa P
The rule for arriving at the measure of the (bent) stick of the bow as well as of the arrow, in the case of a figure having the outline of a bow :
734. The square of the arrow moasure is multiplied by 6. To this is added the square of the string measure. The square
704. The figare reseinbling a bow is obviously tho segment of a cirole. The area of the segment as given here = c * ?X v10. This formula is not accurate. It seems to be bred on the analogy of the role for obtaining the aron of semi-circle, which area is ovidently equal to the pro. duct of the diameter and one-fourth of the radius, 1.6., * 3r .
The figure resembling the longitudinal soction of yava grain may be evil: men to be made up of two similar and equal segments of a circle applied to osol other so to have a common chord. It is evident that in this case the value o the arrow-line becomes doubled. Thus the samo formula is made to hold goo here sloo. 784 & 74. Algebraically,
arc=v Ray perpendicular - chord Wap.