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 400

CHAPTER VII-MEASUREMENT OF AREAS.
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The rule for arriving at the minutely accurate values relating to a figure resembling (the longitudinal section of the yava grain, and also to a figure having the outline of a bow:
70. It should be known that the measure of the string (chord) multiplied by one-fourth of the measure of the arrow, and then multiplied by the square root of 10, gives rise to the (accurate) 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. 713. In the case of a figure resembling (the longitudinal) section of the yava grain, the (maximum) length is 12 andas; the two ends are needle points, and the breadth in the middle is 4 dandas. What is the area ?
72. 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 measure. What may be the minutely accurate valne of the area ?
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:
l'he square of the arrow measure is multiplied by 6. To this is added the square of the string measure. The square
704. The figure resembling a bow is obviously the segment of a circle. The area of the segment as given here=cx?.* 10. This formula is not accurate. It seems to be based on the analogy of the rule for obtaining the area of a semi-circle, which area is evidently equal to the product of , the diameter and one-fourth of the radius, i.e., * * 27 * .
The figure regembling the longitudinal section of a yava grain may be easily seen to be made up of two similar and equal segments of a circle applied to each other so as to have a common chord. It is evident that in this case the value of the arrow-line becomes doubled. Thus the same formula is made to hold good here also. 731 & 743. Algebraically,
arc =V6px +ca; perpendicular = chord =Vã — 6 på.