CHAPTER VII-MEASUREMENT OF AREAS. The rule for arriving at the minutely accurate values relating to a figure resembling (the longitudinal section of) the yara 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 (accu- rate) 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. 71. In the case of a figure resembling (the longitudinal) section of the yava grain, the (maximum) length is 12 dandas; 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 value 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 :- 73. The square of the arrow measure is multiplied by 6. To this is added the square of the string measure. The square 20€ 70. The figure resembling a bow is obviously the segment of a circle. The area of the segment as given here = c x √IO. 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 pro- duct of r, the diameter and one-fourth of the radius, 3.e., π x 2r x. arc=6²+²; a perpendicular == N 6 chord=a²6 p². C 22 The figure resembling 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. 73 & 74. Algebraically,
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