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196
GANITASARASANGRAHA.
An example in illustration thereof.
44. A bow-shaped field is seen whereof the string-measure is 28, and the arrow-measure is 13. Tell me quickly, O mathematician, what the calculated measure of this area) is, and what the measure of this (bent) stick (curve).
The rule for arriving at the arrow-measure as well as the string-measure in relation to a bow-shaped field):
45. The difference between the squares of the string and of the bent bow is divided by 5. The square root of the resulting quotient) gives the intended measure of the arrow. The square of the arrow is multiplied by o; and (this product) is subtracted from the square (of the aro) of the bow. The square root (of the resulting quantity) gives the measure corresponding to the string.
Examples in illustration thereof.
46. In the case of this (already given bow-shaped) field the measure of the arrow is not known; and in the case of another (similar field) the measure of the string is not known. O you who know calonlation, give out both these measures.
The rule for arriving at the practically approximate value of the area of the circle which is oiroumsoribed about or inscribed within & four-sided figuro:
47. Half of three times (the measure of the area of the inscribed quadrilateral figure) gives the measure of the area of the oirole in the case in which it is circumscribed outside. In the case where it is inscribed within and the quadrilateral is the other way (1.e., escribed), half of the above measure (is the required quantity).
47. The formula here given may be seen to be accurate in the case of a quare, but only approximate in the one of other quadrilaterale, if 8 bo takon to be the correot valao otr.
