# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९२

एतत् पृष्ठम् परिष्कृतम् अस्ति
196
GAṆITASĀRASAṄGRAHA.

An example in illustration thereof.

44. A bow-shaped field is seen whereof the string-measure is 26, 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 5; and (this product) is subtracted from the square (of the arc ) 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 calculation, give out both these measures.

The rule for arriving at the practically approximate value of the area of the circle which is circumscribed about or inscribed within a four-sided figure :-

47.[1] Half of three times (the measure of the area of the inscribed quadrilateral figure) gives the measure of the area of the circle in the case in which it is circumscribed outside. In the case where it is inscribed within and the quadrilateral is the other way (i.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 square, but only approximate in the case of other quadrilateral, if 3 be taken to be the correct value of ${\displaystyle \pi }$