# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९६

एतत् पृष्ठम् परिष्कृतम् अस्ति
200
GAṆITASĀRASAṄGRAHA.

56. In the case of a longish quadrilateral, the (horizontal) side is 12 in measure and the perpendicular side is 3 in measure. Tell me quickly what the measure of the diagonal is and what the accurate measure of the area.

57. The basal side of an equi-bilateral quadrilateral is 36. One of the sides is 61 and the other also is the same. The top side is 14. What is the diagonal and what the accurate measure of the area?

58. In the case of an equi-trilateral quadrilateral, the square of 13 (gives the measure of an equal side); the base, however, is 407 in measure. What is the value of the diagonal, of the basal segments, of the perpendicular and of the area ?

59. The (right and the left sides of an inequilateral quadrilateral are 13 x 15 and 13 x 20 (respectively in measure) : the top side is ${\displaystyle 5^{3}}$, and the side below is 300. What are all the values here beginning with that of the diagonal ?

Hereafter (are given) the rules for arriving at the minutely accurate values relating to curvilinear figures. Among them the rule for arriving at the minutely accurate values relating to a circular figure is as follows:-

60.[1] The diameter of the circular figure multiplied by the square root of 10 becomes the circumference (in measure). The circumference multiplied by one-fourth of the diameter gives the area. In the case of a semicircle this happens to be half (of what it is in the case of the circle).

Examples in illustration thereof.

61. In the case of one (circular) field the diameter of the circle is 18; in the case of another it is 60 ; in the case of yet another it is 22. What are the circumferences and the areas ?

60. ^  The value of a given in this stanza is ${\displaystyle {\sqrt {10}}}$, which is equal to 3.16....... Compare this with the more approximate value ${\displaystyle {\tfrac {62832}{20000}}(=3.1316)}$ given by Āryabhaṭa. Bhāskarācārya also gives to it the same value, and represents it in reduced terms as ${\displaystyle {\tfrac {3927}{1250}}}$