पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९८

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एतत् पृष्ठम् परिष्कृतम् अस्ति
202
GAṆITASĀRASAṄGRAHA.

breadth (of the figure) as diminished by half the (breadth of the) mouth, and the square of one-fourth of the (breadth of the mouth are added together; and the resulting sun is multiplied by the square root of 10. This gives rise to the minutely accurate measure of the area in the case of the conchiform figure.

An example in illustration thereof.

66. In the case of a conchiform curvilinear figure the (maximum breadth is 18 daṇdas, and the breadth of the mouth is 4 (daṇdas). What is the measure of the perimeter and what the minutely accurate measure of the area as calculated ?

The rule for arriving at the minutely accurate measures in relation to outreaching and inlying annular figures:-

67. The (inner) diameter, to which the breadth (of the annulus) is added, is multiplied by the square root of 10 and by the breadth (of the annulus). This gives rise to the value of the area of the out-reaching annulus. The (outer) diameter as diminished by the breadth (of the annulus) gives rise (on being treated in the same manner as above) to the value of the area of the inlying annular figure.

Examples an illustration thereof.

68. Eighteen daṇdas measure the (inner or the outer) diameter of the annulus (as the case may be) ; the breadth of the annulus is, however, 3 (daṇdas). You give out the minutely accurate value of the area of the outreaching as well as the inlying annular figure.

69. The (outer) diameter is 18 daṇdas, and the breadth of the inlying annulus is 4 daṇdas. You give out the minutely accurate value of the area of the inlying annular figure.


maximum breadth, and in the measure of the mouth of a conchiform figure. As observed in the note relating to stanza 23 of this chapter, the figure intended is obviously made up of two unequal semicircles