# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३८३

एतत् पृष्ठम् परिष्कृतम् अस्ति
187
CHAPTER VĪ--MEASUREMENT OF AREAS.

Calculation relating to approximate measurement
(of areas).

The rule for arriving at the (approximate) measure of the areas of trilateral and quadrilateral fields:-

7.[1] The product of the halves of the sums of the opposite sides becomes the (quantitative) measurement (of the area) of trilateral and quadrilateral figures. In the case of (a figure constituting a circular annulus like) the rim of a wheel, half of the sum of the (inner and outer) circumferences multiplied by (the measure of) the breadth (of the annulus gives the quantitative measure of the area thereof). Half of this result happens to be here the area of (a figure resembling) the crescent moon.

Examples in illustration thereof.

8. In the case of a trilateral figure, 8 daṇdas happen to be the measure of the side, the opposite side and the base; tell me quickly, after calculating, the practically approximate value (of the area) thereof.

9. In the case of a trilateral figure with two equal sides, the length (represented by the two sides) is 77 daṇdas and the breadth (measured by the base) is 22 daṇdas associated with 2 hastas. (Find out the area)

7. A trilateral figure is here conceived to be formed by making the topside, i.e., the side opposite to the base, of a quadrilateral so small as to be neglected. Then the two lateral sides of the trilateral figure become the opposite sides, the topside being taken to be nil in value. Hence it is that the rule speaks of opposite sides even in the case of a trilateral figure.

As half the sum of the two sides of a triangle is, in all cases, bigger than the altitude, the value of the area arrived at according to this rule cannot be accurate in any instance.

In regard to quadrilateral figures the value of the area arrived at according to this rule can be accurate in the case of a square and an oblong, but only approximate in other cases.

Nēmi is the area enclosed between the circumferences of two concentric circles; and the rule here stated for finding out the approximate measure of the area of a Nēmikṣētra happens to give the accurate measures thereof. In the case of a figure resembling the crescent moon, it is evident that the result arrived at according to the rule gives only an approximate measure of the area.