# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९०

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एतत् पृष्ठम् परिष्कृतम् अस्ति
194
GAṆITASĀRASAṄGRAHA.

declare the measure of the di-deficient area. That which is less (than the latter product here) by half of this (above-mentioned quantity to be subtracted) is the measure of the area of the uni-definient figure.

An example in illustration thereof.

38. The length is 36 and the breadth is only 18 daṇdas. What is the resulting measure of the area in the case of a di-deficient area, and what in the case of the uni-deficient area ?

The rule for arriving at the practically approximate measure of the area of fields resembling the outline of a multiplex vajra:-

39.[1] One-third of the square of half the perimeter, divided by the number of sides and (then) multiplied by the number of sides as diminished by one, gives indeed in the result the value of the area of all figures made up of sides. In the case of the area

di-deficient figure is that in which any two of the opposite triangles out of the four making up the quadrilateral are left out of consideration, the uni-deficient figure being that in which only one out of the four triangles is neglected.

39.^  The rule stated in this stanza gives the area of figures made up of any number of sides. If s is half the sum of the measures of the sides, and n the number of sides, the area is said to be equal to ${\displaystyle {\tfrac {s^{2}}{3}}\times {\tfrac {n-1}{n}}}$. This formula is found to give the approximate value of the area in the case of a triangle, a quadrilateral, a hexagon and a circle conceived as a figure of infinite number of sides. The other part of the rule deals with the interspace bounded by parts of circles in contact, and the value of the area arrived at according to the rule here given is also approximate. The figure below shows an interspace so bounded by four touching circles.