पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९३

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CHAPTER VII--MEASUREMENT OF AREAS.

An example in illustration thereof.

48. In relation to a quadrilateral figure, each of whose sides is 15 (in measure), tell me the practically approximate value of the inscribed and the escribed circles.

Thus ends the calculation of practically approximate value in relation to areas.

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The Minutely Accurate calculation of the
Measure of Areas.

Hereafter in the calculation regarding the measurement of areas we shall expound the subject of treatment known as minutely accurate calculation. And that is as follows:-

The rule for arriving at the measure of the perpendicular (from the vertex to the base of a given triangle) and (also) of the segments into which the base is thereby divided):-

49. The process of saṅkramaṇa carried out between the base and the difference between the squares of the sides as divided by the base gives rise to the values of the two segments (of the base) of the triangle. Learned teachers say that the square root of the difference between the square root of the difference between these (segments) and of the (corresponding adjacent) side gives rise to the measure of the perpendicular.

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49. Algebraically represented

$c_{1}=\left(c+{\tfrac {a^{2}-b^{2}}{c}}\right)\times {\tfrac {1}{2}};$

$c_{2}=\left(c+{\tfrac {a^{2}-b^{2}}{c}}\right)\times {\tfrac {1}{2}};$

$p={\sqrt {a^{2}-c_{1}^{2}}}{\text{ or }}{\sqrt {b^{2}-c_{2}^{2}}}$. Here a,b,c represent the meaesures of the sides of a triangle $c_{1},c_{2}$ the measures of the segments of the base whose total length is c; and p represents the length of the perpendicular.