पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३९५

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. 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 sankramana 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 squares of (either of) these (segments) and of the (corresponding adjacent) side gives rise to the measure of the perpendicular. 49. Algebraically represented- a²62 C₁ = C₂=== + a² 197 C C X, × , 2 ZA C₁ C₂ C p=√a²c₂² or b²c. Here a, b, c, represent the measures of.the sides of a triangle, c₁, C, the measures of the segments of the base whose total length 18 c, and p represents the length of the perpendicular.