पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३८९

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198
CHAPTER VII--MEASUREMENT OF AREAS.

(require dmeasurement of) area is that which results by multiplying half the sum of the end measure and the middle measure by the length.

Examples in illustration thereof.

33. In the case of an are resembling the configuration of a yuva grain, the length is 80 and the breadth in the middle is 40. Tell me, what may be the calculated measure of that area ?

34. Tell (me what may be the calculated measure of the area) in relation to a field which has the outline configuration of the mṛdaṅga, and of which the length is 80 daṇdas, the end measure is 20 and the middle measure is 40 daṇdas.

35. In the case of a field having the outline of the paṇava, the length is 77 daṇdas, the measure of each of the two ends is 8 daṇdas, and the measure in the middle is 4 daṇdas. (What is the measure of the area ?)

36. Similarly in the case of a field having the outline of the vajra, the length i8 96 daṇdas, in the middle there is the middle point ; and at the ends the measure is ${\displaystyle 13{\tfrac {1}{2}}}$daṇdas. (What is the measure of the area ?)

The rule for arriving at the measure of areas such as the ubhaya-niṣēdha or de-deficient area :

37. On subtracting the product of the length into half the breadth from the product of the length into the breadth, you

The measures of the area arrived at according to the rule given in this stanza are approximately correct in the case of all the figures, as the rule is based on the assumption that each of the bounding curved lines may be taken to be equal to the sum of two straight lines formed by joining the end of the curves with the middle point thereof.

37. The figures mentioned in this stanza are those given below:-

These are looked upon as being derived from a quadrilateral figure which is divided into four triangles by means of its diagonals crossing each other. The