पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३८७

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एतत् पृष्ठम् परिष्कृतम् अस्ति
191
CHAPTER VII--MEASUREMENT OF AREAS.

sacrificial fire-pit and like that of (the back of) the tortoise, (the required result is to be arrived at).

An example in illustration thereof.

26. In the case of the area of a sacrificial fire-pit the measure of the diameter is 27, and the measure of the circumnference is seen to be 56. What is the calculated measure of the area of that same (pit) ?

An example about a convex circular surface resembling (the back) of a tortoise.

27. The diameter is 15, and the circumference is seen to be 36. In the case of this area resembling the (back of a) tortoise, what is the practically approximate measure as calculated ?

The rule for arriving at the practically approximate value of the area of an in-lying annular figure as well as of an out-reaching annular figure:-

28.[1] The (inner) diameter increased by the breadth (of the annular area) when multiplied by three and by the breadth (of the annular area) gives the calculated measure of the area of the out-reaching annular figure. (Similarly the measure of the calculated area) of the in-lying annular figure (is to be obtained) from the diameter as diminished by the breadth (of the annular area).

Examples in illustration thereof.

29. The diameter is 18 hastas, and the breadth of the out reaching annular area is 3 in this case: the diameter is 18 hastas and again the breadth of the in-lying annular area is 3 hastas. What may be (the area of the annular figure in each case) ?


28.^  The shape of the अन्तश्चक्रवालवृत्तक्षेत्र I as well as of the बहिश्चक्रवालवृत्तक्षेत्र is identical with the shape of the नेमिक्षेत्र mentioned in the note to stanza 7 in this chapter. Hence the rule given for arriving at the area of all these figures works out to be the same practically.