# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४०२

एतत् पृष्ठम् अपरिष्कृतम् अस्ति
206
GAṆITASĀRASAṄGRAHA.

of the annulus, and again multiplied by the square root of 10. (The result gives the value of the required area.) Half of this is the (required) value of the area in the case of figures resembling the crescent moon or (the longitudinal section of) the tusk of an elephant.

Examples in illustration thereof.

81${\displaystyle {\tfrac {1}{2}}}$. In the case of a field resembling (the circular annulus forming) the rim of a wheel, the outer curve is 14 in measure and the inner 8; and the (breadth in the) middle is 4. (What is the area?) What is it in the case of a figure resembling the crescent moon, and in the case of a figure resembling (the longitudinal section of the tusk of an elephant (the measures requisite for calculation being the same as above) ?

The rule for arriving at the minutely accurate value of the area , of a figure forming the interspace included inside four (equal) circles (touching each other):-

82${\displaystyle {\tfrac {1}{2}}}$. [1] If the minutely accurate measure of the area of any one circle is subtracted from the quantity which forms the square of the diameter (of the circle), there results the value of the area of the interspace included within four equal circles (touching each other):-

An example in illustration thereof.

83${\displaystyle {\tfrac {1}{2}}}$. What is the minutely accurate measure of the area of the interspace included within four mutually touching (equal) circles whose diameter is 4 (in value)?

82${\displaystyle {\tfrac {1}{2}}}$.^  The rationale of the rule will be clear from the figure below:-