# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३९१

एतत् पृष्ठम् परिष्कृतम् अस्ति
195
CHAPTER VII--MEASUREMENT OF AREAS.

included between circles (in contact), one-fourth of the result thus arrived at gives the required measure).

Examples in instruction thereof.

40. In the case of a six-sided figure the measure of a side is 5, and in the case of another figure of 16 sides the measure of a side is 3. Give out (the measure of the area in each case).

41. In the case of a trilateral figure one of the sides is 5, the opposite (i.e., the other) side is 7, and the base is 6. In the case of another hexalateral figure the sides are in measure from 1 to 6 in order. (Find out the value of the area in each case).

42. (Give out) the value of the interspace included inside four (equal) circles (in contact) having a diameter which is 9 in measure; and (give out) the value of the area of the interspace included inside three circles having diameters measuring 6, 5 and 4 (respectively).

The rule for arriving at the practically approximate area of a field resembling a bow in outline:-

43. In the case of a bow-shaped field the calculated measure (of the area) is obtained by adding together (the measure of) the arrow and (that of) the string and multiplying the sum by half (the measure of) the arrow. The square root of the square of the (measure of the) arrow as multiplied by 5 and (then) as combined with the square of the (measure of the) string gives the (measure of the bent) stick (of the bow).

43.^  The field resembling a bow in outline is in fact the segment of a circle, the bow forming the arc, the bow-string forming the chord, and the arrow measuring the greatest perpendicular distance between the arc and the chord. If a, c and p represent the length of these three lines, then, according to the rules given in stanzas 43 and 45-

${\text{ Area}}=(c+p)\times {\tfrac {p}{2}}$ {\begin{aligned}{\text{Length }}&{\text{of bow }}={\sqrt {5p^{2}+c^{2}}}\\{\text{ ,, }}\quad &{\text{of arrow }}={\tfrac {\sqrt {a^{2}-c^{2}}}{5}}\\{\text{ ,, }}\quad &{\text{of bow-string}}={\sqrt {a^{2}-5p^{2}}}\end{aligned}} For accurate value see stanzas $73{\tfrac {1}{2}}{\text{ and }}74{\tfrac {1}{2}}$ in this chapter. 