Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 392

CHAPTER VIT-MEASUREMENT OF AREAS.
196
included between circles (in contact), one-fourth thus arrived at gives the required measure).
of the result
Examples in illustration 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 bexalateral figure the sides are in measure from 1 to 6 in order. (Find out the value of the area in each case).
12. (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 iuclnded 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 cirole, 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 lengths of these three lines, then, according to the rules given in stanzas 43 and 45 --
Area = c + v) * Length of bow =V5p2 + c
, of arrow = 5
» of bow-string av a' -50 For accurate value see stanzas 731 and 74} in this chapter.