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 439

242
GANITASĀRASANGRAHA.
the ratio values of the (various) parts are respectively multiplied. To each of the products (so obtained), the square of the measure of the top-side (of the given figure) is added. The square root (of the sum so obtained) gives rise to the value of the base of each of the parts). The area (of each part divided by half the sum of the values of the base and the top-side (thereof) gives in (the requisite) order the value of the perpendicular (which for purposes of approximate measurement is treated as the side).
Examples in illustration thereof. 1761. The measure of the top-side is given to be 7; that of the base below is 23, and that of each of the remaining) sides is 30. The area (included within such a figure) is divided between two so that each obtains one (share). What is the value of the base (to be found out here) ?
1773-1781. The measure of the base (of a quadrilateral with two equal sides) is 162, and that of the top-side (thereof) is seen to be 18. The value of each of the (two equal) sides is 400. The area of this (figure 80 enclosed) is divided among 4 men. The parts obtained by the men are in the proportion of) 1, 2, 3, and 4 respectively. Give out, in accordance with this proportionate distribution, the values of the area, of the base, and (of either) of the two equal) sides (in each case).
1794. The measure of the base of the given quadrilateral figure) is 80, that of the top-side is 40 ; the measure (of either) of
m
-
-72
d
+ A D
AB (BO + AD) - BCP-AD2 ..AE (EF + AD E F2 - AD
AB (B C + AD)m +n + 2 +9.. BC-AD2 Bat
m +n + p + q. "AE (EF+AD)
. F2--A D2 = EF- m (B 0 -A D) 2
X m + Ba; m + n + P + 9
m +n + P + 9 and E F=N
Vm + + p + q* m + bo. Similarly the other formulas may also be verified.
* Although the text simply states that the quotient has to be multiplied by the value of the parts, what is intended is that the quotient has to be multiplied by the number representing the value of the parts up to the top-side in each case. That is, in the figure on the previous page, to arrive at GH, for instance,
- has to be multiplied by m + n and not by n merely. m +n + p + q**