Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 464

+362
GANITASĪBASANGBAHA. three, gives rişe to the value of the (required) perimeter in the case of triangular and circular excavations. In the case of a quadrilateral excavation, (this same value of the required perimeter rosults) by multiplying the quantity four (with the value of the breadth as before).
In the case of excavations having central masses tapering upwards or downwards the operation (for Karmäntskaphala) is to add the value of) half the breadth of the excavation to that of the breadth of) the central nass, and (for Aundraphala), to add (the value of) the breadth (of the excavation to the value of the breadth of the central mass); then the procedure is) as (given) before.
Examples in illustration thereof. 214. The already mentioned trilateral, quadrilateral, and circular (areas) have ditohes thrown round them. The breadth measures 80 dandas, and the ditches are as much as 4 (dandas) in breadth, and 3 (dandas in depth. (Find ont the cubioal contents.)
and the excavation may be of the same width both at the bottom and the top, or may be of diminishing or increasing width. The role enables us to find out the total longth of the ditoh in all these cases.
I. When the width of the ditch is uniform, the length of ditch = (a + b)x 3 in the orso of nn equilateral triangular or ciroular ditch, where d is the measure of a side or of the diameter of the oentral mass and b is the width of the ditch: bat this length = (d + b) x 4 in the case of a square oxcavation with a cuntral mass, square in section.
II. When the ditch is ta pering to a point at the bottom or the top, the length
of the ditoh for finding out the Karmantika-phala =
* 4, sooording as the oentral masa (1) is in section trilateral or circular, or (3) square.
Length of ditoh for finding out Aundra-phala = (a + b) x 8 and (a + b) x 4 respectively,
Those expressions have to be multiplied by half of the width of the ditob and by ito dopth for finding out the respective oubioal phalas. The formulas given above in relation to triangular and oiroular excavations give only approximate results. With the aid of the total length of the ditoh to obtained, the oubica! contents are found out in the one of ditches with Wloping side by applying the ralo piven in start to 11} above.