262 GANITASĀRASANGRAHA. three, gives rise 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 peri- meter results) by multiplying the quantity four (with the value of the breadth as before). In the case of excavations having central masses tapering up- wards or downwards the operation (for Karmantikaphala) is (to add the value of) half the breadth of the excavation to (that of the breadth of) the central mass, 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. 21 The already mentioned trilateral, quadrilateral, and circular (areas) have ditches thrown round them. The breadth measures 80 dandas, and the ditches are as much as 4 (dandus) in breadth, and 3 (danlas) in depth. (Find out the cubical 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 rule enables us to find out the total length of the ditch in all these cases. 1. When the width of the dii ch is uniform, the length of ditch = (d+ b) x 3 m the case of an equilateral triangular or cu cular ditch, where d is the nieasure of a side or of the diameter of the central mass and b is the width of the ditck but this length= (a + b) x 4 in the case of a square excavation with a central mass, square in section. II. When the ditch is tapering to a point at the bottom or the top, the length of the ditch for finding out the Karmantika-phala = + X 3, or + x 4, according as the central mass (1) is in section trilateral or circular, or (2) square. Length of ditch for finding out Aundra-phala = (a + b) x 3 and (a + b) x 4 respectively. These expressions have to be multiplied by half of the width of the ditch and by its depth for finding out the respective cubical phalas. The formulas given above in relation to triangular and circular excavations give only approximate results. With the aid of the total length of the ditch so obtained, the cubical contents are found out in the case of ditches with sloping sides by applying the rule given in stanzas 9 to 11 above.
