पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४६१

CHAPTER VIII--CALCULATIONS REGARDING EXCAVATIONS. 263 22. The length of a longish quadrilateral is 120 (danlas) and the breadth is 40. The ditch around is as big as 4 damlas in breadth and 3 in depth. (Find out the cubical contents.) The rule for arriving at the value of the cubical contents of an excavation, when the depth of the excavation varies (at various points), and also for arriving, when the cubical contents of an excavation are known, at the depth of digging necessary in the case of another (known) area (so that the cubical contents may be the same):- 23. The sum of the depths (measured in different places) is divided by the number of places; this gives rise to the (average) depth. This multiplied by the top area (of the excavation) gives rise to the (required) cubical contents of the excavation in the case where that area is trilateral, quadrilateral or circular. The cubical contents (of a given excavation), when divided by the (known) value of another area, gives rise to the depth (to which there should be digging, so that the resulting cubical contents may be the same). Examples in illustration thereof. 24. In an equilateral quadrilateral field, the ground covered by which has an extent measured by 4 hastas (in length and breadth), the excavations are (in depth) 1, 2, 3, and 4 hustas (in four different cases). What is the measure of the average depth (of the excavations)? 25. There is a well with an equilateral quadrilateral section, the sides whercof are 18 hustas in measure; its depth isi hastas. With the water of this (well), another woll measuring 9 hastas at each of the sides (of the section) is filled. What is the depth (of this other well)? When the measures of the sides of the top (sectional area) and also of the bottom (sectional area) are known, and when the 22. For finding out the total length of the surrounding ditch when the central mass of earth is rectangular in section, the measures of the sides as increased by the width or half the width of the ditch are added together, according as the Ka- mántika or the Aundra result is required.