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 460

CHAPTER VIII-CALCULATIONS REGARDING EXCAVATIONS. 263
221. The length of a longish quadrilateral is 120 (dandas) and the breadth is 40. The ditch around is as big as 4 dandas 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 (80 that the cubical contents may be the same) :--
231. 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. 243. 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 hastas (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 whereof are 18 hastas in measure; its depth is hastas. With the water of this (well), another well 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 aren) are known, and when the
22. For finding out the total length of the surrounding ditch when the central mess of earth is rectangular in section, the measnres of the sides as increased by the width or half the width of the ditch are added together, according as the Ka: mantika or the Aundra result is required.