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 274

CHAPTER IV-MISCELLANEOUS PROBLEMS (ON FRACTIONS). 77 combine it with the known number remaining, and (then extract) the square root (of this sum, and make that square root become) combined with half of the previously mentioned (coefficient of the) square root (of the remaining part of the unknown collective quantity). The square of this (last sum) will here be the required result, when the remaining part (of the unknown collective quantity) is taken as the original (collective quantity itself). But when that remaining part (of the unknown collective quantity) is treated merely as a part, the rule relating to the bhaga variety (of miscellaneous problems on fractions) is to be applied.
Examples in illustration thereof.
square
41. One-third of a herd of elephants and three times the root of the remaining part (of the herd) were seen on a mountainslope; and in a lake was seen a male elephant along with three female elephants (constituting the ultimate remainder). many were the clephants here?
How
42 to 45. In a garden beautified by groves of various kinds of trecs, in a place free from all living animals, many ascetics were scated. Of them the number equivalent to the square root of the whole collection were practising yoga at the foot of the trees. One-tenth of the remainder, the square root (of the remainder after deducting this), (of the remainder after deducting this), then the square root (of the remainder after deducting this), (of the remainder after deducting this), the square root (of the remainder after deducting this), (of the remainder after deducting this), the square root (of the remainder after deducting this), (of the remainder after deducting this), the square root (of the remainder after deducting this), (of the remainder after deducting this), the square root (of the remainder after deducting this)-these parts consisted of those who were learned in the teaching of literature, in religious law, in logic, and in politics, as also of those who were versed in controversy, prosody, astronomy, magic, rhetoric and grammar and of those who possessed the power derived from the 12 kinds of austerities, as well as of those who possessed an intelligent knowledge of the twelve varieties of the anga-śāstra; and