पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२७५

CHAPTER IV- MISCELLANEOUS PRO LEMS (ON FRACTIONS) 77 combine it with the known number remaining, and (then extract) the square root (of this suni, 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 quan- tity) is taken as the original collective quantity itself). But when that remawing part (of the unknown collective quantity) is treated mercly as a part, the rule relating to the bhiga variety (of miscellaneous probleras on fractions) is to be applied Examples m illustration thereof 41. One third of a herd of elephants and three times the square root of the remaining part (of the herd) were seen on a mountain- slope; and in a lake was seen a male elephant along with three female clephants (constituting the ultimate remainder) How nany were the elephants here? 12 to 45. In a garden beautified groves of various kinds of trees, 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 yugu 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-sastra; and