पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२७३

विकिस्रोतः तः
Jump to navigation Jump to search
एतत् पृष्ठम् परिष्कृतम् अस्ति

CHAPTER IV--MISCELLANEOUS PROBLEMS(ON FRACTIONS).

combined 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 tho 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 bhāga variety (of miscellaneous problems on fractions) is to be applied.

Examples in illustratino thereof.

41. One-third of a herd of elephants and three times tho 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 female elephants (constituting the ultimate remainder). How many were the elephants here ?

42 to 45. In a garden beautified by groves of various kinds of trees, in a place free from all living animals, many ascetics were seated. Of them the number equivalent to the square root of the whole collection were practising yōga 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 ańga-śāstra; and