# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२७५

एतत् पृष्ठम् परिष्कृतम् अस्ति
79
CHAPTER IV--MISCELLANEOUS PROBLEMS (ON FRACTIONS).

Examples in illustration thereof.

48. A single bee (out of a swarm of bees) was seen in the sky; ${\displaystyle {\tfrac {1}{5}}}$ of the remainder (of the swarm), and ${\displaystyle {\tfrac {1}{4}}}$ of the remainder (left thereafter), and (again), ${\displaystyle {\tfrac {1}{3}}}$ of the remainder (left thereafter) and (a number of bees equal to the square root (of the numericial value of the swarm, were seen) in lotuses and two (bees remaining at last were seen) on a mango tree. How many are those (bees in the swarm)?

49. Four (out of a collection of) lions were seen on a mountain; and fractional parts commencing with ${\displaystyle {\tfrac {1}{6}}}$ and ending with ${\displaystyle {\tfrac {1}{2}}}$ of the successive remainders (of the collection) , and (lions equivalent in number to) twice the square root (of the numerical value of the collection),as also (the finally remaining) four (lions, were seen a forest. How many are those (lions in the collection )?

50. (Out of a herd of deer) two pairs of young female deer were seen in a forest; fractional parts commencing with ${\displaystyle {\tfrac {1}{5}}}$ and ending with ${\displaystyle {\tfrac {1}{3}}}$ of the (successive) remainders (of the herd were seen) near a mountain; (a number) of them (equivalent to) 3 times the square root (of the numerical value of the herd) were seen in an extensive paddy field; and (ultimately) only ten remained on the bank of a lotus-lake. What is the (numerical) measure of the herd १

Thus ends the Śēșamūla variety involving two known quantities.

The rule relating to the Amsamūla variety (of miscellaneous problems on fractions).

51. Write down (the coefficient of) the square root (of the given fraction of the unknown collective quantity) and the known quantity (ultimately remaining, both of these) having been

50. The word hariņī occurring in this stanza not only means a 'female deer' but is also the name of the metre in which the stanza is composed.

51, Algebraically stated, this rule helps us to arrive at cb and ab, wich are required to be substituted for c and b respectively in the formula ${\displaystyle x-bx={\Big \{}{\tfrac {c}{2}}+{\sqrt {\left({\tfrac {c}{2}}\right)^{2}+a}}{\Big \}}^{2}}$, as in the Śēșamūla variety. As pointed out in the note