# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२७२

एतत् पृष्ठम् परिष्कृतम् अस्ति
76
GAŅIITASĀRASAŃGRAHA.

the big theatre of the mountain top; and 5 times tho square root (of that collection) stayed in an excellent forest of vakula trees; and (the remaining) 25 were seen on a punnāga tree. O arithmetician, give out after calculation (the numerical measure of) the collection of peacocks.

86. One-fourth (of an unknown number) of sārasa birds is moving in the midst of a cluster of lotuses; ${\displaystyle {\tfrac {1}{9}}}$ and ${\displaystyle {\tfrac {1}{4}}}$ parts (thereof) as well as 7 times the square root (thereof) move on a mountain; (then) in tho midst of (some) blossomed vakula trees (the remainder) is (found to be) 56 in number. O you clever friend, tell me exactly how many birds there are altogether.

37. No fractional part of a collection of monkeys (is distributed anywhere); three times its square root are on a mountain; and 40 (remaining) monkeys are seen in a forest. What is the measure of that collection (of monkeys) ?

38. Half (the number) of cuckoos were found on the blossomed branch of a mango tree; and 18 (were found) on a tilaka tree. No (multiple of the) square root (of their number was to be found anywhere). Give out (the numerical value of) the collection of cuckoos.

39. Half of a collection of swans was found in tho midst of vakula trees ; five times the square root (of that collection was found) on the top of tamāla' trees ; and here nothing was seen (to romaim therafter). O friend, give out quickly the numerical measure of that (collection).

Here ends the Mūla variety (of miscellaneous problems on fractions).

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

40. (Take) the square of half (the coefficient) of the square root (of the remaining part of the unknown collective quantity), and

40. Algebraically, ${\displaystyle x-bx={\Big \{}{\tfrac {c}{2}}+{\sqrt {\left({\tfrac {c}{2}}\right)^{2}+a}}{\Big \}}^{2}}$. From this the value of x is to be found out according to rule 4 given in this chapter. This value of x-bx is obtained easily from the equation ${\displaystyle x-bx+(c{\sqrt {x-bx}}+a)=0}$.