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83

CHAPTER IV--MISCELLANEOUS PROBLEMS (ON FRACTINOS).

(remaining) 15 (of them) are seen grazing grass on a mountain. How many are they (in all) ?

63. (A number) of elephants (equivalent to) ${\tfrac {1}{16}}$ of the herd minus 2, as multiplied by that same ( ${\tfrac {1}{10}}$ a of the herd minus 2), is found playing in a forest of sallakā trees. The (remaining) elephants of the herd measurable in number by the square of 6 are moving on a mountain. How many(together) are (all) these elephants here?

An example of the plus variety.

64.^[64] (A number of peacocks equivalent to) ${\tfrac {1}{15}}$ of their whole collection plus 2, multiplied by that same ( ${\tfrac {1}{15}}$ of the collection plus 2), are playing on a jambā' tree. The other (remaining) proud peacocks (of the collection), numbering 2² x 5, are playing om a mango tree. O friend, give out the numerical measure of (all) these (peacocks in the collection).

Here ends tho Aṃśavarya variety charecterised by plus or minus quantities.

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

65.^[65]To the square of the (known) combined sum (of the square roots of the specified unknown quantities), the (given) minus quantity is added, or the (given) plus quantity is subtracted (therefrom); (then) the quantity (thus resulting) is divided by twice the combined sum (referred to above); (this) when squared gives rise to the required value (of the unknown collection). In relation to the working out of the Mūlamiśra variety of problems, this is the rule of operation.

64.^ The word meta mattamayūra occurring in the stanza means a proud peacock and is also the name of the metre in which the stanza is composed.

65.^ Algebraically $x={\Big \{}{\tfrac {m^{2}\mp d}{2m}}{\Big \}}^{2}$ . This is easily derived from the equation ${\sqrt {x}}+{\sqrt {x\pm d}}=m$ . The quantity m is here the known combined sum mentioned in the rule.