पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३२२

126

GAŅITASĀRASAŃGRAHA.

quantities to be distributed in accordance with the problem). Each (of the quotients so obtained) happens to be the required (quantity which is to be multiplied by the given) multiplier in the process of Bhinnakuṭṭikāra.^[*]

An example in illustration thereof.

135${\tfrac {1}{2}}$. A certain quantity multiplied by 6, (then) increased by 10 and (then) divided by 9 leaves no remainder. Similarly, (a certain other quantity multiplied by 6, then) diminished by 10 (and then divided by 9 leaves no remainder). Tell me quickly what those two quantities are (which are thus multiplied by the given multiplier here).

 

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Sakala-kuṭṭīkāra

The rule in relation to sakala-kuṭṭīkāra.

136${\tfrac {1}{2}}$^[*]. The quotient in the first among the divisions, carried on by means of the dividend-coefficient (of the unknown quantity to be distributed), as well as by means of the divisor and the (successively) resultiug remainders, is to be discarded. The other quotients obtained by means of this mutual division ( carried on till the divisor and the remainder become equal) are to be written down (in a vertical chain along with the ultimately equal remainder and divisor); to the lowermost figure (in this chain), the remainder (obtained by dividing the given known quantity in the problem by the divisor therein), is to be added. (Then by means of those numbers in the chain), the sum(which has to be) obtained by adding (successively to the lowermost number) the product of the two

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136${\tfrac {1}{2}}$.^  This rule will become clear from the following working of the problem given in 137${\tfrac {1}{2}}$:-

The problem is, when ${\tfrac {177x\pm 240}{201}}$ is an integer, to find out the value of x. Removing the common factors, we have ${\tfrac {59x\pm 80}{67}}$is an integer.