पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३०८

110 GANITASARASANGRAHA. Proportionate Division. Hereafter we shall expound in (this) chapter on mixed problems the working of proportionate division - 79 The operation of proportionate division is that wherein the (given) collective quantity to be divided) is first divided by the sum of the numerators of the common-denominator-fractions (representing the various proportionate parts), the denominators of which fractions are struck off out of consideration; and (then it) has to be multiplied (respectively in each case) by (these) propor- tional nunicrators This is called huttikära by the learned. Examples in illustration thereof 80 Here, in this problem,) 120 gold pieces are divided among 4 servants in the (respective) proportional parts of ,1, and 2. O arithmetician, tell me quickly what they obtained 81. (The sum of) 363 dinaras was divided among five, the first one (among them) getting 3 parts and being the common ratio successively (in relation the shares of the others). What was the share of each ? 82 to 85. A certain faithful śrävaka took a number of lotus flowers, and going into the Jina temple conducted (therein) with devotion the worship of the chief Jinas that were worthy of worship. He offered part to Vrsabha, to worthy Parśva, aud to Jinapati, and to sage Suvrata; he dovotedly gave to Aristanémi who destroyed all the eight kinds of karmas and who was beloved by the world; and of to Jinaśänti 480 lotuses were brought (for this purpose.) By adopting the operation known 79. In working the example in stanza 80 according to this rule we get 114 115 12 12 12. After removing the denominators here, we have 6, 4, 3 and 2. These are also called puksepas or proportional numerators The sum of these 18 15, by which the amount to be distributed, viz, 120, is divided, and the resulting quotient 8 is separately multiplied by the proportional numerators 6, 4, 3 and 2. Then the amounts thus obtained are 6 x 8 or 48, 4 x 8 or 32, 3 x 8 or 24, 2 x 8 or 16. It is worthy of note that praksipa means both the operation of proportionate division and a proportional numerator.