पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२६८

70 GANITASARASANGRABA. CHAPTER IV. MISCELLANEOUS PROBLEMS (ON FRACTIONS). The Third Subject of Treatment. 1 After saluting the Lord Jina, Mahävira, whose collection of infinite attributes is highly praiseworthy, and who vouchsafes boons to (all) the three worlds that worship (him), I shall treat of miscellancous problems (on fractions). 2. May Jina, who has destroyed the darkness of unrighteous- ness, and is the authoritative exponent of the syadvada, and is the joy of learning, and is the great disputant and the best of sages, be (ever) victorious. Hereafter we shall expound the third subject of treatment, viz, miscellaneous problems (on fractions). 3. There are these ten (varictics in miscellaneous probleins on fractions, namely), Bhaga, Sesa, Mulu, Sesamüla, the two varieties 3 The Bhaga variety consists of problems wheiem is given the numerical value of the portion emaining after removing certain specified fractional parts of the total quantity to be found out. The fractional paits iemoved ale each of them called a bhäge, and the numerical value of the known remainder is termed dṛśya. The a variety consists of problems wherein the numerical value is given of the portion remaining after removing a known fractional part of the total quantity to be found out as also after removing certain known fractional parts of the successive se as or iemandeis. The Müla variety consists of problems wherein the numerical value is given of the portion remaining after subtracting from the total quantity certain fractional parts thereof as also a multiple of the square 1oot of that total quantity. The Seamula vaiety is the same as the mala variety with this difference, viz., the squale 10ot here is of the remainder after subti acting the given fiactional paits, instead of being of the whole. The Don agra-s samila variety consists of problems wherein a known number of things is first removed, theu some fractional parts of the successive iemainders and then some multiple of the square root of the further remainder are 1emoved, and lastly the numerical value of the remaining portion is given. The known number first removed is called pürvägra. In the Asamüla variety, a multiple of the square root of a tractional part of the total number is supposed to be first removed, and then the numerical value of the remaining portion is given.