CHAPTER IV.
MISCELLANEOUS PROBLEMS (ON FRACTIONS).
The Third Subject of Treatment.
1. After Saluting the Lord Jina, Mahavira, whose collection of infinite attributes is highly praiseworthy, and who vouchsafes boons to (all) the three worlds that worship (him), I shall treat of miscellaneous problems (on fractions)
2. May Jina, who has destroyed the darkness of unrighteousness, and is tho authoritative exponent of the syādvāda, 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 (varieties in miscellaneous problems on fractions, namely), Bhāga, Śēșa, Mūla, Śēșamūla, the two varieties
3. The Bhāga variety consists of problems wherein is given the numerical value of the portion remaining after removing certain specified fractional parts of the total quantity to be found out. The fractional parts removed are each of them called a bhāga, and the numerical value of the known remainder is termed dŗśya.
The Śēșa 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 sēșas or remainders.
The Mūla 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 root of that total quantity.
The Śēșamūla variety is the same as the mūla variety with this difference, viz., the square root here is of the remainder after subtracting the given fractional parts, instead of being of the whole.
The Dvirogra-śēşamūla variety consists of problems wherein a known number of things is first removed, then some fractional parts of the successive remainders and then some multiple of the square root of the further remainder are removed, and lastly the numerical value of the remaining portion is given. The known number first removed is called pūrvāgra'
In the Amśamūla variety, a multiple of the square root of a fractional part of the total number is supposed to be first removed, and then the numerical value of the remaining portion is given.
