पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२६४

GANITASARASANGRAHA. The rule for finding cut any unknown fraction in other required places (than the beginning) :- 125. The optionally split up parts of the (given) sum, when divided in order by the simplified known quantities (in the intended Bhaganubandha fractions), and (then) diminished by one, become the unknown (fractional quantitics) in the required places of our choice Thus ends the Bhagānubandha class (of fractions). 66 Bhagāpavaha Fractions. Then (comes) the rule for the (simplification of) Bhagāpavāha (or the dissociated) variety (in fractions) :- 126. In the operation concerning (the simplification of) the Bhagapavāhu class (of fractions), subtract the numerator from the (product of the dissociated) whole number as multiplied by the denominator. (When, however, the dissociated quantity is not integral, but is fractional,) mulitiply (respectively) the numerator and the denominator of the first (fraction to which the other fraction is negatively attached) by the denominator diminished by the numerator, and by the denominator (itself, of this other fraction). Examples on Bhagapavāha fractions containing dissociated integers. 127 Karsus 3, 8, 4 and 10, diminished by ,, and of a karşa, are offered by certain men for the worship of tarthankaras. What is (the sum) when they are added ? 125. The method given in this rule is similar to what is explained under stanza No. 122 only the results thus obtained have to be, in this case, each diminished by one. 126. Bhagapaváha literally means fiactional dissociation As in Bhaganu- bandha, there are two varieties here also. When an integer and a fraction are in Bhagapaváha relation, the fraction is simply subtracted from the integer. Two or more fractions may also be in such relation, as for example, dissoci- ated from of itself or dissociated from ., and of itself. It is meant here that of 1s to be subtracted from in the first example, and the second example comes to - of-of (1 of 4) - of {tof - of (f.- & of)}.