Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 262

CHAPTER III-FRACTIONS.
85
120. O friend, subtract (the following) from 3 : 1 associated with of itself and with 1 of this (associated quantity), & associated with 5, and 4 of itself (in additive consecution), š (similarly) associated with (fractions thereof) commencing with ; and ending with }, and associated with of itself.
121. O friend, you, who have a thorough knowledge of Bhāgānubandha, give out the result) after adding associated with of itself, to associated with of itself, i associated with of itself, 1 associated with of itself, and associated with of itself.
Now the rule for finding out the one unknown (element) at the beginning (in each of a number of associated fractions, their sum being given): .
122. The optionally split up parts of the (given) sum, which are equal (in number) to the intended) component elements (thereof), when divided in order by the resulting quantities arrived at by taking one to be the associated quantity (in relation to these component elements), give rise to the value of the required) unknown (quantities in association).
Examples in illustration thereof.
123. A certain fraction is associated with }, } and of itself (in additive consecution); another (is similarly associated) with }, į, and ß of itself; and another (again is similarly associated) with , and of itself; the sum of these (three fractions so associated) is 1 : what are these fractions ?
124. A certain fraction, when associated (as above) with 1, }, and ß of itself, becomes 1 Tell me, friend, quickly the measure of this unknown (fraction).
122. This rule will be clear from the working of example No. 123 as explained below:
There are three sets of fractions given; and splitting up the sum, 1, into three fractions according to rule No. 75, we get, and . By dividing these fractions by the quantities obtained by simplifying the three given sets of fractions wherein 1 is assumed as the unknown quantity, we obtain , 1 and 16, which are the required quantities.