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 266

CHAPTER III-FRACTIONS.
69
Bhagamat? Fractions. The rule for (the simplification of) that class of fractions which contains all the foregoing varieties of fractions :
138. In the case of the Bhāgamātr class of fractions (or that class of fractions which contains all the foregoing varieties), the respectivo rules portaining to the different) varieties beginning with simple fractions (hold good). It, i.e., Bhāgamāty, is of twenty-six kinds.
One is (taken to be) the denominator (in the case) of a quantity which has no denominator.
Examples in illustration thereof. 139 and 140. (Given) }; }); } of } ; & of $; }; }; 13; 1}; } associated with ļof itself; then associated with } of itself; 1 diminished by ); 1 diminished by ti diminished by of itself; and diminished by } of itself : after adding these according to the rules which are strung together in the manner of a garland of blue lotuses made up of fractions, give out, o friend, (what the result is).
Thus ends the Bhāgamõtr variety of fractions..
Thus ends the second subject of treatment known as Fractions in Sārasangraha which is a work on arithmetic by Mahāvīrācārya.
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138. The twenty-six varieties here mentioned are Bhàga, Prabhaga, Bhägabhaga, Bhågänubandha, hnd Bhāgāpavāla, in combinations of two, three, four or five of these at a time; such as, the variety in which Bhäga and Prabhaga are mixed, or Bhaga and Bhagabhäga are mixed, and so on. The number of varieties obtained by mixing two of them at a time is 10, by mixing three of them at a time is 10, and by mixing four of them at a time is 5, and by mixing all of them at a time is 1; so there are 26 varieties. The example given in stanza 139 belongs to this last-mentioned variety of Bhagamăts in which all the five simple varieties are found.
139. The word utpalamālika, which occurs in this stanza, means a garland of blue lotuses, at the same time that it happens to be the name of the metre in which the stanza is composed.