Bhāgamātŗ Fractions.
Tho rule for (the simplification of) that class of fractions which contains all the foregoing varieties of fractions:--
138. In the case of the Bjāgamātŗ class of fractions (or that class of fractions which contains all the foregoing varieties), the respective rules pertaining to the (different) varieties beginning with simple fractions (hold good). It, i.e., Bhāgamātŗ, 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) associated with of itself; then associated with of itself; 1 diminished by ; 1 diminished by . 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 Bhāgamātŗ variety of fractions.
Thus ends the second subject of treatment known as Fractions in Sārasańgraha which is a work on arithmetic by Mahāvīrācārya
18. The twenty-six varieties here mentioned are Bhāga, Prabhāga, Bhāgabhaga, Bhāgānubandha, and Bhāgāpavāha, in combinations of two, three, for or five of these at a time; such as, the variety in which Bhāga and Prabhāga are mixed, or Bhāga and Bhāgabhāga 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 Bhāgamātŗ in which all the five simple varieties are found.
139. The word utpalamālikā 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!
