पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३०८

एतत् पृष्ठम् परिष्कृतम् अस्ति
112
GAŅITASĀRASAŃGRAHA.

The required result is well arrived at by going through the process of the rule-of-three.

Examples in illustration thereof.

90${\displaystyle {\tfrac {1}{2}}}$ and 91${\displaystyle {\tfrac {1}{2}}}$. Pomegranates, mangoes and woodapples are obtainable at the (respective) rates of 3 for 2, 5 for 3, and 7 for 5 paṇas. O you friend, who know the principles of calculation, come quickly having purchased fruits for 76 paṇas, so that tho mangoes may be thrē times as the woodapples, and the pomegranates six times as much.

99${\displaystyle {\tfrac {1}{2}}}$ to 94${\displaystyle {\tfrac {1}{2}}}$. A follower of Jina had the image of Jina bathed in potfuls of curds, ghee and milk. Three pots became filled with 72 palas(of those); 32 palas were found in the first pot and 24 in the second pot and 16 in the third pot. From those (potfuls of mixed-up) curd, ghee and milk, find out each of those (ingredients) separately and give them out, there being altogether 24 palas of ghee, 16 palas of milk and 32 palas of curds.

95${\displaystyle {\tfrac {1}{2}}}$ and 96${\displaystyle {\tfrac {1}{2}}}$. Three puraṇas formed the pay of one man who is a mounted soldier; and at that rate there were 65 men in all. Some (among them) broke down, and the amount of their pay was given to those that remained in the field. Of this, each man obtained 10 purāṇas. You tell me, after thinking well, how many remained in the field and how many broke down.

The rule for the operation of proportionate division, wherein there is the addition or the subtraction of certain optionally chosen integral quantities:-

97${\displaystyle {\tfrac {1}{2}}}$[*]. The given total quantity is diminished by the integral quantities that are to be added, or is combined with the positive integral quantities that are to be subtracted; then with the help of this resulting quantity the operation of proportionate division is to be conducted, and the resulting proportionate parts are respectively combined with those (integral quantities that are to be added to them), or they are diminished (respectively) by those (integral quantities that are to be subtracted).

97${\displaystyle {\tfrac {1}{2}}}$^ . The operation of proportionate division to the conducted here is according to any of the rules in stanzas 87${\displaystyle {\tfrac {1}{2}}}$ to 89${\displaystyle {\tfrac {1}{2}}}$.