ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

RULE OF THREE AS A PARTICULAR CASE 183 number on the side of the smaller set of terms is 300. Therefore the required result is 3000 / 300 = 10. Rule of Three as a Particular Case According to Brahmagupta, the above method of "com- pound proportion" may be applied to the Rule of Three. Taking the example solved under the Rule of Three : If one pala and one karṣa of sandal wood are obtained for ten and a half paṇas, for how much will be obtain- ed nine palas and one karṣa ? (4 karṣas = 1 pala). We shall represent them according to the Rule of Com- pound Proportion as Pramāṇa pakṣa : 1 pala, 1 karṣa, 10½ paṇa or 5/4 pala , 21/2 paṇa, Icchā pakṣa : 9 pala, 1 karṣa, x paṇa or 37/4 pala , x paṇa This we shall represent as ┌────┬────┐ │ 5 │ 37 │ │ 4 │ 4 │ ├────┼────┤ │ 21 │ 0 │ │ 2 │ │ └────┴────┘ Transposing the fruits, we have ┌────┬────┐ │ 5 │ 37 │ │ 4 │ 4 │ ├────┼────┤ │ 0 │ 21 │ │ │ 2 │ └────┴────┘ Transposing denominators ┌────┬────┐ │ 5 │ 37 │ │ 4 │ 4 │ ├────┼────┤ │ 0 │ 21 │ │ 2 │ │ └────┴────┘ The product of numbers on the side of the larger set is divided by the product of the numbers on the side of the smaller set, 0 in this case is not a number. It is the symbol for the unknown or absence. Hence the result is : (37 . 4 . 21) / (5 . 4 . 2) paṇas