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