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

182 BRAHMAGUPTA AND ARITHMETIC Three, in the Rule of Seven three Rules of Three, and so on. This I shall point out in the examples. Brahmagupta gives the following rule relating to the solu- tion of problems in compound proportion : In the case of odd terms beginning with three terms up to eleven, the result is obtained by transposing the fruits of both sides, from one side to the other, and then dividing the product of the larger set of terms by the product of the smaller set. In all the fractions, the transposition of denominators, in like manner, takes place on both sides.¹ This may be illustrated by taking an example from the commentary of Pṛthūdaka Svāmī on the Brāhmasphuṭasid- dhānta : Example —If there is an increase of 10 in 3 months on 100 (niṣkas), what would be the increase on 60 (niṣkas) in 5 months. Here the Pramāṇa pakṣa (the first set of terms) is 100 niṣkas, 3 months, 10 niṣkas (phala) The second set or the icchā pakṣa is 60 niṣkas, 5 months, x niṣkas The terms are written in compartments as below : | 100 | 60 | | 3 | 5 | | 10 | 0 | In the above 10 (written lowest) is the fruit of the first side (pramāṇa pakṣa), and there is no fruit on the second side or the iccā pakṣa. Interchanging the fruits we get | 100 | 60 | | 3 | 5 | | 0 | 10 | The larger set of terms is on the second side (icchā pakṣa). The product of the numbers is 3,000. The product of the

1. व्यस्तं त्रैराशिक फलमिच्छा भक्तः प्रमाणफलघातः । त्रैराशिकादिषु फलं विषमेष्वेकादशान्तेषु ॥ फलसंक्रममुभयतो बहुराशि वधोऽल्पवधहृतो ज्ञेयम् । सकलेष्वेवं भिन्नेष्वथवैतच्छेदसंक्रमकम् ॥ —BrSpSi: XII. 11-12.