182 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: BRAHMAGUPTA AND ARITHMETIC S This may be illustrated by taking an example from the commentary of Prthudaka Svāmi on the Brahmasphutasid- dhanta :
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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 Example-If there is an increase of 10 in 3 months on 100 (nişkas), what would be the increase on 60 (nişkas) in 5 months. Here the Pramana paksa (the first set of terms) is 100 nişkas, 3 months, 10 nişkas (phala) The second set or the iccha paksa is 60 nişkas, 5 months, x nişkas 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 (pramana pakşa), and there is no fruit on the second side or the icca paksa. Interchanging the fruits we get & 100, 60 3 5 0 10 ★ The larger set of terras is on the second The product of the numbers is 3,000. The 1. व्यस्त राशिक, फलमिच्छा भक्तः प्रमाणफलधातः। त्रैराशिकादिषु फलं विषमेष्वेकादशान्तेषु ॥ फलसंक्रमणमुभयतो बहुराशि वषोऽल्पवधहतो हेयम् । • सक्लेष्वेवभिनेषूमतरछेदसंक्रमणम् ॥ side (iccha pakşa). product of the -BrSpSi. XII. 11-12.