40 ARYABHATIYA

27. The denominators of multipliers and divisors are multi-
plied together. Multiply numerators and denominators by the
other denominators in order to reduce fractions to a common
denominator.

For the first part of the rule I have given what
seems to be the most likely literal translation. The
exact sense is uncertain. Kaye (agreeing with Rodet)
translates, "The denominators are multiplied by one
another in multiplication and division." If that is the
correct translation the genitive plural is curious.
Paramesvara explains gunakdra as gunagunyayor
dhatir atra gunakdrasabdena vivaksitd. hdrya ity arthah
and then seems to take bhdgahdra as referring to a
fractional divisor of this product. Can the words bear
that construction? In either case the inversion of
numerator and denominator of the divisor would be
taken for granted.

It is tempting to take gunakdrabhdgahdra as mean-
ing "fraction" and to translate, "The denominators
of fractions are multiplied together." But for that
interpretation I can find no authority.

28. Multipliers become divisors and divisors become multi-
pliers, addition becomes subtraction and subtraction becomes
addition in the inverse method.

The inverse method consists in beginning at the
end and working backward. As, for instance, in the
question, "What number multiplied by 3, divided by
5, plus 6, minus 1, will give 5?"

29. If you know the results obtained by subtracting suc-
cessively from a sum of quantities each one of these quantities
set these results down separately. Add them all together and
divide by the number of terms less one. The result will be the
sum of all the quantities.