134 GANITASĀRASANGRAHA. multiplied by the total number of things purchased; (the latter products are subtracted in order from the former products; the positive remainders are all written down in a linc below, the negative remainders in a line above; and all these are reduced to their lowest terms by the removal of the factors which are common to all of them. Then each of these reduced) differences is multiplied by (a separate) optionally chosen quantity; (then those products which are in a line below as well as those which are so above are separately added 'together); and the sums are written upside down, (the sum of the lower row of numbers being written above and the sum of the upper row being written below. These sums are also reduced to the lowest terms by means of the removal of common factors, if any; and the resulting quantities) are each of them written down twice, (so as to make one he below the other, as often as there are component elements in the correspond- ing alternate sum. These numbers thus arranged in two rows) are multiplied by their respective rate-prices and rate-values of things, (the rate-price multiplication being conducted with one row of figures and the rate-number multiplication being in relation to the other row of figures. The products so obtained are again reduced to their lowest terms by the removal of such factors as are com- mon to all of them. The resulting figures in each vertical row are separately) multiplied (each) by (means of its corresponding originally chosen) optional multiplier. (And the products should be written down as before in two horizontal rows. The numbers in the upper row of products give the proportion in which the purchase money is distributed; those in the lower row of products give the proportion in which the corresponding things purchased are distributed. Therefore) what remains thereafter is only the operation of praksepaka-karana (proportionate distribution in accordance with rule-of-three). An example in illustration thereof. 152 and 153. Pigeons are sold at the rate of 5 for 3 (panas), särasa birds at the rate of 7 for 5 (panas), swans at the rate of 9 for 7 (panas), and peacocks at the rate of 3 for 9 (panas). A certain man
