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104
Vaishali Institute Research Bulletin No. 4
Patākā
Nārāyana gives a generalisation of the meru as contained in the Ratoa Mañjūsā in the form of his patākā. Rule for the formation of the same may be given as stated 15 below.
Cells are formed in vertical lines. Their number in a line is equal to a number in the spindle line, in order. The spindle line is formed by repeated multiplication of p lines of separated units each of measure q i.e., 1, 1, 1..., 1, 1 (q units). Numbers in the spindle line are the multinomial coefficients of x' in the expansion of (1+x+-x2+...+x9-1), r=0, 1, 2,...,(-1).]
Numbers of the multiplicative line which are 1, 2, ..., 9, 29, ..., q”, 292, ..., 98, 298, ..., q are written in the first horizontal line of the patāka. This determines their positions in the patākā, as well. For numbers lying between two numbers of the multiplicative lige, his rule is as follows.
The greatest digit' is called the additive' and tbat lying ahead (i, e., 29) is called the sādhya. The additive is added to all the previous (i. e., to 1, 2, 3, ..., 9-1), separately and the results are placed horizontally.
Next, supposing the sādhya (i. e., 29) as the additive and the next number (of the multiplicative line i. e., 39) as the sādhya, the process is repeated by starting from the next horizontal cell lying below. Thus, q+1 is kept in the cell next to that containing and lying below q and so op. The process is repeated again and again, by supposing the next number (of the multiplicative line) as the sādhya and the previous sädhya as the additive, by starting from the next horizontal cell lying below. Thus, q2 + 1 is kept in the cell next to that containing 1 and lying below 4+1. Similarly, q8+1 is kept in the cell next to that containing 1 and lying below q2 +1. The process is continued until all the numbers (upto q') are filled in the cell.
Nārāyana illustrates 16 his rule with the help of the following example.
15. GK., xiji, 29-36 (a-b). 16. GK., p. 302 and p. 332.
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