1875.] G. Thibaut— On the S'ulvasutras. 273 



Now for constructing the paitriki vedi from the saumiki vedi, Baudhayana 

 gives the following short rule : 



The commentator, supplying several words, explains this sutra in the 

 following way : If we make a square, the area of which is equal to 972 

 square padas, its side will be equal to 31 padas, 2 angulis, and 26 tilas. 

 The third part of this ( = 10 padas, 5 angulis, and 31 tilas) is to be taken 

 for the side of a square, the area of which will be equal to the ninth part of 

 the mahavedi. 



For a proof we are directed to turn the 972 square padas into square 

 tilas by multiplying 972 by 225 and then by 1056, to extract the square- 

 root of the result, to turn the tilas again into padas by dividing the square- 

 root by 34 and then by fifteen, and finally to divide the result by three. 



In accordance with this process, the commentator translates the above 

 sutra in the following manner : 



The side (" karani" to be supplied) of that area (" bhumeh" to be sup- 

 plied) which is made a square with the third part of the mahavedi (which 

 has been itself turned into a square previously) is the tritiyakarani ; the 

 ninth part (of the mahavedi) is produced (by making a square with this 

 tritiyakarani). — This translation is certainly wrong. In the first place, the 

 word ' karani', which the commentator supplies, could not be missed in the 

 text of the sutra. In the second place, the commentator ascribes to the 

 word ' tritiyakarani' a meaning which it cannot possibly have. He inter- 

 prets it as the line which is the third part (of the side of the mahavedi) ; 

 but that line is called the navamakarani, as its square is equal to the ninth 

 part of the area of the mahavedi, and tritiyakarani can only mean the line 

 which produces, or the square of which is the third part (of some area). 



To arrive at the right understanding of the sutra, we must consider by 

 what method the task of constructing the paitriki vedi could be accomplish- 

 ed in the shortest way. The thing was to construct a square, the area of 

 which would be equal to the ninth part of another area which contained 

 972 square padas, i. <?., to 108 square padas. If 108 would yield an integral 

 square-root, the matter would have been easy enough ; but this not being 

 the case, another method had to be devised. The commentator, as we have 

 seen, proposes to construct a square of 972 padas, and to take the third part 

 of its side ; but this method besides, as shown above, not agreeing with the 

 words of the sutra, required several tedious preparatory constructions. The 

 same remark applies to the direct construction of a square of 10S padas, and 

 a shorter process could therefore not but be highly welcome. Now the 

 third part of 972 is 324, and the square-root of 324 is exactly IS ; in other 

 words, the side of a square of 324 square padas is eighteen padas. Accord- 

 ingly, instead of the navamakarani of 972, the tritiyakarani of 324 was 



