272 G. Thibaut — On the S'ulvasutras. [No. 3, 



But a striking proof of the contrary is given by the commentators of 

 the S'ulvasutras who represent the later development of Indian mathema- 

 tics. Trustworthy guides as they are in the greater number of cases, their 

 tendency of sacrificing geometrical construction to numerical calculation, 

 their excessive fondness, as it might be styled, of doing sums renders them 

 sometimes entirely misleading. I shall illustrate this by some examples. 



As mentioned above, the area of the saptavidha agni had, at each repe- 

 tition of the construction of the altar, to be increased by one square puru- 

 sha. In order to effect this increase, without changing the proportion of 

 the single parts of the agni, Baudhayana gives the following rule : 



That which is different from the original form of the agni (i, e., that 

 area which has to be added to the 7f- square purushas of the primitive agni) 

 is to be divided into fifteen parts, and two of these parts are to be added to 

 every one of the seven square purushas of the primitive agni (the one remain- 

 ing part is consequently added to the remaining half purusha) ; with seven 

 and a half of these increased purushas, the agni has to be constructed. 



According to the commentator, we have to apply this rule in the fol- 

 lowing fashion. The one square purusha, which has to be added to the 

 saptavidha agni, contains 14400 square angulis. "We divide 14400 by 

 fifteen, multiply the quotient by two, and add the product to 14400 : result 

 = 16320. These 16320 angulis are the square content of the new increas- 

 ed square purusha, and we have therefore, in order to get the required mea- 

 sure of length, to extract the square root of 16320. This root indicates the 

 length which had to be given to the cane used for measuring out the ashta- 

 vidha agni. 



Such a proceeding is of course not countenanced by the rules of the 

 S'ulvasutras themselves. Baudhayana's method was undoubtedly the fol- 

 lowing. The square purusha which had to be added was divided into fifteen 

 parts, either into fifteen small oblongs, by dividing one side of the square 

 into three, the other into five parts or into fifteen small squares ; in the latter 

 case, the panchadas'amakarani had to be found according to the paribkasha 

 rules. Two of these fifteenth parts were then combined into one ; if squares, 

 by taking the dvikarani of one of them ; if oblongs, by turning one of them 

 into a square and then taking the dvikarani. Lastly — following the rules 

 for chaturasra-samasa — the square containing the two fifteenth parts was 

 added to a square purusha, and the side of the resulting square furnished 

 the measure of the purusha which had to be employed for the ashtavidha 

 agni. 



Another example is furnished by the rules for the paitriki vedi, the 

 altar used at the pitriyajna, the area of which had to be equal to the ninth 

 part of the vedi used at the soma sacrifices. The measures of the sides of 

 this vedi have been mentioned above ; its area amounts to 972 square padas. 



