1875.] G. Thibaut — On the S'ulvasutras. 241 



error in tlie determination of the value of the savis'esha. When the side 



33 



of a square was reduced from 17 to 16 — the area of the square of that 



reduced side was not 288, but 288 + tt. 7T7- Or putting it in a 



34+34 l ° 



different way: taking 12 for the side of a square, dividing each of the 



12 parts into 34 parts (altogether 408) and dividing the square into the 



corresponding small squares, we get 408 X 408 = 166464. This dou- 



33 



bled is 332928. Then taking the savis'esha-value of 16 — for the 



34 



diagonal and dividing the square of the diagonal into the small squares 



just described, we get 577 X 577 = 332929 such small squares. The 



difference is slight enough. 



33 



The relation of 16 — to 12 was finally generalized into the rule : in- 

 crease a measure by its third, this third by its own fourth less the thirty- 



/ 33 12 12 12 \ 



fourth part of this fourth ^ 16 - = 12 + - + 3 _-^_ § _ T _j 



33 



The example of the savis'esha given by commentators is indeed 16 ■— : 12 ; 



Orfc 



the case recommended itself by being the first in which the third part of 

 a number and the fourth part of the third part were both whole numbers. 



Regarding the practical use of the savis'esha, there is in Baudhayana 

 or rather, as far as I am able to see, in all s'ulvasutras only one opera- 

 tion, for which it was absolutely necessary ; this is, as we shall see later, 

 the turning of a circle into a square, when the intention was to connect the 

 rule for this operation with the rule for turning a square into a circle. 

 A'pastamba employs (see further on) the savis'esha for the construction of 

 right angles, but there were better methods for that purpose. The com- 

 mentators indeed make the most extended use of the savis'esha, calcula- 

 ting by means of it the diagonals wherever diagonals come into question ; 

 this proceeding, however, is not only useless, but positively wrong, as in all 

 such cases calculation cannot vie in accuracy with geometrical construction. 



At the commencement of his sutras, Baudhayana defining the mea- 

 sures he is going to employ, divides the anguli into eight yavas, barley 

 grains, or into thirty-four tilas (seeds of the sesame). I have no doubt that 

 the second division which I have not elsewhere met, owns its origin to 

 the savis'esha. The anguli being the measure most in use, it was conven- 

 ient to have a special word for its thirty-fourth part, and to be able to 

 say " sixteen angulis, thirty-three tilas", instead of " sixteen angulis, 

 and thirty-three thirty-fourths of an anguli." Therefore some plant was 

 searched for of which thirty-four seeds might be considered as equal in 



