1S75.] G. Thibaut — On the S'ulvasutras. 235 



Baudhayana : 



This (viz. that the diagonal of an oblong produces by itself, &c.,) is 

 seen in those oblongs the sides of which are three and four, twelve and five, 

 fifteen and eight, seven and twenty-four, twelve and thirty-five, fifteen and 

 thirty-sis (literally, the sides of which consist of three parts and four parts, 

 &c.) 



This sutra contains the enumeration of, as we should say, five Pytha- 

 gorean triangles, i. <?., rectangular triangles, the three sides of which can 

 be expressed in integral numbers. (Baudhayana enumerates six ; but the 

 last is essentially the same with the second, 15 and 36 being 3x5 and 

 3 X 12.) Baudhayana does not give the numbers expressing the length 

 of the diagonals of his oblongs or the hypotenuses of the rectangular trian- 

 gles, and I subjoin therefore some rules from A'pastamba, which supply 

 this want, while they show at the same time the practical use, to which the 

 knowledge embodied in Bauclhayana's sutra could be turned. 



The vedi or altar employed in the soma sacrifices was to have the 

 dimensions specified in the following : 



The western side is thirty padas or prakramas long, the prachi or east 

 line (i. e., the line drawn from the middle of the western side to the mid- 

 dle of the eastern side of the vedi) is thirty-six padas or prakramas long ; 

 the eastern side twenty-four ; this is the tradition for the vedi at the soma 

 sacrifices. 



Now follow the rules for the measurement of the area of this vedi : 



Add to the length of thirty-six (i. e.,io a cord of the length of thirty- 

 six either padas or prakramas) eighteen (the whole length of the cord is 

 then 54), and make two marks on the cord, one at twelve, the other at 

 fifteen, beginning from the western end ; tie the ends of the cord to the 

 ends of the prishthya line (the prishthya is the same as the prachi, the line 

 directed exactly towards the east and west points, and going through the 

 centre of the vedi. The fixing of the prachi was the first thing to be done 

 when any altar had to be measured out. The methods devised for this 

 end will not be discussed here, as they are based on astronomical observa- 

 tions ; for our purpose it is sufficient to know that a line of 36 padas length 



