1875.] G. Thibaut— On the S'ulvasdtras. 243 



Baudhayana's and A'pastamba's commentators disagree in tbe expla- 

 nation of tbe sutra; tbe methods they teach are, however, both legitimate. 

 Dvarakanatkayajvan directs us to divide tbe given square into nine small 

 squares by dividing the side into three parts, and to form with tbe side 

 and tbe diagonal of one of these small squares an oblong ; tbe diagonal 

 of this oblong is tbe tritfyakarani. 



Kapardisvamin proposes to find the trikarani of the given square 

 and to divide it into three parts ; one of these parts is the tritiyakarani ; 

 for its square is tbe ninth part of a square of three times the area of the 

 given square, and therefore the third part of the given square. This ex- 

 planation seems preferable, as it preserves better the connexion of the rule 

 with tbe preceding rule for the trikarani. 



The fourth, fifth, &c, parts of a square were found in the same way. 



A'pastamba and Katyayana give some special examples illustrating 

 tbe manner in which the increase or decrease of the side affects tbe increase 

 and decrease of the square. 



A'pastamba : 



A cord of the length of one and a half purusha produces two square 

 purushas and a quarter ; and a cord of tbe length of two purushas and a 

 half produces six square-purusbas and a quarter. 



Katyayana : 



f%i SWRT ^gwRT^Tt f^: swt^T T^WT ^g:swTH!T ^T^^PC^ I 



A cord of double tbe length produces four (squares) ; one of three 

 times the length produces nine, and one of four times tbe length produces 

 sixteen. 



A'pastamba and Katyayana : 



By a measure of half the length a square is produced equal to the 

 fourth part of the original square. 

 A'pastamba : 



Katyayana : 



By tbe third part tbe ninth part is produced, 

 Katyayana : 



The sixteenth part is produced by tbe fourth part. 

 Next follow tbe rules for squares of different size. 

 A'pastamba : 



