242 G. Thibaut — On the S'ulvdsutfag. [Xo. 3, 



length to one anguli ; if the tilas really had that exact property, was 

 after all a matter of little relevancy. 



Having once acquired the knowledge of the Pythagorean proposition, 

 it was easy to perform a great number of the required geometrical 

 operations. The diagonal of a square being the side of a square of double 

 the size, was, as we have seen, called dvikaraui ; by forming with this 

 dvikarani and the side of the square an oblong and drawing the 

 diagonal of this oblong, they got the trikarani or the side of a square the 

 area of which was equal to three squares of the first size. 



Baudh. A'past. Katy. 



Take the measure (the side of a square) for the breadth, the diago- 

 nal for the length (of an oblong) ; the diagonal cord is the trikarani. 



By continuing to form new oblongs and to draw their diagonals, 

 squares could be constructed, equal in area to any number of squares of 

 the first size. Often the process could be shortened by skilful combina- 

 tion of different karanis. Katyayana furnishes us with some examples. 



Take a pada for the breadth, three padas for the length of on ob- 

 long ; the diagonal is the das'akarani (the square of the diagonal com- 

 prises ten square padas, for it combines the square of the karani of one 

 pada and of the navakarani which is three padas long). 



Take two padas for the breadth, six padas for the length of an ob- 

 long ; the diagonal is the chatvarims'at-karaui, the side of a square of 

 forty square padas (2 2 -f- 6' 2 = 40). 



On the other hand, any part of a given square could be found by 

 similar proceedings. 



Baudhayana, after the rule for the trikarani : 



Thereby is explained the tritiyakarani, the side of a square the area 

 of which is the third part of the area of a given square ; it is the ninth 

 part of the area. 



A'pastamba : 



Katyayana : 



