246 G. Thibaut — On the S'iclvasutras. [No. 3, 



When one side of the oblong which had to be turned into a square, 

 was more than double the length of the other, it was not sufficient to cut 

 off a square once, but this had to be done several times, according to the 

 length of the oblong, and finally all squares had to be combined into one. 



Katyayana has a rule to this purpose : 



I add the rules for the reverse process, the turning of a square into 

 an oblong. 



Baudhayana : 



If you wish to turn a square into an oblong, divide it by the diago- 

 nal ; divide again one of the two halves into two 

 parts, and join these two parts to the two sides (those 

 two sides of the other half which form the right 

 angle) as it fits (when joining them, join those sides 

 which fit together). 



Proceeding as directed, we turn the square 

 abed into the oblong b d e f. This rule is, of 

 course, very imperfect as it enables us to turn the 

 square into one oblong only. 



Katyayana has the following : 



A'pastamba's rule helps us somewhat further : 



In order to turn a square into an oblong, make a side as long as you 

 wish the oblong to be (*. e., cut off from the square an oblong one side of 

 which is equal to one side of the desired oblong) ; then join to that the 

 remaining portion as it fits. 



Given for instance a square the side of which is equal to five, and re- 

 quired an oblong one side of which is equal to three. Cut off from the 

 square an oblong the sides of which are five and three. There remains an 

 oblong the sides of which are five and two ; from this we cut off an oblong 

 of three by two, and join it to the oblong of five by three. There remains 

 a square of two by two, instead of which we take an oblong of 8 by l-§-. 

 Joining this oblong to the two oblongs joined previously we get altoge- 

 ther an oblong of 3 by Si, the area of which is equal to the area of the 

 square 5 by 5. 



