1875.] 



G. Thibaut — On tlie S'ulvasutras. 



247 



In this way the siitra, as it appears from the commentaries, must be 

 explained. The method taught in it was no doubt sufficient for most cases, 

 but it cannot be called a really geometrical method. 



I subjoin the description of a method for turning squares into oblongs, 

 which is given by Baudhayana's commentator, although it is not founded 

 on the text of the sutras. He, after having explained Baudhayana's way 

 of proceeding, continues — 



^^^ WITS I ^T^f^^ TTT^T^T TH3T "STSffafflT ^'rTCtT'lf ^WT^Tn^^?- 

 W! ^TfflMTlt W^T r^frT^^T^i *pi faqTrfrT rTrT ^tIT f%«?T ^f%- 



And there is another method. Lengthen the north side and the south 

 side of the square towards east by as much as you want (i. e., give to 

 them the length of the oblong you wish to construct) and stretch (through 

 the oblong formed by the two lengthened sides and the lines joining their 

 ends) a cord in the diagonal from the north-east to the south-west corner. 

 This diagonal cuts the east side of the square, which (side) runs through 

 the middle of the oblong. Putting aside that part of the cut line which 

 lies to the north of the point of intersection, take the southern part for the 

 breadth ; this is the required oblong. 



For example : 



Given the square abed and required an oblong 

 of the same area and of the length b g. Lengthen a e 

 and b d into a f and b g ; draw f g parallel to c d ; 

 draw the diagonal f b, which cuts c d at h ; draw i k 

 parallel to a f and b g ; then b g i k is the desired 

 oblong. 



This method is purely geometrical and perfectly 

 satisfactory ; for a b f = b f g, and b d h = b h i 

 and c f h = f h k ; therefore achi = dghk, and 

 consequently a b c d = b g k i. q. b. p. 



In this place now we have to mention the rules 



which are given at the beginning of the sutras, the 



rules, as they call it, for making a square, in reality 



for drawing one line at right angles upon another. Their right place is 



here after the general propositions about the diagonal of squares and 



oblongs, upon which they are founded. 



Baudhayana : 



^retffc^ ^i^tSit^ ^r^5 3ffTrf?r > ws*r^*«i*i. 1 ^fiSS^Wht i suTf^-p tot 

 * Make two ties at the ends of a cord the length of which is double 



