248 G. Thibaut — On the S'ulvasutras. [Xo. 3, 



the measure (of the side of the required square) and a mark at its middle. 

 This piece of the cord (i. e., its half) gives us the prachi (of the required 

 square; the prachi of a square has the same length as its side). Then 

 make a mark at the western half of the cord less the fourth part (of the 

 half. If we wish, for instance, to make a square the side of which is twelve 

 padas long, we take a cord twenty-four padas long ; stretching this cord 

 on the ground from the west towards the east, we find its middle by a 

 measurement beginning from the western end, and having fixed the point 

 which lies at the distance of twelve padas from both ends, we measure 

 three padas back, towards the west, and make at the point we arrive at a 

 mark; this mark divides the cord into two parts of 15 and 9 padas 

 length). The name of this mark is nyanchhana. Then another mark is 

 to be made at the half (of the western half of the cord), in order to fix by 

 it the four corners of the square. (This second sign is at a distance of 

 18 padas from the eastern end of the cord.) Having fastened the two 

 ties at the ends of the prishthya line, we take the cord at the nyanchhana 

 mark and stretch it towards the south ; the four corners of the square are 

 then fixed by the half (of the cord).. 



The same method is known to A'pastamba : 



Or the length of the prachi of the desired square, is to be doubled ; 

 the length and the fourth part of the added piece form the diagonal cord ; 

 the rest, i. e. three quarters of the added piece form the breadth (the 

 shorter side of the oblong). 



And the S'ulvaparis'ishta : 



These rules make use of one of the Pythagorean triangles which 

 were, as we have seen above, known to the Sutrakaras, viz. of that one 

 the sides of which are equal to three, four, and five. It recommended it- 

 self by the ease with which the three sides can be expressed in terms of 

 each other, 3+5 being the double of 4, and 3 being equal to half the 

 sum of 3 and 5, minus one quarter of half that sum. 



Of course any other oblong with measurable sides and diagonal could 

 be employed for the same purpose, and so we find in A'pastamba a rule 

 for chaturasrakarana abstracted from the dirghachaturasra, of which the 

 sides are five and twelve and the diagonal thirteen. 



Take a measure equal to the length (of the side and prachi of the 

 desired square) and increase it by its half. Make a mark at the western 

 third less its sixth part. Fasten the ends of the cord, &c. 



