1S75.] G. Thibaut— On the S'ulvasutras. 253 



afraid we should not be justified in giving to A'pastamba the benefit of this 

 explanation. The words ' yavad dhiyate, &c.' seem to indicate that he was 

 perfectly satisfied with the accuracy of his method and not superior, in this 

 point, to so many eircle-squarers of later times. The commentator who, 

 with the mathematical knowledge of his time, knew that the rule was an 

 imperfect one, preferred very naturally the interpretation which was more 

 creditable to his author. 



Katyayana's S'ulvaparis'ishta : 



Let us now see what the result of the above rule would be by making 



the side of the square equal to 2. a c = 2; a i = 1; ae= \/ 2 



0-414213 

 = 1-414213... ; ; = 0-138071 ; radius of the circle = 1-138071. 



o 



Multiplying the square of 1-138071 by tt = 3-141592..., we find as 

 area of the circle : 4-069008 , while the area of the square = 4. 



The next thing was to find a rule for turning a circle into a square. 

 There we have at first a rule given by Baudhayana only : 



If you wish to turn a circle into a square, divide the diameter into 

 eight parts, and again one of these eight parts into twenty-nine parts ; of 

 these twenty-nine parts remove twenty-eight and moreover the sixth part 

 (of the one left part) less the eighth part (of the sixth part). 



The meaning is : | + A- _ _i_ + _i_ f the diameter of 



a circle is the side of a square the area of which is equal to the area of the 

 circle. 



Considering this rule closer, we find that it is nothing but the reverse 

 of the rule for turning a square into a circle. 



It is clear, however, that the steps taken according to this latter rule 

 could not be traced back by means of a geometrical construction ; for if we 

 have a circle given to us, nothing indicates what part of the diameter is to 

 be taken as the " atis'ayatritaya" (the piece f g in diagram 10). 



It was therefore necessary to express the rule for turning a square into 

 a circle in numbers. This was done by making use of the " savis'esha", which 

 we have considered above. Baudhayana assumed a i as equal to 12 singulis 

 ( = 408 tilas), and therefore a e = 16 afigulis, 33 tilas. Difference = 4 

 afig. 33 til. = 169 til. ; the third part of this difference = 56 j til. Ra- 



