1875.] G-. Thibaut— On tie S'ulvasutras. 233 



Tbese propositions are as follows : 

 Baudhayana : 



Tbe cord which is stretched across — in the diagonal of — a square 

 produces an area of double the size. 



That is : the square of the diagonal of a square is twice as large as 

 that square. 



Apastamba : 



Katyayana : 



The cord in the diagonal of a square is the cord (the line) producing 

 the double (area). 



" Samachaturasra" is the term employed throughout in the S'ulva- 

 sutras to denote a square, the " sama" referring to the equal length of 

 the four sides and the chaturasra implying that the four angles are 

 right angles. The more accurate terminology of later Indian geometry 

 distinguishes two classes of samachaturas'ras, or samachaturbhujas, viz. 

 the samakarna samachaturbhuja and the vishamakarua samachaturbhuja ; 

 the S'ulvasutras, having to do only with the former one, make no such 

 distinction. Akshnayarajju is the ancient term, representing the later 

 " karnarajju" or simply " karna." "Area" is here denoted by "bhumi," 

 while in later times " kshetra" expressed this idea, and " bhumi" became 

 one of the words for the base of a triangle or any other plane figure. 



The side of a square is said to produce that square (karoti), a way of 

 speaking apparently founded on the observation that the square is found 

 by multiplying the number which expresses the measure of the side by it- 

 self ; if the side was five feet long, the square was found to consist of 

 5x5 little squares, &c. The expression was not applicable to other plane 

 figures, to an oblong for instance ; for there the area is the product of two 

 sides of different length, neither of which can be said to produce the figure 

 by itself. 



The side of a square, or originally the cord forming the side of a square, 

 is therefore called the "karani" of the square. That " rajju" is to be 

 supplied to " karani", is explicitly stated by Katyayana : 



By the expressions : karani, karani of that (of any square) &c., we 

 mean cords. 



The side of a square being called its karani, the side of a square of 

 double the size was the " dvikarani", the line producing the double (I 

 shall for convenience sake often employ the terms "side" or "line" 



