500 



Journal of the Asiatic Society of Bengal, [July, 1907. 



is said to be based, did not give it. Tbe point at issue lies 

 between M. ibn Musa, Bralimagupta and Bbaskara. 



BTaliniagii.pt a (circ. 600 A.D,) 

 The diameter and the semi- 



J/. ibn Miisa {circ. 800 A,D.) 

 In any circle, the product of 



-diameter being severally multi- its diameter, multipled by three 



plied by three are the practical 

 circumference and area. The 

 square root extracted from ten 

 times the squa'res are the neat 

 values. 



Bhaskara (circ. 1150 A.D,) 



Rule ; When the diameter of 

 a circle is multiplied by three 

 thousand nine hundred and 

 twenty, and divided by twelve 

 hundred and fifty, the quotient 

 is the circumference : or, multi- 

 ply by twenty-two and divide 

 by seven, it is the gross circum- 

 fei^nce adopted to practice. 



and one-seventh, will be equal 

 to the periphery. This is the 

 rule generally followed in prac- 

 tical life. The geometricians 

 have two other methods. One 

 of them is that you multiply 

 the diameter by itself, then by 

 ten^ and hereafter take the root 

 of the product : the root will be 

 the pei'iphery. The other me- 

 thod 



used by astronomers : it 

 is this, that you multiply the 

 diameter by 62882 and then 

 divide the product by 20000 : the 

 quotient is the periphery,^ 



[Note. — There is another and more interesting reference to 

 the 'squaring of the circle' in Hindu writings given by Dr. 

 Thibaut in his translation of the Sulvasutras. It is the follow- 



rule 



turn 



comers 



and describe the circle together with the third part of the piece 

 standing over ; this line gives a- circle exactly as large as the 

 square; for as much as there is cut off from the square (viz., the 

 coniers of the square) quite as much is added to it (viz., the 



segment of 



This gives 7r = 3-0886. The construction arose out of the 

 custom of building altars of different shapes but of equal areas, 

 which has a very strange resemblance to the celebrated Delian 

 problem.] 



The ratios used by the Hindus have no claim to priority. 

 Ahmes (ctrc. 1700 B.C.) gave a value equivalent to 7r=(16/9)» = 

 3*1604. Ai*chimedes srave a rie^orous nroof showino'that the value 



1 V'10-31623V3-J= 31429; the other values give x = 3'U16. Aryab- 



177 



hata's valae is 3 -^;^-» 3*1416. In practical applications Brabmagupta and 



Bhaskara use the value ira=3, while Aryabhata ia widely erratic in one of the 

 problems attacked by him that requires a knowledge of the value of ir. 



Albiruni states that the value 3 -— - was employed by Pulisa {Indian I, 168). 



