130 THE SQUARING OF THE CIRCLE. 



useful for practical applications. Strange to say, the good ap- 

 proximate value of Aryabhatta does not occur in Brahmagupta, the 

 great Hindu mathematician who flourished in the beginning of the 

 seventh century ; but we find the curious information in this author 

 that the area of a circle is exactly equal to the square root of 10 

 when the radius is unity. The value of it as derivable from this 

 formula, a value from two to three hundredths too large, has 

 unquestionably arisen on Hindu soil. For it occurs in no Grecian 

 mathematician ; and Arabian authors, who were in a better position 

 than we to know Greek and Hindu mathematical literature, declare 

 that the approximation which makes n equal to the square root of 

 10, is of Hindu origin. It is possible that the Hindu people, who 

 were addicted more than any other to numeral mysticism, sought 

 to find in this approximation some connection with the fact that 

 man has ten fingers, and that accordingly ten is the basis of their 

 numeral system. 



Reviewing the achievements of the Hindus generally with re- 

 spect to the problem of quadrature, we are brought to recognise 

 that this people, whose talents lay more in the line of arithmetical 

 computation than in the perception of spatial relations, accom- 

 plished as good as nothing on the purely geometrical side of the 

 problem, but that the merit belongs to them of having carried the 

 Archimedean method of computing n several stages farther, and of 

 having obtained in this way a much more exact value for it a cir- 

 cumstance that is explainable when we consider that the Hindus 

 are the inventors of our present system of numeral notation, pos- 

 sessing which they easily outdid Archimedes, who employed the 

 awkward Greek system. 



With regard to the Chinese, this people operated in ancient 

 times with the Babylonian value for it, or 3; but they possessed 

 knowledge of the approximate value of Archimedes at least since 

 the end of the sixth century. Besides this, there appears in a num- 

 ber of Chinese mathematical treatises an approximate value pe- 

 culiarly their own, in which 7T = 3 T \; a value, however, which not- 

 withstanding it is written in larger figures, is no better than that of 



