AND OTHER SURD EQUATIONS. 227 



Standard, and bow ; and with one he cut off the head of the 

 foe. How many were the arrows that Arjuna let fly ? * 



" The instructions which follow (p. 212) are : — * In this 

 case, put the number of the whole of the arrows ya, v, 1.' 

 In other words, assume that number to be x^. But why not 

 X ? In this instance there appears to be but one answer 

 for the Oriental investigator to give, viz., we must avoid surds. 

 And this answer explains the peculiar form of the assumption 

 in the first example. Had x^ been assumed as the total 

 number of bees, we should have had the surd V2 introduced 

 into the expression of the problem. But, why object to the 

 introduction of surds ? It was not that the Orientals did 

 not recognise surds ; on the contrary, their knowledge of 

 their properties was extensive and accurate (pp. 145-155). 

 It was not that they had not a convenient notation, for 

 such a surd number as V2 would be denoted by ca, 2, or 

 (adopting Mr. Colebrooke's variation) by c 2 ; and, if we 

 say with Narayana (page 145, note 1), that * a quantity, 

 the root of which is to be taken, is named Carani,'' I can- 

 not see why ca or c should not have been applied to ya — 

 thus, c, ya. This quantity would have corresponded to our 

 V^. The solution of the problem would then have been 

 effected by our supposing the sum of ya, ^, and c, ya, 

 4 and rw, 10 to be equal to ya, 1 ; and we should thence 

 arrive at 



[c, ya, 1 ru, 4] 



[c, ya, ru, 6], 



whence we obtain 100 as the value of ya ; and the further 

 advantage that yavat-tavat is the very qucBsitum of the pro- 

 blem, the number of arrows. But, even if we suppose the 

 word carani to be exclusively applied to number, those who 

 achieved in notation the results which we see in the Vija- 

 ganita would not have had much difficulty in expressing 

 the square root of ya. Is it improbable, then, that the 



