AS PRACTISED BY THE ARABS. 73 



-J- (this sought number) 6 . 



The sum of all these added together may not exceed the last 

 Resolvend. 



(b'".) Place the number now found to the right hand of the found 

 figures of the Root in the semicircle Art. b). Call the number now found 

 the last found figure of the Root, and the whole of the figures in the semi- 

 circle, the found figures of the Root. 



(c'".) Call the sum found by Art. /" the last Subtrahend. 



(d'".) Subtract the last Subtrahend from the last found Resolvend, 

 and call the Result the next Remainder. 



(e!".) To the right hand of this Remainder annex the next Period, 

 and continue this circle of operations till there be no period in the origi- 

 nal given number so to annex. 



And thus it will be found that — 



The fourth figure of the Root is 5. 



The fourth Subtrahend is — 



6-2340 s -5 -f- 15'2340 4 5 2 -f- 202340 3 5 3 -{- 152340 2 '5 4 -f 62340-5 5 -f- 5 6 

 = 2,116,025,521,169,640,625. 



The fourth Remainder is 285,266,324,208,246,683. 



Then the fifth figure of the Root is 6. 



The fifth Subtrahend is 255,443,315,383,323,683,729,856. 



The fifth Remainder is 29,823,008,824,922,999,566,169. 



