AS PRACTISED BY THE ARABS. 79 



+ 6 p <p c s -{- c 6 ) or P' — p' 6 or'R" is expounded by 18,535,911/758,593, 

 — 16,134,619,913,216, or 2,401,291,845,377 the third Remainder. 



And by a continuation of analogous reasoning, it will be found that 

 d is expounded by 5, the fourth found figure of the Root. 



6 p' 5 <p s d -f 15 p' A <p* d* -f 20 p' 3 <p s d 3 -f 15 p n <p* d* + 6 p 1 <p d 5 -f- 

 d 6 is expounded by 2,116,025,521,169,640,625, the fourth 

 Subtrahend. 



p' <p -j- d or p" by 2,345, and that is the approximate sixth Root of 

 166,571,800,758,593,887,308, the four first periods of the given 

 number. 



Y"—p" 6 is expounded by 285,266,324,208,246,683, the fourth 

 Remainder or R /;/ . 



e is expounded by 6, the fifth found figure of the Root. 



6 p //s 'p s e + 15p //4 <pV -I- 20 p^fe 3 +15 p"*tfe* -f 6 p^e 5 -f e 6 is 

 expounded by 255,443,315,383,323,683,729,856, the fifth 

 Subtrahend. 



p"<p -f e or p'" by 23,456, and that is the approximate sixth Root of 

 166,571,800,758,593,887,308,296,025, the five first periods of the 

 given number. 



P'"-]y" 5 is expounded by 29,823,008,824,922,999,566,169, the fifth 

 Remainder or R iv . 



x 



