80 AN ESSAY ON THE ROOTS OF INTEGERS, 



f is expounded by 7, the sixth found figure of the Root. 



-f / fi is expounded by 29,823,008,824,922,999,565,181,681,169, 

 the sixth Subtrahend. 



p"> <p _j_ forp lv by 234,567, and that is the approximate sixth Root of 

 the given number, 166,571,800,758,593,887,308,296,025,335,490. 

 That is jo iv rs m. 



pi v __p ,T 6 j s expounded by 987,654,321 the last Remainder, and since 

 by Par. 25). P IV = M so P-/ 4 = R v =: M — m 6 = r of 

 Par. 28.) 



And it is evident this reasoning may be continued to any number of 

 periods. 



(35.) I now proceed in order to — 



III. Exhibit this operation as directed by the Arabian Arithmeti- 

 cians, and then explain its conformity to the original Demonstration. 

 This operation occupies a much more extended space, and is delineated 

 in the annexed Diagram. — (See Lithographized Figure.) 



(36.) The outlines which constitute the upper part of this Diagram, 

 and are there called the Rank of the Number, and contain the same figures 

 as in the European Operation of Par. 31), are technically called by the 

 Arabian Arithmeticians ^ j^ JCi. Shukloon Mimbureeoon, or Pulpit Dia- 

 gram or Figure, from its fancied resemblance to the ascending steps which 

 constitute a Mohammadan Pulpit. This term will perhaps sound oddly 

 in European ears, but we shall be less inclined to deride the quaintness of 



