AN ESSAY ON THE ROOTS OF INTEGERS, 

 Then the sixth figure of the Root is 7. 



"o" 



The sixth Subtrahend is 29,823,008,824,922,999,565,181,681,189. 



And the sixth Remainder, with which the operation concludes, is 

 987,654,321. 



(33J. I now proceed to show the conformity of this Rule, with the 

 demonstration given in Par. 11). et seq. and for this purpose must pre- 

 mise the following — 



Lemma 6. If to the right hand of a Row of a figures another Row 

 consisting of an n th number of places be annexed, this is equivalent to 

 multiplying the first Row by 10° and adding to the product the number 

 expressed by the second Row. 



Thus let 9,876 be a Row of figures, and 123,456 a second Row. In 

 this second Row there are 6 figures, then if it be written to the right hand 

 of, and in one line with the first Row, it will become 9,876,123,456 z= 

 9,876,000,000 -f- 123,456 — 9,876 -J- 10 6 -f 123,456. This is too evident to 

 require farther illustration. 



(34.) Now M (Par. 15.) is expounded in the present example by the 

 number 166,571,800,758,593,887,308,296,025,335,490, so placing the dots 

 over every 6th place, as directed in Par. 22, Art. a), distinguishes it by 

 Lem. 6 as follows : 



166,000,000,000,000,000,000,000,000,000,000 



■f 571,800,000,000,000,000,000,000,000,000 



4- 758,593,000,000,000,000,000,000 



4- 887,308,000,000,000,000 



+ 296,025,000,000 



■f 335,490 



