116 AN ESSAY ON THE ROOTS OF INTEGERS, 



No demonstration is required here. 



43.) The division of the given number into periods written in the 

 Pulpit Diagram, by Par. 37 and 38), is evidently the same as in the 

 European Rule, Par. 32) and is therefore explained in Par. 34). Then 



Since 166 the first period = A so as in Par. 34 Art. b.) its nearest 

 approximate 6th Root which is 2, is = a. 



a. Then 2 = a is the number written in the Rank of the Latus. 



b. Then 2x2 = 4zflX«=ffi s is the number written in the 

 Rank of the Square. 



c. Then 4x2 = 8 = a* Xa = a 3 is the number written in the 

 Rank of the Cube. 



d. Then 8x2 = 16 = a 3 X a = a 4 is the number written in the 

 Rank of the Biquadrate. 



e. Then 16 x 2 = 32 = a 4 x a = a 5 is the number written in the 

 Rank of the Quadratus Cubi. 



/. Then 32 X 2 = 64 = a 5 X a = a 6 is the number written in the 

 Rank of the Number or Pulpit Diagram, and is the first subtrahend, 

 agreeing with the first subtrahend of the European method, Par. 34 Art. c.) 



g. h. i. Then 166 — 64 = 102 = A — a 6 and is the first Remainder 

 which agrees with the first Remainder of the European method, Par. 34 

 Art. d) and is therefore zz R. (Par. 18.) 



j. Since by Par. 34 Art. e.) 102,571,800 = Rp 6 -f B, hence the first 

 Resolvend of the European and Arabian methods agree. 



