the Cube Root in Nuinlens. 361 



ihe second coefficient construct a column of two numbers, so that 

 each number mav advance two places of figures before the units 

 place of the coefficient under which they are placed, and under 

 the remainder construct a coluinn of one number so as to ad- 

 vance three places of figures before the remainder. 



3. Annex the quotient figure to the first coefficient, and the 

 sum will be the first num'Der underneath ; each of the two re- 

 maining numbers will be found by increasing the number above 

 it by the quotient figure. 



4. Multiply each of the first two numbers in the first column 

 in succession by the quotient figure, and the opposite number in 

 the second column will be found by adding the product to the 

 number above it. 



5. Multiply the first number under tlie second coefficient by 

 the quotient figure and sul)tract the product from the remainder, 

 and this last remainder is the number which forms the third co- 

 lumn: then if the product be less than the preceding remain- 

 der, the quotient figure is the second figure of the root ; but 

 if not, the quotient figure must be diminished till it is found to 

 be so. 



Now, considering the last two numbers in the first and se- 

 cond coliimns as the first and second coefficienti^, and the last re- 

 mainder as a new absolute number, the step of the work for the 

 next figure will be found exactly in the same manner as that tor 

 the last figure. 



Example. — Extract the cube root of the number 13. 



Here the nearest cube to 13 is S, the root of which is 2 ; there- 

 fore the coefficients of the first step are 6 and 12, and the re- 

 mainder or aljsolute number is 5 : now 5 will be found to con- 

 tain 1, which is the second coefficient wanting the last figure '5 

 times : now -5 being tried will be found not to succeed, therefore 

 try 3 in the operation : thus 



6 12 .') . . .('3 Proceed with these opposite columns 



^ lH^S9 H'ili "^ numbers according to the se- 



66 15S7 cond, third, fourth and fifth parts 



gq of the rules. 



Since 3 succeeds, divide 833 by l.iS, which is the coefficient 

 of the second term witt>out the last figure, and the quotient 5 is 

 the next figure of t'.ie root, which must now succeed; therefore 

 proceed with the next step 



1S20. Z ? A^^\ill 



