[ 56 ] 



will converge fo llowly, that a very great number of terms muft 

 be calculated, and therefore the labour will be immenfe. This, 

 however, is an inconvenience that may be remedied ; for in- 

 ftead of refolving the given number into a binomial, let it be 

 multiplied into feme cube number, fo as that the produd may 

 be nearly equal to fomc other cube number; and let this pro- 

 dud be refolved into a binomial, and its root found; which 

 being multiplied into the cubic root of the divifor, as above, 

 and divided by the cubic root of the number into which the 

 given number was multiplied, the quotient is the root re^ 

 quired. 



Thus if the cubic root of 2 be required, it might be refolved 

 into 8 — 6, and dividing by 8 it would become i — ^. But this 

 is to be rejeded for the reafon given above. Multiplying there- 

 fore 2 into 8, the produd i6 gives the binomial i — — . But 

 here alfo the fradion ^'' (though lefs than the former,) is too 

 great. Multiplying then 2 into 27, the next cube number, the 

 produdt 54 gives the binomial i — 1^» where the fradion is 

 ftill lefs, and might be ufed, only that on multiplying 2 into 

 64, the next cube number, the produd 128 gives the binomial 



i4--^i which is as convenient as can be defired. 

 125 



Find therefore its cubic root, by the method above, and 

 multiply it into 5, (the cubic root of the denominator of the 

 fradion,) and the produd is the root of 128 : And this root be- 

 ing divided by 4, (the cubic root of the multiplier 64,) the quo- 

 tient is the cubic root of 2, as was defired. 



That 



