[ 7a ] 



afterwards, is much increafed. Indeed when the given number 

 confifts of many places of figures, the labour of dividing by a 

 large divifor cannot be avoided. But the trouble of inveftigation 

 may be faved, as the cube number next greater or next lefs 

 than the given number, may be made the firft member of the 

 binomial, into which the given number is refolved. 



If the given number be a decimal fradion, or an integer 

 with a decimal annexed, it will be convenient to reduce it to 

 an integral number, by removing the nota feparatrix to the 

 right hand over a number of places which muft always be di- 

 vifible by 3 : (one or two cyphers being added after the figni- 

 cant figures, when neceffary, to make the number of decimal 

 places a multiple of 3 :) And when the root of the integral num- 

 ber is found, as many of its integral figures are now to be added 

 to the decimals, as there were ternaries of decimal figures, before 

 added to the integers. 



If the given number be a vulgar fradion, (either proper or im- 

 proper,) let the fquare of the denominator be multiplied by the 

 numerator, and the cubic root of the produd be found as 

 above; and let the given denominator be fubfcribed under this 

 root, if a vulgar fradion be fufiicient : Or let this root be divided 

 by it, if a decimal fradion be neceffary. 



By a like procefs (/nutatis mutandis) any root may be extraded 

 out of a given number : but when the index of the root is any 

 term of the duple progrefllon, beginning from unity, the operation, 

 as is well known, may be otherwife performed in a more fimple 

 manner. 



