Mtjcellanea Curio fa. 



75 



much pains it would have coft, the Skilful 

 very well know. This Calculus a Man may 

 continue as far as he pleafes, by encreafing the 



which Corre&ion, in this cafe will give, but 

 the encreafe of Unity in the 14th Figure of 

 the Root. 



Exemp. 2d. Let it be proposed to find the 

 fides of a Cube equal to that Englifh Meafure 

 commonly call'd a Gallon, which contains 231 

 folid Ounces. The next lefs Cube is 216, 

 whofe fide 6=2 a, and the remainder 1 5 1=: ^ • 

 and fo for the firft Approximation, we have 



3+VVj-— = tne Root. Andfince ^9,8333. . 

 6 



is 3,1358 ... , 'tis plain that 6,358!=: a-\-e* 

 Now,let 6,1 3 581=5 ^and we (hall then have for 

 its Cube 23 1 ,0008 5 38947 1 2,&according to the 

 Rule,3,o<579+V9, 41 20 1 04 1 0008 5 83947 1 2 



is molt accurately equal to the fide of the gi- 

 ven Cube, which within the fpace of an Hour, 

 1 determin'd by Calculation to be 6.1 357924 

 3966195897, which is exacrin the 18th Figure, 

 defective in the 1 9th. And this Formula is 

 defervedly preferable to the Rationale, upon 

 the account of the great Divilbr, which is not 

 to be manag'd without a great deal of Labour i 

 whereas the extraction of the fquare Root, 

 proceeds much more eafily, as manifold Ex- 

 perience has taught me. 



But the Rule for the Root of a pure Surfb- 

 lid, or the 5th Power, is of fomething a higher 

 Enquiry, and does much more perfectly yet., 



■,. eee . 

 quantity — 7 



3 a 



1 8,4070 



do 



