Mtfcellanecb Curio fa, yy 



And thus much may fuffice to be faid, con- 

 cerning the extraction of the Roots of pure 

 Powers ; which notwithftanding, for common 

 TJfes, may be had much more eafily by the 

 help of the Logarithms. But when a Root is 

 to be determin'd very accurately, and the Lo- 

 garithmick Tables will not reach fo far, then 

 we muft neceflarily have recourfe to thefe, or 

 fuch like Methods. Farther \ the Invention 

 and Contemplation of thefe Formulae, leading 

 me to a certain Univerfal Rule, for adfecled 

 Equations (which I hope will be of ufe to all 

 the Students in Algebra and Geometry) I was 

 willing here to give fome account of this Dif- 

 covery, which I will do with all the perfpe- 

 cuity I can. I had given at N 0 ' 1 88 of the 

 Tranfattions, a very eafy and general conftru- 

 6tion of all adtc&ed Equations, not exceeding 

 the Biquadratick Power ; from which time I 

 had a very great defire of of doing the fame in 

 Numbers. But quickly after, Mr. Rafhfon 

 Teem'd in great meafure to have fatisfy'd 

 this Defire, till Mr. Lagney by what he 

 had performed in his Book, intimated that the 

 thing might be done more compendioufly yet. 

 Now, my Method is thus. 



Let z. the root of any Equation, be imagined 

 to be compos'd of the parts a -\r or — e 1 of 

 which, let a be affum'd as near z as is poffible, 

 which is notwithftanding not nccejfaryfixkt only 

 commodious. Then from the Quantity a-\~e or 

 a— <?, let there be form'd all the Powers of £ T 

 found in the Equation, and the Numerical 

 Co-efficients be refpe&ively affix'd to them : 

 Then let the Power to be refMd^ be fub- 

 ftra&ed from the fum of the given Parts fin- 



