7* 



& V 



And the root of the 5th Power «N b 1 he 

 makes 



'tis \ aa, not * aa y as 'tis erroneoufly Printed 

 in the French Book ) Thefe Rules were com- 

 municated to me by a Friend, I having not 

 feen the Book *, but having by tryal found the 

 goodnefs of them, and admiring the Compen- 

 dium, I was willing to find out the Demon- 

 ftration- Which having done, I prefently 

 found that the lame Method might be accom- 

 modated to the Refohitionof all forts of Equa- 

 tions* And I was the rather inclin'd to im- 

 prove thefe Rules, becaufe I faw that the 

 whole thing might be Explained in a Synoyfis ; 

 and that by this means, at every repeated 

 ftep of the Calculus , the Figures already found 

 in the Root, would be at leaft Trebled, which 

 all other ways, are encreafed but in an -equal 

 Number with the given ones* Now, the fore- 

 mention'd Rules are eafily demonftrated 

 from the Genefis of the Cube, and the 5th 

 Power. For, fuppofing the fide of any Cube 

 v=ta-\ e^ the Cube arifingfromthen.ee, is a«a-\-> 

 iee-\ eee. And confequently, if we fup- 

 pole naa the next lefs Cube, to any given Non- 

 cubick Number, then eee will be lefs than 

 Unity, and the remainder b, will w the 

 6ther Members of the Cube, $aze\ ^aee\-eee. 

 Whence rejecting eee upon the account of its 

 fmallnels, we have^ $«ae-\$aee. And fince 



aa ( where Note, that 



