£5© DEPECTIYE ALGORITHW OF IMAGINARY QUANTITIE«|. 



1 31 ^Hf I to find the square of 4. — y'— f 



Therefore 



^^^ //'-U— V-f) + 2 + //-(^+V-|) or 



''=2 — p/i - V-i - ^i + V-f or 



and therefore by addition, we have 



Now if this be a legitimate result, I see no reason why this 

 value of a* should not be considered asa root of the proposed 

 equation as well as the other two; and if it be admitted as 

 such, then I can tind any number of other roots at pleasure ; 

 which will totally destroy the established theory of equa- 

 tions; but if, on the contrary, this cannot be admitted as a 

 root, then it necessarily follows, that the present algorithm 

 of imaginary quantities is defective, or otherwise that I have 

 deviated from that algorithm in the preceding operation. 

 In order to discover the errour wherever it moy lie, and that 

 the connection of it may be made public, 1 am induced to 

 request the publication of this paper in your Journal ; which, 

 if you should think proper to comply with, will much oblige 



Yours &c. % 



MATHEMATICUSe 



HI. 



