DEfSCTITA ALGORITHM Ot tMAGINART QUANTITIES* g54 



»re some among us, who wish to cramp the power of ana- 

 lysis, by r<^jecting in that science every species of quantity 

 coming under an imaginary form. 1 think I can perceive 

 where the mystery lies ; but still I should be glad to see the ' 

 opinion of more able analysts on this apparent incongruity; 

 if however no such should appear, I will, through the me- 

 dium of your Journal, publish tpy ideas on the subject. 

 The equation to which I have alluded is this : 



X* ■\- X n 2 



and the three roots of it are the following, 



1st root X — 1 

 2d root X zz. — 2 



i 



3d root X zz 



f/^^V-i^p/i 



V— f 



The two first of which evidently answer the conditions of 

 the equation, and with the third 1 proceed as follows. 



X zz 



f/ii 



+ ^/{i—/- 



And now in order that I may be certiin of my results, t " 

 multiply these quantities under.the radicals at full length, 

 as follows ; viz. 







_| I to find the square of | + V'— -^ 



I + ;^Z! I forthe product (i+ V— i) X (i~/— I) 





