Ellery W. Davis 



since they held for the real joints (x f , y') and {x' -f- x" , y' -f- y"). 

 We do not here consider imaginary axes. 



NOTATION 



Blaxk hrxz 



Bla<z line 



I?ed line 



Black point . as P' 



Blew poinf » as T" 



Composite, poirtf m 



• d& P 



3. The addition of real quantities to the coordinates shifts the 

 red vector without changing its length or direction, but not so 

 with the addition of a complex quantity. 



In fact, the change is a double-vector addition, the black vector 

 of (x -\- x r , y -{- y x )^^P 2 being the vector sum of the black 

 vectors of {x, y)^P and (x 1} y x ) ==P V while the red vector of 



Y 



-X 



Fig. 2. 



the sum is similarly the sum of the red vector of the summands 

 (see fig. 2). 

 4. The multiplication of both coordinates by real numbers mul- 



