1894.] 



BAKER — GRAPHIC IMAGIXARIES. 



153 



plain question is, what can we do to > so that a repetition of 



the operation shall produce < ? The answer stares you in the 



face, viz., turn > to the position | , i. e., swing it 90° counter- 

 clockwise. A repetition of the operation swings it to the position 

 < . Hence, if -[-i is represented by >, and — i by 



< , then ]/ ( — i) is represented by | and the ideograph of 



l/{ — i) is a real symbol of the same class as the other symbols and 

 no longer imaginary. 



We might have swung > clockwise and have found a 



second symbol J. for p/( — i). This is in accordance with the algebraic 

 proposition that extraction of square root gives two answers \/{ — i) 

 I is adopted as the equivalent of the positive answer 



± V 



I. 



and is denoted pseudographically by -\-i = +i/(-i) and I by 



— ^ = — 1/(-0- 



Ideographs as here used are merely strokes upon the surface of 

 the paper, the performance of the stroke carrying the pen along the 

 paper through a certain distance in a given direction. 



The addition of two strokes can always be considered as the equiv- 

 alent of some third single stroke, thus : — > -\ > = > 



or 



+ : = 



Arranging the pseudographs and ideographs in columns to 

 facilitate comparison we have : 



PSEUDOGRAPHS. 



+ I 



IDEOGRAPHS. 



l/'(-l) = ^- 



-i./(-0 = 



I + i 



V 



A 



2 + 2 



