PftOJECTION IN TWO DIMENSIONS. 9 



intersect in a point C, of which the coordinates are x = a, 



y = b. Draw FG parallel to ED, and GK parallel to Oy ; 



on GK take a length KL, so that NG being parallel to 



AB, 



KL = y/iNG; 



then L will be a point on the projected curve. If through 

 L we draw parallel to Ox a line LM such that 



LM=mrG, 



then M will be another point on the curve. By proceed- 

 ing in this manner, the entire curve may be constructed. 

 A curve generated in this manner from the primitive curve 

 may, for brevity, be termed its projectrix. 



The equation to the primitive being given, that of its 

 projectrix may be deduced as follows : — 



NG=CGcosGCH, 



X and y being coordinates of G, we shall have 



cosGCH= ^'^-^^^+j^-^^^^ 

 LG 



therefore 



l^G—{x-a)l+{y — b)m; 

 and 



Yih = m{{x — a)l-\- {y—b)m} ; 



therefore, if tj and ^ be coordinates of the corresponding 

 point on the projectrix^ we shall have 



^=0K = ^, (3) 



r) = m{l{x-a)+m{y-b)}, ... (4) 



and if the primitive curve be 



J\.v,y)=0, 



