igo4\ 



Henderson — Graphic Representation. 



129 



That this meets the line ch is obvious by inspection. Deter- 

 mining-, in similar fashion, the equations of the remaining- 

 five lines, we obtain 



2: y = 0, x -f Zz = 0; 



3: # = 0, 3^ + 4^ = 0; 



4: x = 0, y — 2 z = 0; 



5: y = 0, 3at+ z = 0; 



6: z=0, 4x + Zy = 0. 



It is worthy of remark that the six lines- 1, 2, 3, 4, 5, 6 lie 

 on the quadric cone, of vertex D, whose equation is 



12 O 2 -f y* + ^ 2 ) — 5 (6jv-2- — 8 *# — 5 #y) = 0, 



since the intersections of this cone by the planes x = 0, 

 y == 0, ^ = respectively, have for their equations 



# = 0, (y — 2 z) (2y — z) = 0; 

 jy = 0, + 3*) (3* + z) = 0; 



* == 0, (3 x + 4jy) (4 * + 3 y) = 0. 



§ 3. It is apparent that, since the lines of, ag, ah all lie in 

 the plane ABC {w = 0), the most convenient location for the 

 plane of projection is the plane of the face ABC of the funda- 

 mental tetrahedron. 



I next calculated the co-ordinates of the points where the 

 six lines bf, bg, b/i, cf, eg, ch meet two faces of the tetrahe- 

 dron ABCD. In the case of the lines af, ag, ah no calcula- 

 tion has to be made, while for each one of the lines 1, 2, 3, 4, 

 5, 6, the co-ordinates of only one point have to be calculated. 

 These results are given below in tabular form: 



