436 APPENDIX ON DRAWING THE 



2 



ment being expressed by 2 A a . The fig. No. 1, has 

 the necessary directing planes drawn upon it, from 

 which it appears that the lines e a, e b, e c, represent 

 three intersections of the secondary planes with each 

 other. If on No. 2 we draw the lines p p', q q', &c. 

 through the middle of the diagonally opposite edges, 

 and from the solid angle at e, draw lines parallel to e a, 

 e b, e c, of No. 1, those lines will be the edges of the 

 new figure, and they will cut the lines p p', &c. at a 

 distance from the edges of the cube equal to -- of its 

 diagonal. This will be apparent if we suppose the 

 central point e of No. 1, to represent the solid angle 

 e of No. 2 ; for the line e a evidently cuts a diagonal 

 of the cube at a distance from its middle point equal 

 to of its whole length. 



The plane a a' b, No. 1, represents one of the 

 secondary planes, through the middle of which, if we 

 draw the line a' a", that line will pass through the 

 centre of the cube, and will consequently bisect its 

 prismatic axes. A line drawn, therefore, from the 

 solid angle at e, fig. 2, through the produced pris- 

 matic axisyg*, will cut that axis at a distance from 

 the surface of the cube equal to | the length of the 

 axis itself, and will pass through the middle of the 

 secondary plane. 



Having thus found the points at which the lines 



p p'-> q #'? & c> an dy*g*5 ^ ? ? an d k i) are cut y tne 



secondary edges, we may readily complete the figure. 



We shall give only one further illustration to com- 

 plete this branch of our subject. In several of the 

 preceding examples, the directing planes and lines 

 have been drawn on separate, parallel, figures, for 

 the purpose of exhibiting more distinctly the described 

 methods of drawing. We may, however, in very 



