LAWS OF DECREMENT. 



317 



REGULAR OCTAHEDRON. 



Whence we may deduce the particular values of p, q, 

 and r, from the ratios of a g : a h, and a g : af. 

 a g : ah:: sin. (120 A 5 ) : sin A 5 



01 r // 



sin. (120 A 5 ) 

 a g : af :: sin. (120 ^ 4 ) : sin 



:: p:q. 



1 Sl11 ' -"4 



sin. (120 A,) 

 The value of s may be found from the following- 

 equation, 



I^I+I^i 



s q r p 



This equation may be thus derived. 



Fig. 338. 





Let a i e c, fig. 338, represent a section passing 

 through the axis of any octahedron whose terminal 

 edges are equal, and through four of those edges. 

 And let the lines g i, hf, be equal to lines which 

 might be drawn on the plane/* g- h i, fig. 337, from g 

 to 2, and from h tof. Both these lines will evidently 

 cut the axis at the same point, which we may call m. 



If we draw g n parallel to a i, we have 

 g n z= g a : a i :: an a m : a m. 



