314 APPENDIX "CALCULATION OF THE 



REGULAR OCTAHEDRON. 



diculars are, from the nature of the figure, equal. 

 We know the angle b a c, which we call J 2 , and we 

 are supposed to know the angle b d e, which is the 

 inclination of one of the planes of class b to the adja- 

 cent primary planes. This inclination we shall call 

 / 3 , and from these angles we may deduce the angle 

 d e a, which we may call / 4 . 

 Hence we have 



a d : a e : : sin. / 4 : sin. (180 / 3 ) : : p : <?, 

 which gives the law of decrement by p rows in breadth^ 

 and q rows in height, on the angle 3 proceeding along 

 the plane a b. 



Intermediary decrements. 



The intermediary decrements of the regular octa- 

 hedron are, as we have already seen, of two kinds; 

 the one producing the modifications class c ? and the 

 other class c? 3 of that form. 



Fig. 336. 



In the modifications class c 9 the general symbol 

 representing which is (Bp B' q b' q br), the edges 

 e, a g, of the defect of the primary form, are equal, 

 a h is less than a e, or a g, and ajf greater. 



It will be sufficient therefore to determine the 

 ratios of af to either a e or a g, and to a h. For 



