332 APPENDIX CALCULATION OF THE 



OCTAHEDRON, RECTANGULAR BASE. 



The inclination of a terminal edge to the axis may 

 be called A 3 , and may be thus found, 



If we suppose a spherical triangle to be 

 represented by a segment kg bfof the octa- 

 hedron, it would obviously be right angled 

 at h ; and we know the side 



Whence we find cos. y g fb, which we call 

 A 3 , by the known formula 



cos A cos.(90 1/ 2 



~R 



sin. | 7 2 cos. 



Ratio of I a diagonal of the base 

 : ^ the axis :: sin. A 3 : cos. A 3 . 

 The relation between 7,, 7 2 , and 7 3 may be thus 

 discovered, 



cos. 7 zz ~ cos '2^2 cos. |7 3 



If we suppose the angle h b i rr 90, to be 

 the side of a spherical triangle, the angles 

 of the same triangle would be 7,, i7 , and 



1/3- 



A general equation to discover 7 , would be 

 cos. 7, ~ 

 cos.\/hb i. sin.i7 2 .sin.|7 3 cos.-7 2 . cos.^/ 3 



* But as cos. V h b i ~ o, the equation be- 

 comes that which has been given. 

 From which formula, any two of the angles 

 being known, the third angle may be found. 



