336 APPENDIX CALCULATION OF THE 



OCTAHEDRON, RHOMBIC BASE. 



The greater lateral plane angle a c 6, may be 

 called A zj and may be thus known, 



cos. A, = cot.U. cot.iJ 3 



K 



Most acute of the lateral plane angles, a b c, 

 may be called A^ and may be thus found, 



cos. A 3 = coMf._cot.jJ. 



Angles of the rhombic base may be thus deter- 

 mined. Let the lesser angle be called A^ and 



cos.-M 4 = R cos " * L > 

 sin.i/ 3 



The required angle \ A^ is the angle 

 e b c of the above figure, and is that side of 

 the spherical triangle nearest to b, which is 

 opposite the angle \ I 2 ; and hence the for- 

 mula which is given. 



Ratio of \ the greater diagonal of the base 

 : \ the lesser diagonal :: R : tang. \ A . 

 Obtuse terminal edges are equal. 

 Acute terminal edges are equal. 

 Inclination of the obtuse terminal edge to the 

 axis being called A 5 , may be thus found, 



A r, COS. \ I 9 



cos. A, = R i i 

 sin. /, 



Inclination of the acute terminal edge to the 

 axis may be called A 6 , and may be thus found, 



. T, cos. \ I, 



cos. A 6 R -i- 



sin. i/ 2 



The angles A 5 and A 6 , are those sides of 

 the upper triangle marked on the figure, 

 which subtend the angles \ I I and \ J 2 . And 

 hence the formulae for their determination. 



