348 APPENDIX CALCULATION OF THE 



RIGHT OBLIQUE-ANGLED PRISM. 



is the ratio of b d, a perpendicular on the diagonal, 

 to the edge bf^ which may be thus found. 

 Let the ratios of the edges be as follows, 



b c : b a :: m : n :: 1 :- 

 m 



b c : b f : : m ; o : : I : 



ba: bf:: n: o ::l :- 

 n 



The angle a b c has been called A t 



b c m A z 



From the ratios of the edges and the angles A l and 

 A z , we may find the angles 



b a c m a c m, call this A 3 

 abm ~ b m c, . . ^ 4 



thus . . b a : b d :: R : sin A 3 :: 1 : Sin ' A * 



R 



therefore b d : bf:: - 2 : :: n sin.^ 3 : o R. 

 R n 



The unit for determinining the laws of simple and 

 mixed decrements belonging to class b is the ratio of 

 e c, a perpendicular on the diagonal, to an edge c w, 

 or bf. 



We have m c ~ a b : e c :: R : sin.A 4 :: 1 : ^ 



R 



and because c n zz 6 /, we must have 



e c : b f:: - i : :: n sin. A. : oR. 



R n 



The ratios of the primary edges may be assumed 

 as the units for determining the decrements producing 

 the remainder of the planes belonging to class a and 

 b ; and they should be so adapted to each particular 



