LAWS OF DECREMENT. 363 



RHOMBOID. 



The inclination of an oblique diagonal to an adja- 

 cent edge, measured over the inferior angle, 

 would be 180 A 5 , and may be denoted by 



A* 



Ratio of a perpendicular upon the axis drawn 

 from a lateral solid angle, to the axis itself, is 

 as - tan.?. 4 3 : R. 



We have already seen that d n is y of the 



axis d , 



and d n : n b :: R : tang. A 3 



Therefore d i 3dn : a b :: 3R : tang. A s 



Ratio off the oblique diagonal, to f the hori- 



zontal diagonal, as R : tang. \ A^. 



Ratio of y of the axis : f half the oblique dia- 



gonal :: cos. A 4 : R. 



Ratio of -3- of the axis : f the horizontal dia- 



gonal :: cot. A^ : tang. 60. 



For d n : n e :: tang. (90 1 Aj : R 

 :: cot.^ 4 : R 



and e b : n e :: tang. 60 : R 



Therefore dn : e b :: cot. A^ : tang. 60'. 

 Ratio of \ an oblique diagonal : an edge 

 :: cos. \A, : R. 



Ratio of \ a horizontal diagonal : an edge 

 :: sin. A : R. 



2 2 



