LAWS OF DECREMENT. 33i 



OCTAHEDRON, RECTANGULAR BASE. 



Whence 



fh : hb :: sec.(90 f/ 2 ) : tang.(90-4/ 3 ) 

 and/A : hb :: R : tang. \A^ 

 Therefore 



tang. \ A, : R :: tang. (90 1/ 3 ) 

 : sec. (90 f 7 a ) 



A R. tang. (90-4 J",) 

 tang, f^f, = - _> -- |__1L 

 sec. (90 | I.) 



r, , R COS 



But as -- _ , 

 sec. R 



and tang. 90 a = cot. a, 

 the equation becomes 



cot.i/ 3 



R 



The second equation must evidently be simi- 

 lar in its character to the first, but substituting 

 J 3 and / a for / 2 and 7 3 . 

 The terminal edges equal. 



Ratio of a terminal edge : a perpendicular on 



the base of plane P :: R : cos. \A,. 



Ratio of a terminal edge : a perpendicular on 



the base of plane M :: R : cos. |^ 2 . 



Ratio of a terminal edge : a greater edge of 



the base : : R : 2 sin. \ A , . 



Ratio of a terminal edge : a lesser edge of 



the base :: R : 2 sin. \ A z . 



Edge d b of the base : edge be:: cot. \ I 3 : 



cot.i/ 2 . 



For gi = %db :: gh~ b e 



:: tang. (90 M 3 ) : tang. (90- i 7.) 

 :: cot. \ 1 3 : cot. | I z 



