LAWS OF DECREMENT. 



RHOMBOID. 



Fig. 359. 





This unit is the ratio of e b : b n, fig. 398 and 399, 

 b n being perpendicular on g w, which is parallel to 

 df. Fig. 398 represents an acute rhomboid, 

 in which e b : b f, or b g :: sin. \ A, : R 



bn : bg :: cos. (90 A 5 ) : R :: m\.A & : II 

 therefore e b : b n :: sin \ A, : sin. A 5 . 



Fig. 399 represents an obtuse rhomboid, 

 in which e b : b g :: sin. \A^ : II 



b n : b g :: cos. (A' 5 00) : R 

 and . . . e b : b n :: sin. \A V \ cos. (A 5 90). 



If in fig. 358 we suppose cp a portion of the oblique 

 diagonal produced, and in both 398 and 399, d p 

 parallel to b w, the assumed value of b n will be 

 readily perceived. 



The unit of comparison, in relation to decrements 

 producing the classes e^/J z, and /, is the ratio of the 

 edges and is consequently zn 1. 



In relation to class w, it is that of two equal per- 

 pendiculars / , / c, on a superior edge, drawn from 

 two lateral angles; and in relation to class p, it is 

 that of two equal perpendiculars h a, h A, on an in- 

 ferior edge, drawn from the parallel superior edges, 

 and it is consequently in both cases ~ 1. 



The determination of the laws of decrement affect- 

 ing the rhomboid, and the developement of the 



