96 TERMINOLOGY. . 98. 



a 2 (c 2 b 2 ) c 2 (b 2 d 2 ) 



cos.x = 



cos . z= cM^-d'O-a 2 (b*+c 2 ) 



-_ d) 2 )]' 



The angles of the principal sections are found by means 

 of the following formulae : 



a 2 + d 2 + c 2 



cos. CBC' = ~ c2 ; 

 b 2 + c 2 



cos. BAB' = ^1 



In most cases, it will be convenient to have the angles 

 BAP and B'AP separately, as given by the formulae : 

 tang BAP =AJ? ; 



tang B'AP = b . "A 

 a 



For finding the Angle of Inclination, or that at which the 

 axis AA' is inclined to the line AP, perpendicular upon 

 the base, we have 



tang MAP = 



ct 



The terminal edge of the horizontal prism belonging to 

 the diagonal c, is expressed in the formula : 



a 2 c 2 



cos. y == _ ; 



a 2 + c 2 



that lateral edge of P -f 03 which is contiguous to the dia- 

 gonal b, in the formula : 



cos. y = ^-^--^-1 

 a 2 b 2 + c 2 (a 2 + d 2 ) 



In such forms as Fig. 42., where the axis is inclined in a 

 plane which, if it intersects the base at right angles, passes 

 through neither of its diagonals, the formulae become more 

 complicated by the introduction of a new variable quantity 

 e = PR, yet the general processes of derivation are still 

 applicable to the same extent in this apparently irregular 

 figure, as they are to the scalene four-sided pyramid, whose 

 axes are perpendicular to each other. 



