46 TERMINOLOGY. . 54. 



4. Among the terminal edges, the greater is said to be 

 the obtuse edge, the lesser the acute edge ; which is likewise 

 the case in the scalene six-sided pyramids (. 55.), and in 

 the eight-sided pyramids (. 5G.). 



5. The horizontal projection is equal and similar to the 

 base, or to that principal section, which is perpendicular to 

 the principal axis. 



5. Let the axis AX of a scalene four-sided pyramid be 

 =. a ; BB' one of its diagonals = b ; CC' the other dia- 

 gonal = c ; the terminal edge AB contiguous to b = y ; 

 the terminal edge AC contiguous to c = x ; the edge BC 

 at the base = z : then 



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

 cos. x = a*c 2 -(a 2 +c 2 )b 2 . 

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



b 2 c 2 + (b 2 +C 2 )a 2 

 and 



cos. y + cos. x + cos. z = 1. 

 Hence 



cos. y SB (1 + cos. x + cos. z) ; 

 cos. x = (1 + cos. y + cos. z) ; 

 cos. z = (1 + cos. y + cos. x), 



7 Suppose cos. y = ; cos. x = ft ; cos. z = y : the fol- 

 lowing ratio among the diagonals will be obtained : 

 a:b:c= ^ [ (1 + ) + 0) 1 ' V [ + ) (1 + 7)] 

 : V [ (1 + A) (1 + y) ] 



. 54}. ISOSCELES SIX-SIDED PYRAMIDS. 



The isosceles six-sided pyramids, Fig. 10., are 

 contained under twelve isosceles triangles. 



1. The isosceles six-sided pyramids have two principal 

 sections : one of them AHXZ, &c. is a rhomb, the other 

 HORZNT a regular hexagon. The latter is at the same 

 time the base of the pyramid. 



