128 TERMINOLOGY. . 120. 



b) its intersection with MNSS' may include an angle 

 with AX, greater than BAX. 



In the first case, two planes of the solid angle B coincide 

 with two planes of the solid angle A, as for instance BAG 

 with ABC, and BAC' with ABC', and consequently two 

 from C likewise with two from C', being altogether eight 

 planes coinciding in a single one, which is not the case in 

 the second. 



The differences which may occur in the fourth case are 

 the following : 



a) the intersection of every two faces, as ABC and AB'C, 

 with the plane PQ.SS', may coincide with the edge of the 

 hexahedron, or 



b) it includes an angle with AX greater than CAX, 

 Suppose the former to take place ; two faces from the 



solid angle A will coincide with two faces from the solid 

 angle C, viz : ABC with CC'A, and ACB' with CC"A ; 

 which is not the case upon the latter supposition. 



The different situations, which a plane moveable round 

 the point A may assume, are therefore the following : 



1. Perpendicular to both the sections ; 



2. Perpendicular to the section of the edge, touching the 



edge of the hexahedron ; 



3. Perpendicular to the section of the edge, intersecting 



the edge of the hexahedron ; 



4. Perpendicular to the section of the face, in the face of 



the hexahedron ; 

 o. Perpendicular to the section of the face, not in the face 



of the hexahedron ; 

 C. Inclined to both the sections, touching the edge of the 



hexahedron ; 

 7 Inclined to both the sections, intersecting the edge of 



the hexahedron. 



. 120. PRODUCTION OF THE FORMS OF SEVERAL 

 AXES. 



Whatever situation of those mentioned in the 

 preceding paragraph the moveable plane may as- 



