. 119. OF THE CONNEXION OF FORMS. 127 



the intersection of MNSS' and PQSS', which is the line 

 SS', or the rhoinbohedral axis of the hexahedron. All the 

 six planes contiguous to that point, will necessarily coin- 

 cide in that plane. 



2. Perpendicular to tlie section of the edge ; but inclined to 

 the section of tlie face. 



Here every two faces situated like ABC and AB'C, &c. 

 coincide in a single plane, which, though always perpendi- 

 cular upon FQSS', yet may be differently inclined to AX. 



3. Perpendicular to the section of the face, inclined to the section 

 of the edge. 



In this case again, pairs effaces like ABC and ABC' coin- 

 cide in a single plane perpendicular to MNSS 7 , inclined to 

 AX. 



4. Perpendicular to none of the sections. 



No two planes contiguous to the same solid angle of the 

 hexahedron coincide, but every two meeting in the same 

 section, as ABC and AB'C in PQ.SS', or ABC and ABC' 

 in MNSS', are inclined to that section at the same angle. 



In the first of the above mentioned cases, the situation 

 of the moveable plane is perfectly determined. 



In the second case, the plane must either 



a) touch AC, the edge of the hexahedron, or 



b) the line of its intersection with PQ.SS' must include 

 an angle with AX, which is greater then CAX.* 



Supposing the first to take place, two faces of the solid 

 angle C, coincide in one single plane, with two faces of 

 the solid angle A, for instance CC'A with ABC, and 

 CC"A with AB'C. This does not take place upon the 

 latter supposition. 

 In the third case, the moveable plane may either 



a) pass through the diagonal AB, and consequently coin- 

 cide with the face of the hexahedron itself, or 



* Should this angle be less than CAX, it would be neces- 

 sary to refer the whole derivation, from the solid angle A, 

 to the solid angle C, where the case is confined within the 

 one above mentioned. 



