4:2 TERMINOLOGY. . 50. 



5. A solid angle, through which a rhonibohedral axis 

 passes, is termed a rhornbohedral solid angle. This applies 

 equally to forms which are not rhombohedrons themselves. 



6. The edges CA, C'A, C"A, BX, B'X, B"X, contigu- 

 ous to the terminal points of the axis, are Terminal Edges ; 

 while CB', B'C", C"B, &c. or those which do not intersect 

 or meet with the axis, are Lateral Edges. 



7- The diagonals of the faces of a rhombohedron, are 

 commonly said to be the diagonals of the rhombohedron 

 itself. Those which are horizontal, like CC", C'C", &c. 

 when the rhombohedron is in its upright position (. 42.), 

 are termed the Horizontal Diagonals ,- those which, on the 

 same supposition, assume a direction inclined to the axis, like 

 AB, AB', &c. are called the Inclined Diagonal* of that form. 



8. The rhombohedron has two principal sections. The 

 first and most useful is a rhomboid, bounded by two parallel 

 terminal edges, and the inclined diagonals contained be- 

 tween them, as ABXC ; the second is a rectangle, as 

 C'C"B'B". The other sections are of the first kind 

 (. 38.), and termed Rhonibohcdral Sections. That through 

 the centre of the form, or the transverse section, is a regu- 

 lar Hexagon. 



9. The horizontal projection of the rhombohedron is a 

 Regular Hexagon, equal to that circumscribed about the 

 transverse section. 



10. Of two rhombohedrons, that with a greater plane 

 angle at the apex, C'AC", is termed the more obtuse ; that 

 with a lesser, the more acute of these forms. The same dis- 

 tinction applies also to pyramids. 



11. The sections CC'C" and BB'B", through contiguous 

 horizontal diagonals, are perpendicular to the axis, and di- 

 vide it in three equal parts, AP, PQ, and Q,X. 



12. If, as it is supposed in all calculations concerning 

 the rhombohedron, the side of the horizontal projection is 

 = 1 ; the horizontal diagonal is = A/ 3. 



13. Let the axis AX be = a ; the angle of inclination at 

 the terminal edge = x ; we obtain : 



cos.x = 2 -!^f. 

 4 a 2 + 



