. 111. OF THE CONNEXION OF FORMS. 113 



axis is a regular hexagon, equal and similar to its 

 horizontal projection. 



Lay planes of intersection through the horizontal dia- 

 gonals of a rhombohedron, whose axis is longer than the 

 side of its horizontal projection. These planes will detach 

 those parts of the rhombohedron which are contiguous to 

 the terminal edges of this form. The remainder, contigu- 

 ous to the lateral edges, is contained under two equilateral 

 triangles in the direction of the axis, and under six isosce- 

 les triangles, being halves of the faces of the rhombohedrons. 

 The equal sides of these triangles are the lateral edges of 

 that form. This solid is the Central Part of the rhombo- 

 hedron. 



In the central part of a more acute rhombohedron, the 

 angles at the bases of the isosceles triangles are greater, but 

 the angles at the vertex are less ; and the horizontal projec- 

 tion always being constant, the sum of the first approaches to 

 two right ones, the latter to nothing, the more the axis 

 of the rhombohedron is elongated. The equal sides in this 

 case approach nearer and nearer to the parallelism with 

 each other and with the axis, and to the equality with 

 one-third of it, which is contained in the central part of the 

 rhombohedron. 



The limits to which these approximations lead, cannot 

 be obtained, while the axis remains a finite quantity. But 

 when the axis becomes infinitely long, these limits are ob- 

 tained ; the triangles are transformed into unlimited paral- 

 lelograms, and contain a regular six-sided prism, which is 

 still unlimited in the direction of its axis. 



As to the transverse section of the prism, we may ima- 

 gine, that in the proportion in which the axis of the rhom- 

 bohedron increases, its faces turn round certain immoveable 

 lines. These lines are the sides of the transverse section of 

 the rhombohedron ; and therefore they are likewise the 

 sides of the transverse section of the prism. 



Let HORZ, Fig. 46., be part of the horizontal projec- 

 tion, and the vertical lines C'D, EB', &c. through the points 



vot.. i. H 



