, 112. OF THE CONNEXION OF FORMS. 115 



may be derived, the lateral edges of which agree 

 in their situation with the lateral edges of the rhom- 

 bohedron. 



We employ here the second method (. 81.), without any 

 farther preparation. Produce the axis of the rhombohe- 

 dron on both sides, to an indefinite but equal length ; or, 

 what is the same thing, multiply the axis of the rhom- 

 bohedron by the number of derivation m, which must be 

 rational, positive, and greater than 1 ; draw from the angles 

 of the rhombohedron, straight lines towards the terminal 

 points of the axis produced, and lay planes on every ad- 

 jacent pair of these lines. The result will be a scalene six- 

 sided pyramid, whose lateral edges coincide with those of 

 the rhombohedron. 



Every determined prolongation of the axis of the rhom- 

 bohedron, or every determined m, determines a scalene 

 six-sided pyramid. A rhombohedron, and all the scalene 

 six-sided pyramids derived from it, which therefore agree 

 in the situation of their lateral edges, and also the pyramids 

 among each other, are said to be forms belonging together or 

 co-ordinate. 



The position in which the scalene six-sided pyramid is 

 placed by the derivation towards the rhombohedron, is 

 termed the parallel position. The pyramid is in a transverse 

 position towards rhombohedrons, which immediately pre- 

 cede or follow that from which it is derived, because the 

 rhombohedrons themselves are in a transverse position to- 

 wards each other. In general the pyramids partake of the 

 position of the rhombohedron from which they are derived, 

 and pyramids belonging together are in a parallel position. 



In general, two scalene six-sided pyramids, or one pyra- 

 mid and a rhombohedron, are said to be in a parallel position, 

 when a plane through the obtuse terminal edge and the 

 axis of the pyramid, intersects the face of the rhombohe- 

 dron in its inclined diagonal, or in the other pyramid like- 

 wise passes through its obtuse terminal edge, and in both 

 forms at the same time also through the axis. The same 



