. 80. 81, OF THE CONNEXION OF FORMS. 67 



. 80. FIRST PROCESS OF DERIVATION. 



The first process of derivation requires tangent 

 planes (. 36.) to be placed on certain edges of the 

 given form, and enlarged till they limit the space 

 either entirely, or at least as far as the number and 

 situation of the faces will allow. 



If the edges to which the tangent planes are applied, be 

 equal or homologous, as, for instance, the terminal edges 

 of the rhonibohedrons, and of the isosceles four-sided pyra- 

 mids, or the acute and obtuse terminal edges of the scalene 

 six or eight-sided pyramids ; this process will yield a simple 

 form at once, which is the derived form itself. 



If, on the contrary, the edges in which the tangent planes 

 are to be laid, be not homologous, as is the case in the 

 acute and the obtuse terminal edges of the scalene four- 

 sided pyramids ; this process will not give a simple form, 

 but a compound one, which is contained under faces 

 not homologous with each other. Compound forms of 

 this kind are not the derived forms themselves (. 79-)* 

 though they either contain them, or at least may be em- 

 ployed for their ulterior derivation. They are considered 

 as Auxiliary or Intermediate Forms. 



All intermediate forms belong to that given form, from 

 which they result by the above mentioned process. 



. 81. SECOND PROCESS. 



The second process requires the axis of a form 

 contained under tetragonal faces, to be produced 

 on both sides, to an undetermined but equal length ; 

 straight lines to be drawn from the lateral angles 

 of the tetragonal faces towards the terminal points 

 of the lengthened axis, and planes to be laid on 

 every contiguous pair of them. The derived form 

 is contained under these planes, 



