TERMINOLOGY. 



Change in dimensions can obviously have no effect upon the form : 

 a Cube remains a Cube, so long as all its faces are squares, An al- 

 teration in the number, or relative position of the faces is requisite for 

 inducing a change of form. 



. 49. KINDS OF MODIFICATION. 



Primary forms suffer alteration from two kinds of modi- 

 fication ; 1. a replacement (or abstraction) of their edges : 

 2. a replacement of their angles. 



1. When a face, which does not belong to a primary form, occupies 

 the place of an edge or angle of that form, such a form is said to 

 have its edge or angle replaced.* The plane thus substituted, not 

 belonging to the primary form, is denominated a secondary plane. 



2. There are several varieties of modification confined to the 

 edge. 1. An edge may be replaced by a single piano inclining 

 equally upon the adjoining planes, as the lateral edge replaced by 

 the plane d, Fig. 42. whose inclination to M and M' is equal. In 

 this case, the plane d, is often called a tangent plane. 2. The face 

 substituted for an edge may incline upon the adjacent faces at une- 

 qual angles, as in Fig. 43. where the inclination of f on M' is 

 greater than /on M. 3. An edge may be replaced by two planes 



Fig. 42. 



Fig. 43. 



* It scarcely needs to be said, that this idea of replacement is not 

 strictly speaking correct, since the edge or angle referred to never did 

 exist, and of course could not have been replaced. The result, however, 

 is precisely the same as respects the primary, form, as though such a re- 

 placement had actually taken place. 



