32 TERMINOLOGY. . 36. 37- 



homologous to each other, belong to one and the 

 same simple form. 



The hexahedron, whose angles are replaced by equilateral 

 triangles, or by equiangular hexagons, Figs. 3. 4., is a com- 

 pound form. The faces of a four-sided or eight-sided figure, 

 homologous to each other, are faces of the hexahedron, 

 which is one of the simple forms ; the triangles or hexa- 

 gons, again homologous to each other, are faces of the se- 

 cond simple form, which is the octahedron, and the com- 

 pound form is said to consist of both. 



It is possible, that a compound form may assume the as- 

 pect of a simple one, in so far as it may be contained under 

 faces, which, according to the given definition, are homo- 

 logous. The particular circumstances, under which this 

 happens, and the reasons, why a form of that kind, never- 

 theless is considered as compound, will be given afterwards. 



. 36. TANGENT PLANES. 



A plane, which touches a simple form in one of 

 its edges, is called a Tangent Plane. 



The edge of the simple form lies in the tangent plane ; 

 and the latter is always supposed to be equally inclined to 

 both the faces meeting in the edge of the simple form, un- 

 less it be expressly mentioned otherwise. 



. 37. SECTIONS. 



A plane, which intersects a simple form, is term- 

 ed a Section. A. Principal Section divides the form 

 into two equal halves, without dissecting an edge ; 

 a Transverse Section is perpendicular to a certain 

 line within the solid. 



The knowledge of Sections is very useful, in a more de- 

 tailed examination of the forms themselves ; and the Prin- 



