12C TERMINOLOGY. . 119. 



one case ; the others allow of a farther distinction in 



two cases. 



Let ACBCOrC'B'X, Fig. 3G., represent a hexahedron, 

 which is brought into an upright position by supposing one 

 of its rhombohedral axes AX vertical. AC, AC', &c. are 

 therefore the terminal edges, AB, &c. the inclined diagonals 

 of this hexahedron, if considered as a rhorabohedron of 90. 



Direct now the planes MNOO', PQRH' and TUVV 

 through the axis AX, so as to make them pass through 

 the inclined diagonals AB, AB', and through the terminal 

 edges AC", AC' which are opposite to these edges. The 

 planes will intersect each other at angles of 60 and 120. 



The part MNSS' of the plane MNOO' turned towards 

 the observer, may be termed the Section of the Face, the 

 part PQSS of the plane PQRR', similarly situated, the 

 Section of the Edge, in so far as they refer to the upper apex 

 A ; because the former passes through the inclined diagonal 

 AB, and bisects the face, while the latter passes through 

 the terminal edge AC of the hexahedron, and bisects the 

 angle at which the faces meet. 



The sections of the face divide every face of the hexa- 

 hedron into two equal and similar triangles, as ABC, 

 ABC', &c. and thus the solid angle A may be conceived to 

 consist of six faces, which, for the sake of derivation, are 

 considered moveable, and their situation is ascertained in 

 respect to both the sections, to that of the face, and that 

 of the edge. Whatever results are found for one of these 

 faces, likewise applies to the other, because the hexahe- 

 dron is a solid of several axes, and it will therefore be suf- 

 ficient to consider the situation of one of these six faces, 

 because the rest must assume an analogous position. This 

 refers evidently not only to those contiguous to A, but 

 also to those belonging to the other solid angles B, C, &c. 

 of the hexahedron. 



The moveable plane may assume the following situations : 



1. Perpendicular to loth sections. 



Upon this supposition, ABC will be perpendicular to 



