36 TERMINOLOGY. . 41. 



which it is perpendicular to its plane. Axes be- 

 longing to homologous sections, are said to be 

 themselves Tiomologous* 



The axes belonging to the equilateral triangles, &c. may 

 for the present be called axes of the first ; those belonging 

 to the squares, &c., of the second ; and those belonging to 

 the rhombs or rectangles, &e., axes of the third kind. 



Some forms contain only one, others two, and others 

 three kinds of axes in different number. The number in 

 which the axes of the first kind appear, is one or four ; that 

 in which those of the second kind are found, one or three ; 

 and that in which those of the third kind are contained in 

 the solids, one, three, four, or sir. 



The hexahedron contains four axes of the first, three of 

 the second, and six of the third kind ; the tetrahedron four 

 of the first, none of the second, three of the third ; the 

 rhombohedron contains only one axis of the first kind. 



. 41. PRINCIPAL AND SUBORDINATE AXES. 



Principal Axes are those whose sections are re- 

 gular, or such figures as allow regular figures to be 

 inscribed into them ; Subordinate Axes such whose 

 sections are no regular figures themselves, and in 

 which no regular figures can be inscribed. If a 

 form contains no principal axis properly so called, 

 one of the subordinate axes is considered as the 

 principal axis. 



The axes of the third kind, in whatever number they may 

 appear, are always subordinate axes, if they occur at the 

 same time with others. But if they occur alone in a form, 

 their number is in no case greater than three ; and then 

 two of them are subordinate ; the third is the principal axis. 



