. 39. 40. OF FORMS IN GENERAL. 35 



the rectangular, as the greater number, determine the kind 

 of the sections. 



The different kinds of sections will be furnished with 

 appropriate and expressive names in the following . 50, 

 62, 53. 



. 39. AXES. 



The straight line passing through the centres of 

 two parallel sections, if it be perpendicular to their 

 planes, is termed an Axis. 



Suppose a hexahedron, Fig. 1., to be intersected by a 

 plane A' B' C' D' parallel to one of its faces ; the section 

 will be a square. The straight line PQ through M and P 

 the centres of this, and of a parallel square, will be an 

 axis. Take from a solid angle of the hexahedron, Fig. 5. 

 equal parts AH, AS, AT upon the edges terminating in 

 this angle, and lay a section through the points thus de- 

 termined. The straight line AG through the centres M , M' 

 of this and of a parallel section R' S" S' T" T' R", even 

 though the figure of the latter should be no triangle, is 

 likewise an axis. Take equal parts AR, AS ; ER', ES' 

 of the parallel edges of a hexahedron, Fig. 6., beginning 

 from two adjacent solid angles A and E, and lay a plane 

 through the points thus determined. Its figure will be a 

 rectangle, or, at a certain distance from the centre of the 

 hexahedron, it will be a square (. 38.) ; and the straight 

 line NO through M and M' the centres of this and of a 

 parallel section, is again an axis. 



Every axis passes through the centre of the solid. 



In the centre of the solid, all axes, which are perpendicu- 

 lar to homologous sections (. 38.), intersect each other at 

 equal angles. 



. 40. HOMOLOGOUS AXES. 



An axis belongs to that section, in the centre of 



