568 
GEOMETRY. 
[790 
27. It may be remarked, as regards the delineation of such solid figures, that if 
we have in space three lines at right angles to each other, say Oa, Ob, 0c, of equal 
lengths, then it is possible to project these by parallel lines upon a plane in such 
wise that the projections 0a', Ob', 0c' shall be at given inclinations to each other, and 
that these lengths shall be to each other in given ratios: in particular, the two lines 
0a', 0c may be at right angles to each other, and their lengths equal, the direction 
of Ob', and its proportion to the two equal lengths Oa', 0c', being arbitrary. It thus 
appears that we may as in the figure draw Ox, Oz at right angles to each other, and 
Oy in an arbitrary direction; and moreover represent the coordinates x, z on equal 
scales, and the remaining coordinate y on an arbitrary scale (which may be that of 
the other two coordinates x, z, but is in practice usually smaller). The advantage, of 
course, is that a figure in one of the coordinate planes xz is represented in its proper 
form without distortion ; but it may be in some cases preferable to employ the 
isometrical projection, wherein the three axes are represented by lines inclined to each 
other at angles of 120°, and the scales for the coordinates are equal (fig. 17). 
Fig. 17. 
For the delineation of a surface of a tolerably simple form, it is frequently 
sufficient to draw (according to the foregoing projection) the sections by the coordi 
nate planes ; and in particular, when the surface is symmetrical in regard to the 
Fig. 18. 
z 
coordinate planes, it is sufficient to draw the quarter-sections belonging to a single 
octant of the surface; thus fig. 18 is a convenient representation of an octant of the