IN TRUE PERSPECTIVE. 
495 
Problem VII. To draw a regular six-sided Prism. 
If M C be MC^^ . the real transverse section of 
the prism will be a rhomb of 120° and 60° ; and the prism 
itself may be transformed into a regular six-sided one, by 
truncating its more acute lateral edges B^^^, and B B^^ 
(Fig. 15.), and allowing the planes of truncation to pass 
through the centres D^, D^^^, E^^^, E^, &c. of the respective 
lines C B^ B^ C" B"^ C"^ B"S &c. 
That this must give a correct result, appears, if we con- 
sider (Fig. 16.) the projection upon a plane parallel to the 
rhomb BC^ B^C. The angle D^^B^D^ is = 60°, the 
triangle D^^^ B^ is therefore equilateral ; now, in the 
regular hexagonal prism D^^^ must be r= D^^^ D^, and 
therefore likewise D^" B^ = i B^ 
Problem VIII. To draw a regular six-sided Prism, 
whose lateral Planes are Squares. 
From the known equality of B B^ and B^ B"^ in Fig. 
14. inasmuch as these projections have been obtained from a 
hexahedron, it will not be difficult to find the length of 
C required for transforming C C^^ E^ D^, and conse- 
quently all the lateral faces of the six-sided prism into 
squares. 
Suppose B B^ to be = 1 ; B C, in the solid itself, will 
be = Jl, and C therefore J_. The portion B^ B^^ 
that must be taken from that line B^ B"^ in order to trans- 
form C H G into a square, must be to that line in the 
ratio of --L- : 1, or B^B^^ = CG must be = 
2V3 SVS' 
