IN TEUE PERSPECTIVE. 
505 
Problem III. To draw the Pyramidal Combination P. 
S 
(Py. ^-^P+a P + x, of the Species of Pyrami- 
dal Zircon. 
Project the hexahedron ABCD A^B^C^^D^HFig- 1^-) 
according to the rules given above (Sect, I. Probl. I.). 
Take A = i A A" . =r C = D B B^. 
By joining the points A with D, and B with determine 
the situation of M, the centre of the square ACDB ; and, 
finally, draw the lines M B\ M A^ &c. and B^ A^ A^ 
&c. The result M B^ A^ is one part of the isosceles 
four-sided pyramid required, which, if likewise applied on 
the opposite side of the axis M M^, will complete the com- 
bination of P with P+oo . The length A^A"^, &c. is quite 
indifferent, and depends upon the relative size of the same 
lines in those natural combinations which are to be repre- 
sented. 
The next form to be added is (P) '^. 
Take O = J C M, P = | A^ P^ J D^, 
and Q = 1 C or in general O =r ^ C M, P 
= A^ P^ = - and Q =: - . C and 
draw the lines OP, O Q, OP, and P Q, P^ Q ; the faces 
OPQ, OP^Q will be those parts of the faces of (P)^, 
which appear in the combination. This becomes quite 
evident, if we consider the dimensions of that eight-sided 
pyramid, and its relations to P. Since (P)^ belongs imme- 
diately to this four-sided pyramid P, the edges of combina- 
tion between the two forms must be parallel to the opposite 
terminal edges of the latter, O P therefore parallel to M A^; 
and if this edge of combination be supposed to coincide 
