IN TRUE PEUSPECTIVE. 
493 
upon the following rule. Project the isosceles four-sided 
pyramid A B C X (Fig. 11.) as above. Bisect its la- 
teral edges, B C in D, C B^ in E, &c. In the continuation 
of M D, M E, &c. take SDznJMD, S^E=:i ME, &c. 
and join all the points S, C, S^, B^, &c. by straight lines 
with the terminal points and of the lengthened axis, 
and the adjacent ones among themselves. 
The latter process, being shorter, is preferable to the 
former one. It depends upon the property of the eight- 
sided pyramids, that S D (Fig. 12.) is always equal to 
!?LTi1 . M D, w beine; the number of derivation of the pv- 
m 4- 1 ^"^ 
ramid. For, let AX be = a, A^X^ z=m.a, A^M will 
be=.^.^^, and A^X = !!!±l-.a. 
Now, A^M : MS r= A^X : XA"S 
and MS = A^MxXA"^ 
A^X 
ButAiM=z|a, XA"i=2MD,and AiX = ~tla; 
therefore M S = . M D, 
m-f-1 
and SD = SM— MD MD . MD. 
3 — 1 
In the present case, m being = 3, SD is = . MD 
. M D. The values of m most generally occurring in 
^ g 
crystals, besides 3, are 4 and 5 ; these make S D = - . MD 
for (P)S and=|.MD for (P)\ 
