406 Short Method of expreffing 
founding, for example, ?G’G* with GG. *The firft fign 
denotes decrements which take place on the faces #'T 
(fg. 8.), proceeding from the edges G towards thofe which 
correfpond with them behind the parallelopipedon ; and the 
fecond denotes decrements which take place on the face M 
proceeding to meet each other. If the two decrements took 
place fimultaneoufly, their reprefentative fign would be *G*. 
In the preceding figns, each letter, fuch as *G or G*, cans 
not be applied but to one edge fituated as that letter itfelf to 
the right or left; but *G* may be applied indifferently. to 
both edges: for this reafon itis needlefs to repeat that letter. 
24, Let us give a new example, taken from the topaze 
diftique, called commonly the Saxon topaz (fig. 15.).| If we 
fuppofe figure 9 to reprefent the primitive form, which is a 
right prifm, with rhombufes for its bafes, : we hail have ag 
the fign of the variety in queftion *G* M B ay P, which 
is explained in the following manner: 1. The planes fimilar 
tootzgr (fig. 14.) arife from a decrement by three ranges 
on each fide of the edges G (fig. 9); 2d, the planes ¢y Az, 
sy Ap, are parallel to the planes M, and thus the preceding 
decrement has not attained to its limits; 3d, the facets 
bkyiv, nkysb, and ghki, buki, arife from two fuccefiive 
decrements on the edges B, one by two ranges, and the other 
by three; 4th, the felis acghux«m, and thofe which cor- 
refpond to them, on the other fide, arife from two fuccefive 
decrements on the angles E, one by one range, and the other 
by two ranges; 5th, in the laft place, the terminating face 
edflig correfponds to the bafe P of the primitive form, 
28, It may be readily concluded from the fame principles, 
that the dodecaedron with rhombufes. for its planes, origi- 
nating, from the cube ( (fig. 8.), is exprefied by the fingle 
letter B; that the ogtaedron originating from the fame nu- 
cleus, Has for fien A, &e. 
29. The rhomboid, fuppofing it placed under the moft 
natural afpeét, that is to fay, in fuch a manner that the two 
folid angles compofed of three pie with equal angles be 
“Upon, 
