of Weiss , Molts , and Haiti/. 259 
may be proved, that the rhomboid, the superior edges of which 
correspond to the lines db, d$, results of a decrement by 00 i 
rows in breadth, on the superior angle of the primitive, and al- 
so that the two rhomboids, the oblique diagonals of which corres- 
pond respectively to db , d$, and da , dc 9 result of decrements 
52 oc • 
bv — — , and rows in breadth on the superior angle of the 
J x + ij z+.y us 
primitive ; and, lastly, that the rhomboid, the inferior edges of 
which correspond to the lines a b, bc 9 cd , results of a decrement 
oc + z — -y 
by 
y 
rows in breadth on the same superior angle. To 
complete the subject of hypothetical primitive forms, let it be 
proposed to find the indices of the dodecaedron (jf b Vj 5*), with 
respect to a rhomboid the sign of which is a n 9 that is resulting 
of a decrement by n rows in breadth on the superior angles of 
111 
the primitive. Let — , — , — , be the required indices. It is 
• t l y i 
obvious that — — will equal £ os £ ( l |) , . anc l as ^he same 
oc 1 — z 1 ■* cos f : 1 ) 
quantity is also equal to ^ the following equation will ob- 
tain 
Si 
*i—y 1 x —y 
Moreover, the preceding formulas being all independent of 
the angle of the primitive, the sign of the rhomboid, the oblique 
diagonals of which are parallel to db 9 dS 9 with respect to the 
rhomboid whose sign is a n 9 will be 
%z 1 
, whilst the sign of 
the same rhomboid, with respect to the primitive form, will be 
£ z 
— 7 —. But I have shewn in the Number of this Journal for 
January 1824, that if n' and n " are the indices of two rhom- 
boids with respect to the primitive, and n! n the index of the se- 
cond with respect to the first considered as the primitive, 
