180 TERMINOLOGY. . 148. 



fundamental form, and consequently n' to be = 0, and 

 R 4- n' = R. The position of R is considered as the nor- 

 mal position. 



The rhombohedron R 4- n is in a transverse position to- 

 wards R ; and since the edges of combination between R, 

 (P 4- n iv ) m and R + n are parallel to the terminal edges of 

 R and to the inclined diagonals of R 4- n, those between 

 R and R 4- n will assume the same situation, if the faces 

 of (P 4- n iv ) m disappear. Hence the two forms are in 

 the relation of R 4- n : R + n 1 (. 145. i. 1.) ; or, for 

 n = 0, in that of R : R 1. Consequently n is = 1 

 and R 4- n = R 1. 



Suppose the faces of R and those of R + n iv to be en- 

 larged till they intersect each other.* R 4- n iv is in the 

 same position towards R as R 1 ; the two forms will 

 produce edges of combination parallel to the inclined dia- 

 gonals of R, and consequently to the terminal edges of 

 R 4- n iv . The forms R + n iv and R are again in the 

 ratio of R 4- n and R 4- n 1 (. 145. i. 1.). And since 

 for R, the expression n 1 is = 0, n iv for R 4- n lv will 

 be = 1, and R 4- n iv = R 4- 1. 



The three rhombohedrons R 1, R and R 4- 1 are 

 consecutive members of one and the same series. 



The edges of combination between (P 4- n v ) n/ and R are 

 parallel to the terminal or to the lateral edges of R, and to 

 the lateral edges of (P 4- n v ) ra ' ; the scalene six-sided pyramid 

 belongs to the rhombohedron (. 145. ii. 1.). In (P 4- n v ) m ' 

 therefore n v is = 0, and the pyramid itself == (P) m '. 



The rhombohedron R 4- 1 is in a transverse position to- 

 wards this pyramid, which is itself parallel to R, and the 

 faces of R 4- 1 take away the more acute terminal edges of 

 (P) m ' with parallel edges of combination. The relation of 

 the forms is therefore as in . 145. ii. 4. ; and we have 



3 m/ - l a 2 a 

 a = ,. 2. a, 



* The faces of R may easily be enlarged by cleavage, 

 (. 162.). 



