MR. G. UDNY YULE OX THE THEORY OF COXSISTEXCE 
114 
Given. Inferred. 
X = 0 . y = O’A 2 = 0 
a; = 0‘4 . ?/ =0 2 = 0. 
These are “ universal-negative ” conclusions of the ordinary syllogistic type 
All C’s are A, 
No A’s are B, 
No C’s are B. 
All B’s are A, 
No A’s are C, 
. No B’s are C. 
§ 20. Case (4). 
A type of the most general case possible. 
pj = 0‘35 ; 2^0 = 0'4 : 2U = 0'45. 
The equations to the bounding planes are 
X = Q y = 0 2=0 
X = 0‘35 y = 0’35 2 = 0'4 
•'« + y + 2 = 0-20 (a) 
X + y - z - 0-35 (/3) 
X — y z — 0-40 (y) 
- cc + y -f 2 = 0-45 (8). 
The form of the surface is shown in fig. 4« opposite, and in figs. 4h and 4c 
from photographs of a model. All the edges of the tetrahedron are now truncated 
by planes representing the conditions of inferior congruence. No infinite series of 
definite inferences are left, but only four special cases corresponding to the points 
KEGF of the figure ;— 
O 
Given. Inferred. 
(I) a: = 0-35 . 
II 
0 
A 
y = 0'35 
(2) y = 0-35 
2 = 0 
a; = 0 
(3) 2 / = 0 
u 
0 
II 
II 
0 
(4) a; = 0-35 
2 = 0 
y = 0. 
The corresponding syllogisms are— 
(1.) All A’s are B, 
all B’s are C, 
.’. all A’s are C. 
(2.) All A’s are C, 
no C’s are B, 
.'. no A’s are B. 
(3.) All B’s are C, 
no C’s are A, 
.'. no B’s are A. 
(4.) All A’s are B, 
no B’s are C, 
.•. no A’s are C. 
§ 21, In extreme cases the congrueiice-surface presents the appearance of a right 
six-face with its corners truncated rather than a tetrahedron with its edges cut down. 
