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joined with C, hence the Aristotelian conclusion Socrates is 
mortal. We may also get any other possible conclusion. 
For instance the class of things not- Man or b is seen from 
the two last combinations to be always a or not- Socrates, 
but either mortal or not-mortal as the case may be. 
Precisely the same obvious system of analysis is applicable 
to arguments however complicated. As an example take the 
premises treated in Boole’s Laws of Thought, p. 1^5. 
(1.) Similar figures consist of all whose corresponding 
angles are equal, and whose corresponding sides are propor- 
tional. 
(2.) Triangles whose corresponding angles are equal have 
their corresponding sides proportional, and vice versa . 
Let 
A = similar. 
B = triangle. 
C — having corresponding angles equal. 
D = having corresponding sides proportional. 
The premises may then be expressed in Qualitative 
Logic,* as follows : — 
A = CD. 
BC = BD. 
Take the set of 16 slips ; out of the A’s reject those which 
are not CD ; out of the CD’s reject those which are not A ; 
out of the BO’s reject those which are not BD ; and out 
of the BD’s reject those which are not BC. There will 
remain only six slips, as follows : — 
A 
A 
a 
a 1 
a 
a 
B 
b 
B 
b 
b 
b 
C 
C 
c 
C 
c 
c 
D 
D 
d 
d 
1 
D 
d 
From these we may at once read off all the conclusions 
laboriously deduced by Boole in his obscure processes. We 
* See Pure Logic, or the Quality of Logic, apart from Quantity, by 
W. Stanley Jevons, M.A., London (Stanford), 1864. 
