230 REASONING. 



All B is C 

 All B is A 



therefore 

 Some A is C, 



where the minor premiss, All B is A, conformably to 

 what was laid down in the last chapter respecting 

 universal affirmatives, does not admit of simple con- 

 version, but may be converted per accidens, thus, 

 Some A is B; which, though it does not express the 

 whole of what is asserted in the proposition All B is 

 A, expresses, as was formerly shown, part of it, and 

 must therefore be true if the whole is true. We have, 

 then, as the result of the reduction, the following 

 syllogism in the third mode of the first figure : 

 All B is C 

 Some A is B, 

 from which it obviously follows, that 



Some A is C. 



In the same manner, or in a manner on which, 

 after these examples, it is not necessary to enlarge, 

 every mode of the second, third, and fourth figures 

 may be reduced to some one of the four modes of the 

 first. In other words, every conclusion which can be 

 proved in any of the last three figures, may be proved 

 in the first figure from the same premisses, with a 

 slight alteration in the mere manner of expressing 

 them. Every valid ratiocination, therefore, may be 

 stated in the first figure, that is, in one of the follow- 

 ing forms: 



Every B is C No B is C 



All A | All A 



Some A } B > Some A 



therefore therefore 



All A } . No A is . 



Some A f 1S C Some A is not V U 



