OF ARTS AND SCIENCES : APRIL 9, 1867. 



269 



Enter at the top the proposition asserting or denying the rule ; 

 enter at the side the proposition asserting or denying the case ; find in 

 the body of the table the proposition asserting or denying the result. 

 In the body of the table, propositions indicated by italics belong to 

 the first figure, those by black-letter to the second figure, and those by 

 script to the third figure. 



I A E O 



I 

 o 



If, as the denial of the result in the second and third figures, we 

 put the form " Any N is N" we have — 



Fig. 2. 



No iHf is N 



Any N \^ N 



.-. No N is M. 



Fig. 3. 



Any N IS N 



Some N is M 

 .-. Some M is N. 



These are the formulje of the two simple conversions. Neither can 

 be expressed syllogistically except in the figures in which they are 

 here put (or in what is called the fourth figure, which we shall con- 

 sider hereafter). If, for the denial of the result in the second figure, 

 we put " No not-iV^ is iV^" (where " not-iV" has not as yet been 

 defined) we obtain 



All M is N, 



No not-iV is N; 



.'. No not-A^ is M. 



In the same way, if we put " Some A^is some-A'"" (where some-A'has 

 not been defined) for the denial of the result in the third figure, we have 



Some N is some-A^ 



All N is M 



.: Some M is some-Ai 



