70 THE PRINCIPLES OF SCIENCE. 



Law of Simplicity (p. 39) some of the repeated letters may 

 be made to coalesce, and we have 



A = ABC . C. 



Substituting again for ABC its equivalent A, we obtain 



A = AC, 

 the desired result. 



By a similar process of reasoning it may be shown that 

 we can always drop out any term appearing in one member 

 of a proposition, provided that we substitute for it the 

 whole of the other member. This process was described 

 in my first logical Essay h , as Intrinsic Elimination, but it 

 might perhaps be better entitled the Ellipsis of Terms. 

 It enables us to get rid of needless terms by strict sub- 

 stitutive reasoning. 



Inference of a Simple from Two Partial Identities. 



Two terms may be connected together by two partial 

 identities in yet another manner, and a case of inference 

 then arises which is of the highest importance. In the 

 two premises 



A = AB (i) 



B - AB, ( 2 ) 



the second member of each is the same ; so that we can 

 by obvious substitution obtain 



A = B. 



Thus in plain geometry we readily prove that Every 

 equilateral triangle is also an equiangular triangle, and 

 we can with equal ease prove that Every equiangular 

 triangle is an equilateral triangle. Thence by substitu 

 tion, as explained above, we pass to the simple identity- 

 Equilateral triangle = equiangular triangle. 

 We thus prove that one class of triangles is entirely 

 identical with another class ; that is to say, they differ 

 only m our way of naming and regarding them. 

 h l\uc Logic , p. 19. 



