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 obtaii 



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 membei 

 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 reas'oning. 



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 (T) 



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 in our way of naming and regarding them. 



k ' fure Logic,' p. 19. 



