334 MEMOIRS OP THE AMERICAN ACADEMY. 



(Jevons.) 

 (Jevons.) 



General Formula. 



The formulae which we have thus far obtained, exclusive of mere explanations of 

 signs and of formulae relating to the numbers of 



(1.) If x — <^ y and y -<^ z, then x -<^ z . 



(2.) (# + jr) + * = # + (r-k?)- 



(3.) x-ky=y-kx. 



(5.) *(y -fc *) = xy -fc xz . 



(6.) (*y> = *(>*). 



(8.) (*,y),* = s,(y,*)« 



(9.) x,y = y,x. 



(10.) (*#)* = *(**) . 



- 



(11.) a* 4r * = &,& , 



(12.) (a? -|- y)* = & -fc 2, (z—^/>) -fe. ^ 



(Jevons.) 



(Boole.) 



(Boole.) 





m + W.^-t:yx + W£pi] .^^^.M^-'H'-^]^ etc 



2-3 



(Boole.) 



(13.) (x,y)* = &,yz. 

 (14.) *_|_o = *. 



(15.) */ = *. 



(16.) (^+^) + = ir + ( y + ) . 



(17.) x + y = y-\-z. 

 (18.) #+3/ — y = *. 



(19.) x i (y-\-z)=zx,y-\-x,z. 



(20.) (a? + ^ = & _f_ [2],aHy, _[_ etc 



We have also the following, which are involved implicitly in the explanations which 

 have been given. 



(21.) x^x^y. 



This, I suppose, is the principle of identity, for it follows from this that 



(Boole.) 

 (Boole.) 

 (Boole.) 



(Boole.) 



X = X . 



(22.) x-^x^ce 



(23.) *,*=;*. 



(Jevons.) 

 (Boole.) 



