and on Algebra as the Science of Pure Time. 311 
the analogy (10.) namely, 
D—C=B—A, 
may be concisely expressed as follows, 
b=a; (42.) 
while the general non-analogy (15.), 
pD—c=tB—A, 
boEa 5 (43.) 
may be expressed thus, 
and the written expressions of its two cases (16.) and (17.), namely, 
D—C>B—A 
and p—c<B—A, 
may be abridged in the following manner, 
b>a, (44.) 
and b<a. (45.) 
Again, to denote a relation which shall be exactly the inverse or opposite of any 
proposed ordinal relation a or b, we may agree to employ a complex symbol such 
as 9 a or © b, formed by prefixing the mark ©, (namely, the initial letter O of the 
Latin word Oppositio, distinguished by a bar across it, from the same letter used for 
other purposes,) to the mark « or b of the proposed ordinal relation ; that is, we may 
agree to use @ a to denote the ordinal relation of the moment a to B, or Ob to 
denote the ordinal relation of ¢ to p, when the symbol a has been already chosen to 
denote the relation of B to a, or b to denote that of p to c: considering the two 
assertions 
B—A=a, and a—B=0 a, (46.) 
as equivalent each to the other, and in like manner the two assertions 
DC =\b; and c—p=0 b, (47.) 
and similarly in other cases. In this notation, the theorems (5.) (6.) (7.) (8.) 
‘may be thus respectively written : 
6 a=0, if a=0; (48.) 
© xb0, if =O; (49.) 
0 a <0, if a2>0; (50.) 
© a>0, if a<0; (51.) 
