and a series of multiple step-couples, namely 
and on Algebra as the Science of Pure Time. 
eee eeneee 
(: E,)=(—a, —ay) +(-a4, —ay) + (Ai, A)s 
(], &)=(—a1, —a,)+(A; 41), 
(A, A:)=(A, 42), 
@,, B )=(a,, ay) Si (A, Ay), 
(8), Bo) = (a, ao) zt (a ’ ay) ar (A; As), 
(©); 
(4, 
(A, 
(2, 
(3', 
ee eeeeeees 
E,)— (A, As)=(—a1, —a2) 
A.) — (A, A2) = (0, 0), 
B,)—(A, A) =(a, aa)» 
B,)y—(A, A)=(a, ao) +(a,, as), 
which may be thus more concisely denoted, 
and 
a 
nig eT we 
(f, Eo) —(Ai, As) = — 2 (a1 
(1, Ey )—(Ay 42)= —1(@, 
«, 
(2, 
(A, 
(2, 
(’ 5] 
E>) =— a (a, a2) + (A, Ay), 
E,)= 
= 
B;) = 
Es) = 
(Ay A, )—(Ay i 
(B, B.)—(A, 4)= +1, 
(3), Bs) — (Ay A,)= 
&e 
—1{(a, 
0, 
+1, 
+2(a, 
O (a1 
+ 2(a, 
ao) +(a, Ao), 
ao) oF (A, Ay)s 
ao) + (A; As), 
ao) + (A, Ad)> 
a,)= —2x (a, 
Ay) = —1x (a1, 
a)= Ox(a, 
ay) = +1x(, 
an) i= +2x(a, 
| 
J 
a a 
e 2)» 
Ue a) 
a 2)> 
a a) 
(12.) 
(14.) 
| 
| 
J 
397 
_ We may also conceive step-couples which shall be swb-multiples and fractions of a 
; given step-couple, and may write 
§ 
(ci, co) — = 
a 
v 
x (b,, by) = Poles bs), 
(16.) 
