and on Algebra as the Science of Pure Time. 808 
means, and may call a and c the antecedents, and 8 and v the consequents ; we do 
not disturb this analogy or non-analogy by interchanging the means among them. 
selves, or the extremes among themselves ; or by altering equally, in direction and in 
degree, the two consequents, or the two antecedents, of the analogy or of the non- 
analogy, or the two moments of either pair ; or, finally, by altering oppositely in di- 
rection, and equally in degree, the two extremes, or the two means. In an analogy, 
we may also put, by inversion, extremes for means, and means for extremes; but if a 
non-analogy be thus inverted, it must afterwards be changed in kind, from subse- 
quence to precedence, or from precedence to subsequence. 
Combinations of two different analogies, or non-analogies, of pairs of moments, 
with each other. 
4, From the remarks last made, it is manifest that 
if D—C=B—A, 
and p'—p=B'—B, (20.) 
then pD’—c=B’—Aa; 
because the second of these three analogies shews, that in passing from the first to the 
third, we have either made no change, or only altered equally in direction and in 
degree the two consequent moments B and p of the first analogy. In like manner, 
if D—c=B-—aA, 
an Cr— Gl Acts (21.) 
then Dp —c’'=B —A; 
because now, in passing from the first to the third analogy, the second analogy shews 
that we have either made no change, or else have only altered equally, in direction 
and degree, the antecedents a and c. Again, 
ne 3) =) Se 
chival Ipc 1b) ==(oy aor (22°) 
then p’—c’=B —A; 
because here we have only altered equally, if at all, the two moments c and p of one 
common pair, in passing from the first analogy to the third. Again, 
if oD — CB —A, 
and c—c’=B —3, (23.) 
then p—c'=B'—a; 
