in Mathematical Reasoning. 365 
fey Sage 
c d 
and by reduction 
y = C08 +edh _ getdh 
“Ser =are Aue 
Chie 
> 
but if 4 began to move first, add h to the time ane and it 
will become 
Be 7 Be +h _J2 F 
d Cc 
and by reduction 
apg a le cdh 
—— cg —df . 
Case II. If the bodies move in opposite directions, and 
if x is, as before, the distance of the body 4 from the poimt of 
meeting, then e — x will be the distance of B from the same 
point, and 2 the time in which 4 will pass over the distance 
x; and 8" will be the time in which B will perform 
the distance e — x. To the less of these times add the difference 
h, namely, to if B first began to move, and thus we shall have 
5 LS Be “ 
c d 
and by reduction 
_ ege —cdh 
"eg + dfy 
If 4 began to move first, add h to the time Sass, and it will 
become 
eg-st,, Sf 
d c’ 
SAaQ 
