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is equal to halj the fluent of the fame fluxlonj^enerated 
whiift z from o becomes rr: m ; which half fluent is 
known by the preceding article. 
It appears, by Ar. 4. that 
I I 
z 
is = — iht flux, of the tang, dt; 
and it appears, by the lafl article, that 
X _I 
m~ y y 
+ 
z 
IS 
V -{■ 2 f y — y"" V -H 3 fz. — 
m 71 — 11 y — 11 z — my z being c=: 0, 
Therefore, by addition, we have 
0 ; 
V X 
+ 
Z X mzY 
m — 
m — y 
•— — the fluxion of the tangent d t. 
Confequently, by taking the corretft fluents, we 
find the tang, dt (=: the tang, fw) =: the arc 
ad — the arc fg ! the abfcifla cp being ■:= n x — y 
m 1 
the abfciflTa zi ~ n x I- , and their relation ex- 
»; 
■ n^'u'' 
^ 1, Z 
m u z) 
preflTed by the equation 
z=Oy u and v being put for cp and cr refpe<fl;ively. 
Moreover, the tangents dt, fw, will each be 
rr^uv 
and Ct xcw = cv^;:^:ac XCg. 
If for the femi-tranfverfe axis eg we fubflitute h 
nflead of 4- the relation of « to *u will be 
VoL. LXI. R r exprefled 
