C 301 ] 
It appears therefore, that, y being X 
I y'^ y 
1 i 
1 2'2 X 
V«" -t- 2/> • — y'' 'lf% 
IS 
z=z \mn^z ^ z y. 
m 
2I i 
I X 
1 z2 i 
«" + 7« Z 1 * 4- 2/ Z — Z‘ 
which, by Art. 2. is = the fuxion of tJoe tang. dt. 
Confequently, taking the fluents, by Art. i. and 
correcting them properly, we find 
DP — AD + FR.~AF=:L + dt. 
II. —I 
CP, in fig. I. being cp, in fig. 2. =« X— ' ; 
CR, perpendicular to the tangent FR == y '^ ; 
DP — AD = the fluent of • 
Vn^ + 2/z — a' 
F R — A F the fluent of ^ — ; 
V«^ 2 f y — 
and L the Limit to which the difference DP— AD, 
or FR — A F, approaches, upon carrying the point 
D, or F, from the vertex A ad inflttitum. 
5* 
Suppofe y equal to Zy and that the points D and F 
then coincide in E, the points d and p being at the 
fame time in e and q refpeCtively. Then c v being 
perpendicular to the tangent ev, that tangent will 
be a maximum and equal to eg — ac — 'drn^ ~\-7r ^ n ; 
the tangent EQj[in the hyperbola) will be=Vw^T^j 
the 
