[ 30 + ] 
r= D P — AD — Z, the elliptic arc dg (fig. 2.) 
whofe ablfifla c p is ~ « x — 
^ m I 
Confequently, putting E for I of the periphery 
of that ellipfis, it appears that the whole fluent of 
rn~- z~ ~ 
=, generated whllH; z from o becomes 
V -p 2/z z"’ ' 
:=^m, is equal to JS— AE — « — 
8 . • 
By taking, in Art. 3. q, r, and each =: | j 
and a =1 — d ~ b — i, and c z=r. we find. 
7n 
mri^-^n^z 
z z 
: + 
y~2y 
that, ify be = — r— — 
n +OTZ sf ^ if % — z,‘‘ *dn^-{-2f y — 
will be r= 0. 
It is obvious therefore, that the fluent of 
generated whilfl: 2; from 0 becomes 
m k 
4 - 2/2 — z 
equal to any quantity is equal to the fluent of the 
fame fluxion, generated whilfl: z from ~r — — ^ be- 
comes = m. 
Now, fuppoling k = 
— \jm n . 
mn 
n^k 
rnk 
, its value will be 
m 
m 
Confequently, the fluent of “ 
+ 2/2 2 * 
rated whilfl: z from 0 becomes = - 
IS 
