Dr\ Waring on 
i c8 
A '+ e 
A + e 
2 • 3 • 4 • 5 
: 4 &c.)) 
A 
- xr 
2 
- x r s -f - 
2 2 
t X ( - X j-r + — 
2r V 2 2 . 
3 r 
X C*T 
X 
I 
2 • 3 • 4 r " 2 . 3 . 4 • 5 
2 a — Arqr£ X 
x c x 
X Cf s + 
fubftitute tr, and 
&c.) = « ; in this equation for r±bc 
for r±bc write t, and the equation refulting will be e-. 
b 
%ir 
S^z = X Ce* zir T x w 4=t x "* 
1.2. 3 1>- 1.2.3. 4 " * " I • 2 . 3 • 4 • 5 '' 
__ &c. =3 7T. From it find e in terms proceeding ac- 
cording to the dimenfions of ir, and there refults e — n r=tr 
bs * . 3/>Vdz het 
—s x 7 r db — — — 2~r x 77 — 06C * 
1 . 2/r 2 « 3* ^ 
This method of refolving Kepler’s and other problems of 
cutting a given area defcribed round a point, whether focus or 
not, in a circle, when an approximate fufficiently near to the 
area to be found is given, will converge as fwift as any known 
method. 
The refolution of this problem may be deduced lomewhat 
different by the following methods. Let the letters b , r, a, 
denote the fame quantities as before, and s be the fine of the arc 
L« to radius 1, and r-Mthe fine of the arc LM nearly = L*» i 
r* r 1 Jfyi reduce the fluxion 
”‘ii * 
5 . — - into a feries Pi + Q<?i 4- Rtf i + Stf i 4 - and find 
the fluents of the fluxions QA Ri> Si, &c., which let be B, 
c t) 
C, D, &c., there will refult the equation 0 + -0 1 + T <> 3 + &c. = 
= ,r where t—Br z ^=br and A = arc Lis; find o 
2 a 
zz.br s—r x A 
in terms of a feries proceeding to the dimenfions of it, and 
confequently s + o the fine of the arc LM required. 
From 
