C**4 1 
to the Suppofition; and if for PIC be fubftituted : 
b 7 *• Lem. z 5 
and for N M : 
n JL 
i 
2 
-~|4 
-if±I , x ' ) + Z_db_x accord- 
3 1 5 J 
ing to G?r. i. Lm. i. the Area of the Seftor will 
appear in a Series, as is above determined. 
But fince the Number n is greater than 2 , and the given 
Arch PN is lefs than a Semicircle, and confequently 
KL or j y the Sine of the Submultiple Arch PK, is 
lefs than the Semidiameter CP or it may thence 
be eafiiy proved, that the Series will approximate to 
the juft Quantity of the Area, ad libitum. 
Corollary i. Hence, if the Number n be: taken 
equal to 25 the Settor NSP will be 
n. nn 
12 1 1 
I P v 3 
y +**** 
1120 lt y 
+ <&c. 
For the Numerator of the Coefficient of the third 
Term in the Series, that determines the Area H y 
namely, 9 ,_;q^|jy is equal to <>?— 7^ 
which, according to the above Determination of the 
Number n, will become nothing ; wherefore, if for 
t—p be put/’ in thefecond Term, and the Value of n 
be iubftituted for n in the Third and Fourth, the Series 
for the Area will appear upon Reduction to be as is 
here laid down. 
Carol. 
