E 443 1 
A denotes the femi-periphery of the circle, whofe 
radius is i ; 
B an arc of the fame circle, whofe cofine is c, and 
fine b } 
j the fine of the arc ~xAj 
g the fine of the arc — x B. 
Concerning the inveftigation of thefe theorems, it 
is fufficient to fay, they are dire&ly obtained by the 
help of my new method of comparing curvilineal 
areas, inferted in the Philof. Tranfadt. for the year 
1 768. 
It is obvious, that, by means of the above the- 
orems, we may very readily compute the whole areas 
(when finite) of the curves, whofe ordinates are 
^ and ^ &cc. fee* 
p-\-lx n + rx 2n +x‘i n1 p + qx n -\•rx ^n ^\-sxV , ^{•x4 n ' , 
ing thefe expreffions may be ealily transformed into 
others fimilar to thofe already confidered. 
Lll 12 
XXXVII. Extra& 
