Refolutton of attractive Powers . i g r 
Cor . 2. The increment of the attraSion of this folid as given 
Jn this propofition Ipx / X x F : (</(>*+/) = 
U, but in the preceding propofition the force of a circle on 
the point P ~p X f au x F : («), where u — and 
a=z 9 and jy or # the only variable quantity contained in the 
fluxion ; and confequently the fluxion of the attra&ion of the 
folid p xz f ■ x F : ((sf +y*f) = W ; therefore, if for 
the fluent of xF : (( a *+y)*) be fubftituted its fluent 
contained between the values a and the value of y 9 which in 
the given equation correfponds to % ; then the fluents of 
• • 
U and W contained between the two values of z 9 which cor- 
refponds to two values of y~o 9 will be equal to each other. 
• • 
The difference of the fluents of Y and V, &c. contained 
between any other two values of % 9 can eafily be deduced from 
the difference of two fegments of fpheres. 
i. It may not be improper to remark in this place, that 
from different methods of finding the fum of quantities, the 
fluents of fluxions, the integrals of increments, &c. quanti- 
ties may often be deduced equal, which otherwife cannot with- 
out fome difficulty ; of which inflances are contained in the 
Meditationes, and I fhall here fubjoin one or two more to thofe 
already given in this Paper. 
Ex. i . Any curvilinear area ABC, &c. may be fuppofed to 
confift of evanefcent areas EF^ of which the bafe EF is the 
arc of a circle, whofe radius is PE = \/{f +jf) and fine ED = 
y 9 and altitude F f, and confequently the fluxion of the area 
~:F f x arc (A) of a circle whofe radius is PE and fine ED = 
G g a ‘PS 
