39% The Inverfe Method 
the curve V W,.to which V P is a tangent, 
continually defcending towards the circle ahd, 
but will never arrive at it in any finite number 
of revolutions. This circle is therefore an 
afymptote to the trajectory. 
In the fame manner, if s be lefs than unity, 
or the velocity-with which the body is projected 
in a line V J, which makes an acute angle 
with V A, be lefs than the velocity of a body 
in the circle VUZ; then with the centre C 
1 
oe 
n—3  |n—l 
and radius C4= 
x r de- 
u—1 . 5° —2 
fcribe the circle 4B D, and from C upon TV 
produced let fall the perpendicular CP, which 
n—1 
make equal to =o then the body, 
sx CA = 
will continually afcend from the centre, but 
will never arrive at the circle 4BD. This 
circle, therefore, is likewife an afymptote to the 
curve in which the body moves, 
Hence, if a body be projected from any 
point, and: defcend towards the centre, the ve- 
locity with which it is projeéted muft be greater 
than either that which it would acquire in 
falling from an infinite height to that point, 
or than that of a body defcribing the circle at 
the 
