[ u<n 
then increafing or diminifhing the Angle contained 
by this Ray and the Perpendicular in the given 
Ratio ot 2 to the Difference between 3 and m, and 
increafing or diminifhing the Logarithm of the Ray 
in the fame given Ratio . The Trajedories defcribed 
in analogous Cafes by centrifugal Forces, are con- 
flruded in a fimilar manner. Thefe are the Figures 
in which the Perpendicular, from a given Centre on 
the Tangent, is always as fome Power of the Ray 
drawn from the fame Centre to the Point of Con* 
tad, which are afterwards found to arife in the Re- 
folution of the moft fimple Cafes of Problems of 
various kinds. 
When the Area defcribed about the Centre of an 
Ellipfe is given, the Subtenfe of the Angle of Con- 
tad, drawn through one Extremity of the Arc parallel 
to the Semidiameter drawn to the other Extremity, 
is in a given Ratio to this Semidiameter and there- 
fore, when an Ellipfe is defcribed by a Force direded 
towards the Centre, that Force is always as the 
Diflance from the Centre. When the Force is di- 
reded toward the Focus , it is inverfely as the Square 
of the Diflance. And thefe Two Cafes are confi- 
dered particularly, becaufe of their Ufefulnefs in the 
true Theory of Gravity. To illuflrate which, the 
Laws of centripetal Forces that would caufe a Body 
to defcend continually toward the Centre, or afcend 
from it, are diftinguifhed from thofe which caufe 
the Body to approach towards the Centre, and recede 
from it by turns. A Body approaches from the 
higher Apfid toward the Centre, when its Velocity 
is lefs than what is requifite to carry it in a Circle 5 
and if its Velocity increafe, while it defcends, in a 
higher 
