( 4 « ) 
ved. In the firft, the Centripetal Force, by which a 
Body defcribes any Curve, is inveftigated after an eafy 
manner ; and a fimple Conftru&ion of all thofe Curves 
that a body would defcribe, if projected with the ve- 
locity it might acquire by falling from an infinite 
Height, in any Hypothecs of Gravity, is demonftrated. 
In the Second, J tis found, that if any body defcribe a 
Curve in a refilling Medium, the Refinance is always 
as the Moment or Fluxion of a Quantity, that expref- 
fes the ratio of the Centripetal Force, to that Force by 
which it would defcribe the Curve in Vacuo , multiplied 
by the Fluxion of the Curve. Tis alfo demonftrated, 
that if a body defcribe any Curve in a refilling Medium , 
which in Vacuo could have been defcribed by a Centri- 
petal Force, proportional to any power of the Diftance, 
the Denfity of that Medium will be reciprocally as 
the Part of the Tangent intercepted between the Point 
of ContadF, and a Line perpendicular to the Radius at . 
the Center of the Forces. This Theorem is applied to 
feveral Curves; and then the ioth Prop, of the Second 
Book of the Principles, and all its Examples, are de- 
monftrated from it. Thefe Propofitions are treated of 
here, not only becaufe they (hew the ufe of Curves 
in Philofophy, but becaufe more fimple Ideas of the De- 
feriptions of (bme Curves may be drawn from them, 
than from any other Method ; and becaufe this is the 
Method, by which Nature herfelf defcribes Curve Lines. 
The whole is concluded by an attempt to draw a 
Line of any given Order, through any given Number 
of Points, that is fufficient to determine the Curve. 
Thus if a Curve of the Order z m is to be defcribed 
through as many Points, as determine a Line of the 
Orders, and three more Points, each of which are 
Nodes, formed by the concourfe of as many Arches* 
of the Curve, as there are Unites in then the 
Curve 
