414 ANTIENT METAPHYSICS. Book V. 



cquabk, and in a given time, I think it would be Itfelf the Mcafure 

 of its Moving Force, which would be fuch as would make the Body 

 move in an ellipfis or a circle of certain dimenfions, and in a given 

 time. But, as the Motion of the Planets is unequable, and quicker 

 or flower in different parts of the Orbit, it is evident that their Mo- 

 tions cannot meafure themfelves, but fome other ftandard or rule of 

 their Motion mufl be found out ; and it is likewife evident that this 

 flandard mufl be a Motion in a flraight line, one or more, as it is 

 impofTible to conceive that it can be meafured by another curve line. 

 But how is fuch a ftraight line or lines to be found out ? How can a 

 ftraight line, or any number of them, be conceived to meafure a 

 curvilineal Motion, if it be true, what I have maintained, that no 

 curvilineal Motion is compofed of flraight lines ? 



And here lies the diiKculty of the cafe, which, I think, would be 

 unfurmountable, if we could not difcover any flraight line with 

 which the curvilineal Motion has a necefTary connexion. But this 

 we can do ; for we find that, if a tangent is drawn to any point of 

 the Orbit of a Planet, the Planet, in its progrefTive Motion, falls 

 towards the centre, fo far below the tangent at the extremity of any 

 given arc taken from the tangential point, or point of contadl : And 

 this fall is meafured by a flraight line from the tangent to the ex- 

 tremity of the arc. And we know farther, that this fall is necef- 

 farily connefted with the two things, which, as I have faid, con- 

 flitute the nature and effence of every Motion, viz. the Moving 

 Force or Velocity, and the direction of the Motion, that is, in the 

 cafe of the Planets, the curviture of the Orbit : For, as the Velocity 

 of the Planet is greater or lefs, with a given Curvature of the Orbit, 

 or as the Curvature of the Orbit is greater or lefs with a given Ve- 

 locity of the Planet, fo the defcent from the Tangent, in the fame 

 time, will be greater or lefs. If, therefore, we can difcover what 

 this defcent is,, and by what law it is governed, we may poffibly from 

 thence be able to infer what is the Law of that Force which carries 



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