424 ANTIENT METAPHYSICS. Book V. 



Further, it is evident tliat the two Motions being fo neceflarily 

 connefted together, they muft be fo adjufted as to balance one ano- 

 ther, fo as that neither fhall prevail over the other : For, If the Cen- 

 tripetal Force is too violent, the Body will be carried too far tovi-ards 

 the Centre ; and, again, if the Projedile Force be too ftrong, the 

 Body will defcribe a Figure different from what we know it docs de- 

 fcribe. 



And not only do the two Motions thus depend upon one another, 

 but they both depend upon one and the fame thing, viz. the diftance 

 of the Planet from the Centre ; for upon that muft depend both the 

 Curvature of the Orbit, and the Velocity by which the Body per- 

 •forms its Revolution in the given time. 



The Motions being thus neceflarily conne£led, and both depend- 

 ing upon one and the fame thing, it is moft natural to fuppofe that 

 the one being given, viz. the Centripetal Motion or Defcent from the 

 Tangent, the other will alfo be given by dedudion from it, I mean 

 the Motion in the Tangential Line, or Line of Projedion ; and it is 

 alfo moft natural to fuppofe, that, as by the diftance from the Centre 

 the Centripetal Motion is governed, fo alfo fhould the Projedile 

 Motion. And, accordingly, Geometry demonftrates that the Velo- 

 city in the Tangential Lines, at different points of the Orbit, is 

 inverfely proportional to perpendiculars drawn from the Sun to the 

 Tangents of the Orbit at thefe points ; and, if the Velocity be fuch 

 in the Tangential Line, it muft of neceftity be the fame in the 

 Orbit of the Planet. 



And thus, I think, the Problem is folved, and a moving Force Is 

 'difcovered, by which the Planet is moved in an Ellipfis of a certain 

 Form and certain Dimenfions, and in a certain Time. And this 

 Moving Force is variable, as the Motion of the Planet is, and va- 



I liable 



