230 OUTLINES OF NATURAL PHILOSOPHY. 



a. Conversely, if a body move in a curve, so that the 

 line drawn from it to a fixed point, describe areas 

 proportional to the times ; the body gravitates to 

 that point, or tends continually to descend to it. 



b. The velocities of a body in different points of the 

 curve which it describes about a centre of force, 

 are inversely as the perpendiculars drawn from the 



centre to the tangents at those points. 



9. By comparing this proposition with the first of 

 KEPLER'S laws, it follows, that the primary planets 

 all gravitate to the Sun, and that the secondary 

 planets gravitate, each to its primary ; and thus 

 the laws of Dynamics are immediately extended 

 to the motions of the heavenly bodies. 



d. If the curve in which the body moves returns into 

 itself, it is called an Orbit, as in the case of the pla- 

 nets ; if it does not, or if it is not known that it 

 does it, is called a Trajectory. 



237. If of two bodies gravitating to the same 

 centre, one descend in a straight line, and the 

 other revolve in a curve ; then, if the velocities 

 of these bodies are equal in any one case, where 

 they are equally distant from the centre, they 

 will always be equal where they are equally 

 distant from it. 



Princip. lib. i. prop. 40. 



*. If, 



