of the reflexion of Bodies in Motion after their Collifion 
and the like. 
Thefe necefTary Pr^cognita being delivered, our Author 
proceeds to confider the Curves generated by the com- 
pofition of a direft impreffed motion with a gravitation 
or tendency towards a Center; and having demonftrated 
that in all cafes the Areas at the Center, defcribed by a. re- 
volving Body, are proportional to the Times ; he (hews 
how from the Curve defcribed, to find the Law or Rule of 
the decreafe or increafe of theTendency or Centripetal for- 
ces (^as he calls it) in differing diftances from the Center. 
Of this there are feveral examples : as if the Curve defcri- 
bed be a Circle palling through the Center of tendency ; 
then the force or tendency towards that Center is in all 
points as the fift power or fquared-cube of the diflance 
therefrom reciprocally. If in the proportional Spiral, re- 
ciprocally as the cube of the diflance. If in an Ellipfe 
^hout : the Center, -rfiereof directry as the diftance. If in 
any of the C^?/^/^)t Se£^ions about the Focus thereof; then 
hedemonftrates tliat thtVisCentrifetafiv tendency towards 
that, ^b^'/i/is in all places reciprocally as the fquareof the 
diftance therefrom; and that according to the Velocity of 
the inipr^lTed Motion, the Curve defcribed is an Hyferr 
hold ; if the Body moved be fwift to a certain degree than 
a Par Ma; if flower 3,a Ellipfe or Circle in one cafe. 
From this fort of tendency or gravitation it follows hke- 
wife that the fquares of the Times of the periodical Revo- 
lutions are as the Cubes of the R^^// or tra^fverfe Axes o? 
the Ellipses. All wliich being found to agree with the Phe- 
mmena of the Celefiial Motions, as difcovered by the 
great. Sagacity and Xyihgenge /of JC^/^^^^^^ our Author ex- 
tends himfelf upon the confequences of this fort of Vis 
ce^trij^eUiiho^wing h^ to find the Cpmk ScQioxi which 
a Bodi^ fbaU defcribe when.caft with any velocity in a 
given Line , fuppafing, the quantity of the faid force 
knowji; and ,Iaj^ingdo\yn feyer^ pe^t conflru£tions,to de- 
' termine 
