Figure for Newton Principia Prop I.6 cor 1
The centripetal force acting on P as it revolves about center of force S is proportional to the inverse of that is, Force ult varies as
When P and Q come together, areas of and are ultimately equal and
represent equal areas decribed in equal times.
Referring back to the figurte in prop. 6, PX (also equal to QR) is twice the sagitta BG, and the rect. SP,QT
is twice the area of triangle SPQ . And since the area described is proportional to the time,
you can substitute the area value for t². So the of prop. 6 becomes .
Newton prefers , so finally the force on P ultimately varies as .