Figure for Newton Principia Prop I.6 cor 1[br]The centripetal force acting on P as it revolves about center of force S is proportional to the inverse of [math]\frac{SP^2×QT^2}{QR}[/math] that is, Force ult varies as [math]\frac{1}{\frac{SP^2×QT^2}{QR}}[/math][br][br]When P and Q come together, areas of [math]\triangle SPQ[/math] and[math] \triangle SPO[/math] are ultimately equal and [br]represent equal areas decribed in equal times.[br][br]Referring back to the figurte in prop. 6, PX (also equal to QR) is twice the sagitta BG, and the rect. SP,QT [br]is twice the area of triangle SPQ . And since the area described is proportional to the time, [br]you can substitute the area value for t². So the [math]\frac{sagitta}{t²}[/math] of prop. 6 becomes [math]\frac{QR}{(SP×QT)²}, or \frac{QR}{SP²×QT²}[/math].[br][br]Newton prefers [math]\frac{SP²×QT²}{QR}[/math], so finally the force on P ultimately varies as [math]\frac{1}{\frac{SP^2×QT^2}{QR}}[/math].