Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/25

Rh continued force retained in thoe curvilinear paths. Since then the Planets move in curvilinear orbits there mut be ome force operating, by whoe repeated actions they are perpetually made to deflect from the tangents.

Now it is collected by mathematical reaoning, and evidently demontrated, that all bodies that move in any curve line decribed in a plane, and which, by a radius drawn to any point, whether quiecent, or any how moved, decribe areas about that point proportional to the times, are urged by forces directed towards that point. This mut therefore be granted. Since then all atronomers agree that the primary Planets decribe about the Sun, and the econdary about the primary, areas proportional to the times; it follows that the forces by which they are perpetually turned aide from the rectilinear tangents, and made to revolve in curvilinear orbits, are directed towards the bodies that are ituate in the centres of the orbits. This force may therefore not improperly be called centripetal in repect of the revolving body, and in repect of the central body attractive; whatever caue it may be imagined to arie from.

But beides, thee things mut be alo granted, as being mathematically demontrated: If everal bodies revolve with an equable motion in concentric circles, and the quares of the periodic times are as the cubes of the ditances from the common centre; the centripetal forces will be reciprocally as the quares of the ditances. Or, if bodies revolve in orbits that are very near to circles, and the apides of the orbits ret; the centripetal forces of the revolving bodies will be reciprocally as the quares of ditances. That both thee caes hold in all the Rh