[T]he motion of comets is found to be not at all dissimilar to the motion of the planets, depending on the same principles and undergoing continual r… - David Gregory

" "

[T]he motion of comets is found to be not at all dissimilar to the motion of the planets, depending on the same principles and undergoing continual revolutions. But, since these planets move in ellipses in which the distance of the foci has a great ratio to the transverse axis, and that major axis is immense, their periodic times greatly exceed the periodic times of the common planets, for they are in the sesquialteral ratio [3:2] of the transverse axes [their squares are as the cubes of the axes]. Thus Descartes’s rectilinear cometary trajectory, which he filched from Kepler, collapses, and many things about comets in his fable of the world may be added, which almost two thousand years ago had been shown to be impossible by Lucretius. Such is the free motion in full spaces, to say nothing of the fact that in his system the motion is from time to time against the motion of the vortex. But, in place of so eccentric ellipses whose more remote parts cannot be observed because the comet is not visible there, parabolae may be assumed in calculation, and many things useful for improving astronomy and physics and advancing them further may thus be deduced with the help of the more intricate geometry.