Wherefore (following the Steps of so Great a Man) I have attempted to bring the same Method to Arithmetical Calculation; and that with desired Succes… - Edmond Halley

By comparing together the Accounts of the Motions of these Comets, 'tis apparent, their Orbits are dispos'd in no manner of Order; nor can they, as the Planets are, be comprehended within a Zodiack, but move indifferently every Way, as well Retrograde as Direct; from whence it is clear, they are not carry'd about or mov'd in Vortices. Moreover, the Distances in their Perihelium's are sometimes greater, sometimes less; which makes me suspect, there may be a far greater Number of them, which moving in Regions more remote from the Sun, become very obscure; and wanting Tails, pass by us unseen.

Hitherto I have consider'd the Orbits of Comets as exactly Parabolick; upon which Supposition it wou'd follow, that Comets being impell'd towards the Sun by a Centripetal Force, descend as from Spaces infinitely distant, and by their Falls acquire such a Velocity, as that they may again run off into the remotest Parts of the Universe, moving upwards with such a perpetual Tendency, as never to return again to the Sun. But since they appear frequently enough, and since none of them can be found to move with an Hyperbolick Motion, or a Motion swifter than what the... Comet might acquire by its Gravity to the Sun, 'tis highly probable they rather move in very Excentrick Orbits, and make their Returns after long Periods of Time: For so their Number will be determinate, and, perhaps, not so very great. Besides, the Space between the Sun and the fix'd Stars is so immense, that there is Room enough for a Comet to revolve, tho' the Period of its Revolution be vastly long.

In the mean time, those that desire to know how to construct Geometrically the Orb of a Comet, by Three accurate Observations given, may find it at the End of the Third Book of Sir Isaac Newton's Principles of Natural Philosophy, entituled De Systemate Mundi, in the Words of its renowned Inventor. Which have since been more fully explained by my very worthy Collegue Dr. Gregory, in his Learned Work of Astronomia Physica & Geometrica.