The Construction and Use of the general Table.As the Planets move in Elliptick Orbs, so do the Comets in Parabolick ones, having the Sun in their com… - Edmond Halley

Wherefore, if, according to what we have already said, it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.

Not long after, that Great Geometrician, the Illustrious Newton, writing his Mathematical Principles of Natural Philosophy, demonstrated not only that what Kepler had found, did necessarily obtain in the Planetary System; but also, that all the Phænomena of Comets wou'd naturally follow from the same Principles; which he abundantly illustrated by the Example of the aforesaid Comet of the Year 1680, shewing, at the same time, a Method of Delineating the Orbits of Comets Geometrically; wherein he (not without the highest Admiration of all Men) solv'd a Problem, whose Intricacy render'd it worthy of himself. This Comet he prov'd to move round the Sun in a Parabolical Orb, and to describe Area's (taken at the Center of the Sun) proportional to the Times.

At length, came that prodigious Comet of the Year 1680, which descending (as it were) from an infinite Distance Perpendicularly towards the Sun, arose from him again with as great a Velocity.
This Comet, (which was Seen for Four Months continually) by the very remarkable and peculiar Curvity of its Orbit (above all others) gave the fittest Occasion for investigating the Theory of the Motion. And the Royal Observatories at Paris and Greenwich having been for some time founded, and committed to the Care of most excellent Astronomers, the apparent Motion of this Comet was most accurately (perhaps as far as Humane Skill cou'd go) observ'd by Mrs. Cassini and Flamsteed.