But all those that considerd Comets, until the Time of Ticho Brahe (th — Edmond Halley

"[I]n the Year 1472, which being the swiftest of all, and nearest to the Earth, was observd by Regiomantanus. This Comet (fo frightful upon the Account both of the Magnitude of its Body,and the Tail) movd Forty Degrees of a great Circle in the Heavens, in the Space of one Day, and was the first, of which any proper Observations are come down to us."

"But in the Year 1577, (Ticho seriously pursuing the Study of the Stars, and having gotten large Instruments for the Performing Cœlestial Mensurations, with far greater Care and Certainty, than the Ancients coud ever hope for) there appeard a very remarkable Comet; to the Observation of which, Ticho vigorously applied himself; and found by many just and faithful Trials, that it had not a Diurnal Parallax that was at all perceptible: And consequently was not only no Aireal Vapour, but also much higher than the Moon; nay, might be placd amongst the Planets for any thing that appeard to the Contrary; the cavilling Opposition made by some of the School-men in the mean time, being to no Purpose."

"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 coud go) observd by Mrs. Cassini and Flamsteed."

"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 woud 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) solvd a Problem, whose Intricacy renderd it worthy of himself. This Comet he provd to move round the Sun in a Parabolical Orb, and to describe Areas (taken at the Center of the Sun) proportional to the Times."

"After this manner... the Astronomical Reader may examine these Numbers, which I have calculated, with all imaginable Care, from the Observations I have met with. And I have not thought fit to make them publick before they have been duly examind, and made as accurate as twas possible, by the Study of many Years. I have publishd this Specimen of Cometical Astronomy, as a Prodromus of a designed future Work, left, happening to die, these Papers might be lost, which every Man is not capable to retrieve, by reason of the great Difficulty of the Calculation."

"So that tis to the Greeks themselves as the Inventors (and especially to the Great Hipparchus) that we owe this Astronomy, which is now improvd to such a Heigth. But yet, amongst these, the Opinion of Aristotle (who woud have Comets to be nothing else, but Sublunary Vapours, or Airy Meteors) prevailed so far, that this most difficult Part of the Astronomical Science lay altogether neglected; for no Body thought it worth while to take Notice of, or write about, the Wandring uncertain Motions of what they esteemed Vapours floating in the Æther; whence it came to pass, that nothing certain, concerning the Motion of Comets, can be found transmitted from them to us."