All the Elements agree, and nothing seems to contradict this my Opinio — Edmond Halley

"By comparing together the Accounts of the Motions of these Comets, tis apparent, their Orbits are disposd 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 carryd about or movd in Vortices. Moreover, the Distances in their Periheliums 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."

"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."

"[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 all those that considerd Comets, until the Time of Ticho Brahe (that great Restorer of Astronomy) believd them to be below the Moon, and so took but little Notice of them, reckoning them no other than Vapours."

"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."

"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."