At length, came that prodigious Comet of the Year 1680, which descending (as it were) from an infinite Distance Perpendicularly towards the Sun, aros… - Edmond Halley

All the Elements agree, and nothing seems to contradict this my Opinion, besides the Inequality of the Periodick Revolutions: Which Inequality is not so great neither, as that it may not be owing to Physical Causes. For the Motion of Saturn is so disturbed by the rest of the Planets, especially Jupiter, that the Periodick Time of that Planet is uncertain for some whole Days together. How much more therefore will a Comet be subject to such like Errors, which rises almost Four times higher than Saturn, and whose Velocity, tho' encreased but a very little, would be sufficient to change its Orbit, from an Elliptical to a Parabolical one.

Next, Hevelius (a Noble Emulator of Ticho Brahe) following in Kepler's Steps, embraced the same Hypothesis of the Rectilinear Motion of Comets, himself accurately observing many of them. Yet, he complain'd, that his Calculations did not perfectly agree to the Matter of Fact in the Heavens: And was aware, that the Path of a Comet was bent into a Curve Line towards the Sun.

[I]n the Year 1472, which being the swiftest of all, and nearest to the Earth, was observ'd by Regiomantanus. This Comet (fo frightful upon the Account both of the Magnitude of its Body,and the Tail) mov'd 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.