A General Table for Calculating the Motions of Comets in a Parabolical Orbit. - Edmond Halley

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 common Focus, and describe equal Areas in equal Times. But now because all s are similar to one another, therefore if any determinate Part of the Area of a given Parabola, be divided into any Number of Parts at Liberty, there will be a like Division made in all Parabolas, under the same Angles, and the Distances will be proportional: And consequently this one Table of ours will serve for all Comets.

So that 'tis to the Greeks themselves as the Inventors (and especially to the Great Hipparchus) that we owe this Astronomy, which is now improv'd to such a Heigth. But yet, amongst these, the Opinion of Aristotle (who wou'd 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.

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.