3. AND from hence finding the comets to be evidently within the sphere of the sun’s action, he concludes they must, necessarily move about the sun, as the planets do[208]. The planets move in ellipsis’s; but it is not necessary that every body, which is influenced by the sun, should move in that particular kind of line. However our author proves, that the power of the sun being reciprocally in the duplicate proportion of the distance, every body acted on by the sun must either fall directly down, or move in some conic section; of which lines I have above observed, that there are three species, the ellipsis, parabola, and hyperbola[209]. If a body, which descends toward the sun as low as the orbit of any planet, move with a swifter motion than the planet does, that body will describe an orbit of a more oblong figure, than that of the planet, and have a longer axis at least. The velocity of the body may be so great, that it shall move in a parabola, and having once passed about the sun, shall ascend for ever without returning any more: but the sun will be placed in the focus of this parabola. With a velocity still greater the body will move in an hyperbola. But it is most probable, that the comets move in elliptical orbits, though of a very oblong, or in the phrase of astronomers, of a very eccentric form, such as is represented in fig. 107, where S is the sun, C the comet, and A B D E its orbit, wherein the distance of S and D far exceeds that of S and A. Whence it is, that they sometimes are found at a moderate distance from the sun, and appear within the planetary regions; at other times they ascend to vast distances, far beyond the very orbit of Saturn, and so become invisible. That the comets do move in this manner is proved by our author, from computations built upon the observations, which astronomers had made on many comets. These computations were performed by Sir ~ISAAC NEWTON~ himself upon the comet, which appeared toward the latter end of the year 1680, and at the beginning of the year following[210]; but the learned Dr. HALLEY prosecuted the like computations more at large in this, and also in many other comets[211]. Which computations are made upon propositions highly worthy of our author’s unparallel’d genius, such as could scarce have been discovered by any one not possessed of the utmost force of invention; 4. THOSE computations depend upon this principle, that the eccentricity of the orbits of the comets is so great, that if they are really elliptical, yet they approach so near to parabolas in that part of them, where they come under our view, that they may be taken for such without sensible error[212]: as in the preceding figure the parabola F A G differs in the lower part of it about A very little from the ellipsis D E A B. Upon which ground our great author teaches a method of finding by three observations made upon any comet the parabola, which nearest agrees with its orbit[213].