In the Principia bk. III Newton develops a theory of cometary motions in which he approximates a parabolic path to the observed part of the comets' orbital motion. This method was successfully applied to both periodic comets with elliptical orbits, and nonperiodic ones with parabolic orbits, neglecting the planetary perturbations that cause a departure from orbits that would be pure conic section. This final theory was long in maturing, and Newton continued to try to use the rectilinear path as an adjunct to computing until almost the completion of the Principia. This paper aims at analyzing the steps toward Newton's cometary theory and his theory of universal gravitation. First, I'll disscuss on Principia bk. III, lemma IV and "example", and especially I'm interested in why Principia concludes with a lengthy presentation of Newton's method of using observed places of the comet of 1680 to determine the elements of its orbit, using the parabolic approximation. The analysis of the progress of the theory shows the importance of Newton's alchemical studies. By the combined influence of alchmey and the cosmic problem of orbital mechanics, Newton's philosophy of nature underwent a profound conversion from Mechanical Philosophy. Henceforth, the ultimate agent of nature would be for him a force acting between particles rather than a moving particle itself. Sometime after 1679, Newton had become converted to nonlinear orbits of comets that curve around the sun. In De Motu, Newton uses the problem on finding the elliptical trajectory by means of the orbital mechanics. Newton's recognition that comets are 'a kind of planet' introduced an additional transformation of the gravitational force by making it even more general than a mutual interaction between the earth and terrestrial objects, between sun and planets. Including a sun-comet force among gravitational effects enlarged the scopes of action of gravity, to establish the theory of universal gravity.