Newton knew what he had done. He was no accidental writer. A parabola, of course, is a curve that keeps on going – and that meant that at the end of a very long and very dense book, he lifted off again from the hard ground of daily reality and said, in effect, look: All this math and all these physical ideas govern everything we can see, out to and past the point where we can’t see anymore.
Most important, he did so with implacable rigor, a demonstration that, he argued, should leave no room for dissent. He wrote “The theory that corresponds exactly to so nonuniform a motion through the greatest part of the heavens, and that observes the same laws as the theory of the planets and that agrees exactly with exact astronomical observations cannot fail to be true.” (Italics added).