  The paragraph that opens Section 11 announces, “Up to this point I have been setting forth the motions of bodies attracted toward an immovable center, such as, however, hardly exists in the natural world…. I now go on to set forth the motion of bodies that attract one another” [P, 561] The section first successfully solves the problem of the motion of two bodies under inverse-square mutual attraction. It then turns to the case of more than two bodies, for which Newton can solve only the case of mutual attraction that varies linearly with the distance between bodies. For the inverse-square case, Newton gives only qualitative results, most of them in 22 corollaries to Proposition 66 that Newton calls “imperfect” in the Preface to the first edition. All of these corollaries identify qualitative tendencies in the motions of a body orbiting a second body and attracted to a third, with the majority of the results directed specifically to the perturbing effects of the Sun on the motion of our Moon. It is with Section 11, then, that the Principia departs from the realm of the “De Motu” tract and begins to consider the complexities of the true motions.