in this caſe, than in the other where the body S revolves about the ſyſtem of the bodies P and T.
Cor. 14. But ſince the forces NM, ML, when the body S is exceedingly diſtant, are very nearly as the force SK and the ratio of PT to ST conjunctly; that is, if both the diſtance PT and the abſolute force of the body S be given, as ST reciprocally; and ſince thoſe forces NM, ML are the cauſes of all the errors and effects treated of in the foregoing corollaries; it is manifeſt, that all thoſe effects, if the ſyſtem of bodies T and P continue as before, and only the diſtance ST and the abſolute force of the body S be changed, will be very nearly in a ratio compounded of the direct ratio of the abſolute force of the body S, and the triplicate inverſe ratio of the diſtance ST. Hence if the ſyſtem of bodies T and P revolve about a diſtant body S; thoſe forces NM, ML and their effects will be (by cor. 2. and 6. prop. 4.) reciprocally in a duplicate ratio of the periodical time. And thence alſo if the magnitude of the body S be proportional to its abſolute force, thoſe forces NM, ML, and their effects, will be directly as the cube of the apparent diameter of the diſtant body S viewed from T, and ſo vice verſa. For theſe ratio's are the ſame as the compounded ratio above-mentioned.
Cor. 15. And becauſe if the orbits ESE and PAB, retaining their figure, proportions and inclination to each other, ſhould alter their magnitude; and the forces of the bodies S and T ſhould either remain, or be changed in any given ratio; theſe forces (that is, the force of the body T which obliges the body P to deflect from a rectilinear
