Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/339

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it is manifeſt that by its own force it will never change its axis, or the inclination of it. Let now this globe be impelled obliquely by a new impulſe in the ſame part of its ſuperficies as before; and ſince the effect of an impulſe is not at all changed by its coming ſooner or later, it is manifeſt at theſe two impulſes ſucceſſively impreſſed will produce the ſame motion, as if they were impreſſed at the ſame time; that is, the ſame motion as if the globe had been impelled by a ſimple force compounded of them both (by cor. 2. of the laws) that is a ſimple motion about an axis of a given inclination. And the caſe is the ſame if the ſecond impulſe were made upon any other place of the æquator of the firſt motion; and alſo if the firſt impulſe were made upon any place in the equator of the motion which would be generated by the ſecond impulſe alone; and therefore alſo when both impulſes are made in any places whatſoever; for theſe impulſes will generate the ſame circular motion, as if they were impreſſed together and at once in the place of the interſections of the equators of thoſe motions, which would be generated by each of them ſeparately. Therefore a homogeneous and perfect globe will not retain ſeveral diſtinct motions, but will unite all thoſe that are irnpreſſed on it, and reduce them into one; revolving, as far as in it lies, always with a ſimple and uniform motion about one ſingle given axis with an inclination perpetually invariable. And the inclination of the axis, or the velocity of the rotation will not be changed by centripetal force. For if the globe be ſuppoſed to be divided into two hemiſpheres, by any plane whatſoever paſſing