Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/128

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circle, or in the ellipſis, if the forces are directed to the centre of the figure placed in the abſciſſa, thoſe forces by increaſing or diminiſhing the ordinates in any given ratio, or even by changing the angle of the inclination of the ordinates to the abſciſſa, are always augmented or diminiſhed in the ratio of the diſtances from the centre; provided the periodic times remain equal; ſo alſo in all figures whatſoever, if the ordinates are augmented or diminiſhed in any given ratio, or their inclination is any way changed, the periodic time remaining the ſame); the forces directed to any centre placed in the abſciſſa, are in the ſeveral ordinates augmented or diminiſhed in the ratio of the diſtances from the centre.