Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/96

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Cor. 2 But the errors that are generated by the proportional forces, ſimilarly applied to the bodies at ſimilar parts of the ſimilar figures, are as the forces and the ſquares of the times conjunctly.

Cor. 3 The ſame thing is to be understood of any ſpaces whatſoever deſcrib'd by bodies urged with different forces. All which, in the very beginning of the motion, are as the forces and the ſquares of the times conjunctly.

Cor. 4 And therefore the forces are as the ſpaces deſcribed in the very beginning of the motion directly, and the ſquares of the times inverſly.

Cor. 5 And the ſquares of the times are as the ſpaces described directly, and the forces inverſly.

Scholium

If in comparing indetermined quantities of different ſorts with another, any one is ſaid to be as any other directly or inverſly: the meaning is, that the former is augmented or diminiſhed in the ſame ratio with the latter, or with its reciprocal. and if any one is ſaid to be as any other two or more directly or inverſly: the meaning is, that the firſt is augmented or diminiſhed in the ratio's in which the others, or the reciprocals of the others, are augmented or diminſhed. As if A is ſaid to be as B directly and C directly and D inverſly: the meaning is, that A is augmented or diminiſhed in the ſame ratio with , that is to ſay, that A and are one to the other in a given ratio.