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

 But the errors that are generated by the proportional forces, imilarly applied to the bodies at imilar parts of the imilar figures, are as the forces and the quares of the times conjunctly.

The ame thing is to be understood of any paces whatoever decrib'd by bodies urged with different forces. All which, in the very beginning of the motion, are as the forces and the quares of the times conjunctly.

And therefore the forces are as the paces decribed in the very beginning of the motion directly, and the quares of the times inverly.

And the quares of the times are as the paces described directly, and the forces inverly.

If in comparing indetermined quantities of different orts with another, any one is aid to be as any other directly or inverly: the meaning is, that the former is augmented or diminihed in the ame ratio with the latter, or with its reciprocal. and if any one is aid to be as any other two or more directly or inverly: the meaning is, that the firt is augmented or diminihed in the ratio's in which the others, or the reciprocals of the others, are augmented or diminhed. As if A is aid to be as B directly and C directly and D inverly: the meaning is, that A is augmented or diminihed in the ame ratio with $$\scriptstyle{B \times C \times \frac{1}{D}}$$, that is to ay, that A and $$\scriptstyle{\frac{BC}{D}}$$ are one to the other in a given ratio.