Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/29

Sect. II ameters applied to that power. Let thoſe diameters be D and E; and if the reſiſtances, where the velocities are ſuppoſed equal, are as Dn and En: the ſpaces in which the globes, moving with any velocities whatſoever, will loſe parts of their motions proportional to the wholes, will be as D3-n and E3-n. And therefore homogeneous globes, in deſcribing ſpaces proportional to D3-n and E3-n, will retain their velocities in the ſame ratio to one another as at the beginning.

Now if the globes are not homogeneous, the ſpace deſcribed by the denſer globe muſt be augmented in the ratio of the denſity. For the motion, with an equal velocity, is greater in the ratio of the denſity, and the time (by this Prop.) is augmented in the ratio of motion directly, and the ſpace deſcribed in the ratio of the time.

And if the globes move in different mediums, the ſpace, in a medium which, cæteris paribas, refills the moſt, muſt be diminiſhed in the ratio of the greater reſiſtance. For the time (by this Prop.) will be diminiſhed in the ratio of the augmented reſiſtance, and the ſpace in the ratio of the time.

The moment of any Genitum is equal to the moments of each of the generating ſides drawn into the indices of the powers of thoſe ſides, and into their coefficients continually.

I call any quantity a Genitum, which is not made by addition or ſubduction of divers parts, but is generated or produced in arithmetic by the multiplication, diviſion, or extraction of the root of any terms whatſoever; in geometry by the invention of contents and ſides, or of the extreams and means of proportionals. Quantities of