Cor. 2. And, ſince the periodic times are in a ratio compounded of the ratio of the radii directly; and the ratio of the velocities inverſely; the centripetal forces are in a ratio compounded of the ratio of the radii directly, and the duplicate ratio of the periodic times inverſely.
Cor. 3. Whence if the periodic times are equal, and the velocities therefore as the radii; the centripetal forces will be alſo as the radii; and the contrary.
Cor. 4. If the periodic times and the velocities are both in the ſubduplicate ratio of the radii; the centripetal forces will be equal among themſelves: and the contrary.
Cor. 5. If the periodic times are as the radii, and therefore the velocities equal; the centripetal forces will be reciprocally as the radii: and the contrary.
Cor. 6. If the periodic times are in the ſeſquiplicate ratio of the radii, and therefore the velocities reciprocally in the ſubduplicate ratio of the radii; the centripetal forces will be in the duplicate ratio of the radii inverſely: and the contrary.
Cor. 7. And univerſally, if the periodic time is as any power of the radius R, and therefore the velocity reciprocally as the power of the radius; the centripetal force will be reciprocally as the power of the radius: and the contrary.
Cor. 8. The ſame things all hold concerning the times, the velocities, and forces by which bodies deſcribe the ſimilar parts of any ſimilar figures, that have their centres in a ſimilar poſition within thoſe figures; as appears by applying the demonſtration of the preceding caſes to thoſe. And the application is eaſy by only ſubſtituting the equable deſcription of areas in the place of equable motion and uſing the diſtances of the bodies from the centres inſtead of the radii.
