Assertion: newton's body | /r/CapableOf | move under any form of centripetal force
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text: The key step in developing this answer is a generalization of uniform circular motion to the case of motion under a “centripetal” force — a term Newton coined from Huygens's “centrifugal” force, by which he meant the tension in the string keeping the body in a circle; and a key to this step was the discovery that a body moving under any form of centripetal force always sweeps out equal areas in equal times with respect to that center, so that the appropriate geometrical representation of time for generalizing uniform circular motion is area swept out rather than angle or arc length.