Isaac Newton

“ Imagine curve lines to be described on any plane, and to revolve about any given axes passing through the centre of force, and by that revolution to describe curve superficies; and that the bodies move in such sort that their centres may be always found in those superficies. If those bodies reciprocate to and fro with an oblique ascent and descent; their motions will be performed in planes passing through the axis, and therefore in the curve lines by whose revolution those curve superficies were generated. ”

“ Any kind of centripetal force being supposed, and the centre of force, and any plane whatsoever in which the body revolves, being given, and the quadratures of curvilinear figures being allowed; it is required to determine the motion of a body going of from a given place, with a given velocity, in the direction of a given right line in that plane. ”

“ And therefore in clocks, if forces were impressed by some machine upon the pendulum which preserves the motion, and so compounded with the force of gravity, that the whole force tending downwards should be always as a line produced by applying the rectangle under the arc TR and the radius AR to the line TN, all the oscillations will become isochronous. ”