Isaac Newton

“ In a parabola, the velocity of a body at any distance from the focus, is to the velocity of a body revolving in a circle at the same distance from the centre, in the subduplicate ratio of the number 2 to 1; in the ellipsis it is less, and in the hyperbola greater, than according to this ratio. ”

“ From the three last propositions it follows, that if any body P goes from the place P with any velocity in the direction of any right line PR, and at the same time is urged by the action of a centripetal force, that is reciprocally proportional to the square of the distance of the places from the centre; the body will move in one of the conic sections, having its focus in the centre of force; and the contrary. For the focus, the point of contact, and the position of the tangent being given, a conic section may be described, which at that point shall have a given curvature. ”

“ For by compounding the proper motion of the body with that motion, which the impulse alone would rate, you'll have the motion with which the body will go off from a given place of impulse, in the direction of a right line given in position. ”