File:Principia Book 1 Proposition 11.jpg

English: In "Feynman's Lost Lecture", David and Judith Goodstein reconstruct a lecture Richard Feynman gave to his students in 1964. In it he attempted to prove using geometric methods that a body moving under an inverse square law directed to a fixed point will move in an ellipse. He states that he is unable to follow Newton's proof in Proposition 11, Book 1 of the Principia because it used 'completely obscure properties of conic sections' that he did not understand. He is referring to the use of conjugate diameters which had tangent and area properties that suited Newton well for his proof. In Proposition 11 Newton shows that a body moving in an ellipse under a central force, directed to a focus requires a force inversely as the square of the distance from the body to that focus. Feynman proves the converse - an inverse square law implies motion in a conic section, a result that Newton did not prove directly.

Newton's proof is difficult for those unfamiliar with the more obscure properties of conic sections. However, his elegant method can be adapted to use familiar notation, and to dispense with the need for conjugate diameters.

See also: Principia, A New Translation, by I. Bernard Cohen and Anne Whitman – University of California Press, 1999

Feynman's Lost Lecture, by David L. and Judith R. Goodstein – Vintage, 1997