An episode in the history of dynamics: Jakob Hermann's proof (1716-1717) of proposition 1, book 1, of Newton's Principia (Q1915876)

Newton's Principia hides a puzzle for historians of science. Any person might think that the ``mathematical principles'' to which Newton refers are those of infinitesimal calculus. However in the Principia calculus is used in only a few isolated cases. Newton's geometric proof of Proposition 1 of Book 1 is based on an intuitive theory of limits. In 1716-1717 the Swiss mathematician, Jakob Hermann, gave a proof of Proposition 1 based on infinitesimals. The present paper discusses both Newton's and Hermann's solutions. A comparison of the two gives us an insight into an episode of the process that led from the geometric style of Newton's Principia to the analytic style of Euler's Mechanica (1736).