(Discourse on Metaphysics). Another major project, which Leibnitz undertook, this time for Duke Ernst August, was writing the history of the Guelf family, of which the House of Brunswick was a part. He made a lengthy trip to search archives for material on which to base this history, visiting Bavaria, Austria and Italy between November 1687 and June 1690. As always Leibnitz took the opportunity to meet with scholars of many different subjects on these journeys. In Florence, for example, he discussed mathematics with Viviani who had been Galileo's last pupil. Although Leibnitz published nine large volumes of archival material on the history of the Guelf family, he never wrote the work that was commissioned. In 1684 Leibnitz published details of his differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus... in Acta Eruditorum, a journal established in Leipzig two years earlier. The paper contained the familiar dx notation, the rules for computing the derivatives of powers, products and quotients. However it contained no proofs and Jacob Bernoulli called it an enigma rather than an explanation. In 1686 Leibnitz published, in Acta Eruditorum, a paper dealing with the integral calculus with the first appearance in print of the notation. Newton's Principia appeared the following year. Newton's 'method of fluxions' was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736. This time delay in the publication of Newton's work resulted in a dispute with Leibnitz. Another important piece of mathematical work undertaken by Leibnitz was his work on dynamics. He criticized Descartes' ideas of mechanics and examined what are effectively kinetic energy, potential energy and momentum. This work was begun in 1676 but he returned to it at various times, in particular while he was in Rome in 1689. It is clear that while he was in Rome, in ad...
