led. Leibnitz visited the Royal Society, and demonstrated his incomplete calculating machine. He also talked with Hooke, Boyle and Pell. While explaining his results on series to Pell, he was told that these were to be found in a book by Mouton. The next day he consulted Mouton's book and found that Pell was correct. At a meeting of the Royal Society, which Leibnitz did not attend, Hooke made some unfavorable comments on Leibnitz's calculating machine. Leibnitz returned to Paris on hearing that the Elector of Mainz had died. He realized that his knowledge of mathematics was less than he would have liked so he doubled his efforts on the subject. The Royal Society of London elected Leibnitz a fellow on 19 April 1673. Leibnitz met Ozanam and solved one of his problems. He also met again with Huygens who gave him a reading list including works by Pascal, Fabri, Gregory, Saint Vincent, Descartes and Sluze. He began to study the geometry of infinitesimals and wrote to Oldenburg at the Royal Society in 1674. Oldenburg replied that Newton and Gregory had found general methods. Leibnitz was, however, not in the best of favors with the Royal Society since he had not kept his promise of finishing his mechanical calculating machine. Nor was Oldenburg to know that Leibnitz had changed from the rather ordinary mathematician who visited London, into a creative mathematical genius. In August 1675 Tschirnhaus arrived in Paris and he formed a close friendship with Leibnitz, which proved very mathematically profitable to both. It was during this period in Paris that Leibnitz developed the basic features of his version of Calculus. In 1673 he was still struggling to develop a good notation for his calculus and his first calculations were clumsy. On 21 November 1675 he wrote a manuscript using the f(x) dx notation for the first time. In the same manuscript the product rule for differentiation is given. By autumn 1676 Leibnitz discovered the familiar d(xn) =...
