nxn-1dx for both integral and fractional n. Newton wrote a letter to Leibnitz, through Oldenburg, which took some time to reach him. The letter listed many of Newton's results but it did not describe his methods. Leibnitz replied immediately but Newton, not realizing that his letter had taken a long time to reach Leibnitz, thought he had had six weeks to work on his reply. Certainly one of the consequences of Newton's letter was that Leibnitz realized he must quickly publish a fuller account of his own methods. Newton wrote a second letter to Leibnitz on 24 October 1676, which did not reach Leibnitz until June 1677 by which time Leibnitz was in Hanover. This second letter, although polite in tone, was clearly written by Newton believing that Leibnitz had stolen his methods. In his reply Leibnitz gave some details of the principles of his differential calculus including the rule for differentiating a function of a function. Newton was to claim, with justification, that not a single previously unsolved problem was solved by Leibnitz's approach but the formalism was to prove vital in the latter development of the calculus. Leibnitz never thought of the derivative as a limit. This does not appear until the work of d'Alembert. Leibnitz would have liked to remain in Paris in the Academy of Sciences, but it was considered that there were already enough foreigners there and so no invitation came. Reluctantly Leibnitz accepted a position from the Duke of Hanover, Johann Friedrich, of librarian and of Court Councilor at Hanover. He left Paris in October 1676 making the journey to Hanover via London and Holland. The rest of Leibnitz's life, from December 1676 until his death, was spent at Hanover except for the many travels that he made. His duties at Hanover as librarian were onerous, but fairly mundane: general administration, purchase of new books and second-hand libraries, and conventional cataloguing. He, however, undertook a whole collectio...
