Leibniz in Paris 1672-1676: His Growth to Mathematical Maturity
Cambridge University Press, 10/13/2008
EAN 9780521081276, ISBN10: 0521081270
Paperback, 388 pages, 22.9 x 15.2 x 2.5 cm
Language: English
When Gottfried Wilhelm Leibniz first arrived in Paris in 1672 he was a well-educated, sophisticated young diplomat who had yet to show any real sign of his latent mathematical abilities. Over his next four crowded, formative years, which Professor Hofmann analyses in detail, he grew to be one of the outstanding mathematicians of the age and to found the modern differential calculus. In Paris, Leibniz rapidly absorbed the advanced exact science of the day. During a short visit to London in 1673 he made a fruitful contact with Henry Oldenburg, the secretary of the Royal Society, who provided him with a wide miscellany of information regarding current British scientific activities. Returning to Paris, Leibniz achieved his own first creative discoveries, developing a method of integral `transmutation' through which lie derived the 'arithmetical' quadrature of the circle by an infinite series. He also explored the theory of algebraic equations. Later, by codifying existing tangent and quadrature methods and expressing their algorithmic structure in a `universal' notation, lie laid the foundation of formal 'Leibnizian' calculus.
1. Introduction
2. The 'Accessio ad Arithmeticam Infinitorum'
3. The first visit to London
4. Oldenburg's communication of 6 (16) April 1673
5. The great discoveries of the year 1673
6. Readings in contemporary mathematical literature
7. First communication about the new results
8. The quarrel over rectification
9. Disputes about clocks
10. Leibniz receives first details of Gregory's and Newton's work
11. Studies in algebra
12. The meeting with Tschirnhaus
13. The invention of the calculus
14. Dispute about Descartes' method
15. The report on Gregory's results and Pell's methods
16. Newton's first letter for Leibniz
17. Leibniz' reply
18. Tschirnhaus' reaction
19. Newton's second letter for Leibniz
20. The second visit to London
21. Conclusion.