03926nam 22007095 450 991098613310332120251031115107.09783031772597303177259810.1007/978-3-031-77259-7(MiAaPQ)EBC31946527(Au-PeEL)EBL31946527(CKB)37783648900041(DE-He213)978-3-031-77259-7(EXLCZ)993778364890004120250306d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLeibniz on the Foundations of the Differential Calculus /by Richard T. W. Arthur, David Rabouin1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2025.1 online resource (409 pages)Frontiers in the History of Science,2662-25729783031772580 303177258X - Part I Interpretive Essay -- Chapter 1. Introduction -- Chapter 2. On the Metaphysics of the Continuum (1669-1676) -- Chapter 3. Mathematical Fictions -- Chapter 4. De Quadratura Arithmetica (DQA) -- Chapter 5. Infinitesimals and Existence after 1676 -- Chapter 6. Leibniz’s Mature Justifications of the Calculus -- Chapter 7. Conclusion -- Part II A selection of translations of key texts -- Chapter 8: Texts for chapter 2, On the Metaphysics of the Continuum (1669-1676) -- Chapter 9: Texts for chapter 3, Mathematical Fictions -- Chapter 10: Texts for chapter 4, De Quadratura Arithmetica (DQA) -- Chapter 11: Texts for chapter 5, Infinitesimals and Existence after 1676 -- Chapter 12: Texts for chapter 6, Leibniz’s Mature Justifications of the Calculus.This monograph presents an interpretive essay on the foundations of Leibniz’s calculus, accompanied by key texts in English translation. The essay examines Leibniz's evolving views on infinitesimals and infinite numbers, tracing their development from his early metaphysical ideas to his mature justifications of the calculus. Leibniz first proposed treating infinitesimals as fictions in the 1670s, in line with the mathematical practices of his time, where abstract concepts could be used in calculations without implying their existence. By 1676, he rejected their status as quantities, yet continued to refine his arguments on this topic into the 1690s. The essay concludes with an analysis of Leibniz’s defense of his calculus in the early 18th century, showing how his later works naturally extended from earlier insights. This monograph will be a valuable resource for scholars and students of Leibniz and the history of science.Frontiers in the History of Science,2662-2572MathematicsHistoryScienceHistoryMathematicsPhilosophyHistory of Mathematical SciencesHistory of SciencePhilosophy of MathematicsHistòria de la ciènciathubHistòria de la matemàticathubFilosofia de la matemàticathubLlibres electrònicsthubMathematics.History.ScienceHistory.MathematicsPhilosophy.History of Mathematical Sciences.History of Science.Philosophy of Mathematics.Història de la ciènciaHistòria de la matemàticaFilosofia de la matemàtica510.9Arthur Richard T. W838594Rabouin David473334MiAaPQMiAaPQMiAaPQBOOK9910986133103321Leibniz on the Foundations of the Differential Calculus4327416UNINA