• 1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century 1.1: The Quaestio de Certitudine Mathematicarum 1.2: The Quaestio in the Seventeenth Century 1.3: The Quaestio and Mathematical Practice 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity 2.1: Magnitudes, Ratios, and the Method of Exhaustion 2.2: Cavalieri's Two Methods of Indivisibles 2.3: Guldin's Objections to Cavalieri's Geometry of Indivisibles 2.4: Guldin's Centrobaryca and Cavalieri's Objections 3. Descartes' Géométrie 3.1: Descartes' Géométrie 3.2: The Algebraization of Mathematics 4. The Problem of Continuity 4.1: Motion and Genetic Definitions 4.2: The "Casual" Theories in Arnauld and Bolzano 4.3: Proofs by Contradiction from Kant to the Present 5. Paradoxes of the Infinite 5.1: Indivisibles and Infinitely Small Quantities 5.2: The Infinitely Large 6. Leibniz's Differential Calculus and Its Opponents 6.1: Leibniz's Nova Methodus and L'Hôpital's Alalyse des Infiniment Petits 6.2: Early Debates with Clüver and Nieuwentijt 6.3: The Foundational Debate in the Paris Academy of Sciences Appendix: Giuseppe Biancani's De Mathematicarum Natura, Translated by Gyula Klima Notes References Index

Students of the history of mathematics and philosophers of mathematics will find this a valuable addition to the literature.