Table of Contents

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' Geometrie 3.1: Descartes' Geometrie 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'Hopital's Alalyse des Infiniment Petits 6.2: Early Debates with Cluver 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

Reviews

"Students of the history of mathematics and philosophers of mathematics will find this a valuable addition to the literature."--Choice "Mancosu's book shows philosophical acumen as well as high technical competence--and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."--Isis "Mancosu tells the story well and is good at bringing out significant points"--International Philosophical Quarterly "Mancosu's book shows philosophical acumen as well as high technical competence--and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."--Isis "This is a very carefully researched and documented analysis of the rich relationship between philosophy of mathematics and mathematical practice during the 17th century."--Mathematical Reviews "...this is an important and interesting book....it is useful to have this material together in one volume, and anyone interested in seventeenth-century philosophy or mathematics is sure to find much here that is valuable."--The Philosophical Review "Students of the history of mathematics and philosophers of mathematics will find this a valuable addition to the literature."--Choice "Mancosu's book shows philosophical acumen as well as high technical competence--and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."--Isis "Mancosu tells the story well and is good at bringing out significant points"--International Philosophical Quarterly "Mancosu's book shows philosophical acumen as well as high technical competence--and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."--Isis "This is a very carefully researched and documented analysis of the rich relationship between philosophy of mathematics and mathematical practice during the 17th century."--Mathematical Reviews "Mancosu's scholarly book is very carefully researched, but it is also clearly written and fascinating to read. It is not to be missed by anyone with a serious interest in philosophy of mathematics."--Philosophia Mathematica