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' 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

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