### Table of Contents

Cover.

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 "Causal" 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 Analyse 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.

Notes.

References.

Index.

A.

B.

C.

D.

E.

F.

G.

H.

I.

J.

K.

L.

M.

N.

O.

P.

Q.

R.

S.

T.

U.

V.

W.

Y. This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics.

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 "Causal" 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 Analyse 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.

Notes.

References.

Index.

A.

B.

C.

D.

E.

F.

G.

H.

I.

J.

K.

L.

M.

N.

O.

P.

Q.

R.

S.

T.

U.

V.

W.

Y. This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics.

Mancosu, Paolo

- Oxford University Press

1996

9780195359152

0195084632

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