## Philosophy of Mathematics and Mathematical Practice in the Seventeenth CenturyThe seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. |

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### Contents

Philosophy of Mathematics and Mathematical Practice in the Early | 8 |

Cavalieris Geometry of Indivisibles and Guldins Centers of Gravity | 34 |

Descartes Geometrie | 65 |

The Problem of Continuity | 92 |

Paradoxes of the Infinite | 118 |

Leibnizs Differential Calculus and Its Opponents | 150 |

Giuseppe Biancanis De Mathematicarum Natura | 178 |

Notes | 213 |

249 | |

267 | |

### Common terms and phrases

algebraic analysis Archimedes Aristotelian Aristotle arithmetic Arnauld Barrow Bernoulli Biancani Bolzano causal Cavalieri center of gravity chapter circle circumference claim Clavius concept conclude cone considered construction curves cylinder debate definition Descartes differential direct proofs discussion epistemological equal equation Euclid Euclid's Elements example finite Fontenelle formal cause foundational Galileo Gassendi geometry given Gottignies Guldin Hobbes hyperbolic solid infinitely long solid infinitely small infinitesimal infinity issue Leibniz Leibnizian calculus magnitudes material cause mathematical practice mathematicians method of indivisibles modus tollens motion nature Nieuwentijt objections Pappus paradox Pereyra perfect demonstration philosophy of mathematics Piccolomini plane figures Posterior Analytics principles problem proceeds Proclus proof by exhaustion proofs by contradiction proposition proved qu'il quadratrix quadrature Quaestio quantities ratio reason reductio reductio ad absurdum right angles Rolle Rolle's segments seventeenth century square straight line superposition tangent theorem theory things Torricelli Torricelli's result triangle truth Varignon Wallis