# Reasoning with the Infinite

## From the Closed World to the Mathematical Universe

- Contents

Introduction

*1: Infinity Eliminated; or, Huygens's Theory of the Motion of Heavy Bodies*

1: Establishing the General Fact of Gravity

2: Mathematical Speculations about Curvilinear Falls

3: The Deductive Scheme of the Science of Motion of Heavy Bodies

*2: First and Last Ratios in the Newtonian Theory of Central Forces*

1: The Construction of Circular Motion

2: Mechanist Interlude: Centrifugal Force and Weight

3: The Deductive Scheme of Newton's Principia

*3: The Science of Motion in the Workshops of Infinity*

1: Satisfying Reason

2: Ratios of the Beginnings, Ends, and Continuous Evolution of Motions

*4: Motion Algorithmized*

1: Introduction and Import of the Leibnizian Calculus

2: The New Algorithmic Science of Motion

*Epilogue: Fontenelle and the Reasons of Infinity*

1: The Mathematics of Infinity

2: Mathematical Physics and the Rationalization of Infinites

Notes

Bibliography

Index

**History: **
European History

**Physical Sciences: **
History and Philosophy of Physical Sciences

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