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TABLE OF CONTENTS

INTRODUCTION

1. THE COMET CONSTRAINED

The education of Euphrosyne

The workings of the solar system: a brief history

Coda: Newton’s proof of K2

Comet C/1680 V1 - the game changer

Halley’s bold predictions

An aside on conic sections – especially ellipses

The cometary orbit described

Extending the solar system

Beyond the 2-dimensional page

Into the public domain

The living Orrery

2. PLANETARY MACHINES

The mechanical universe

The Orrery and Planetarium

Beyond the circle

Desaguliers mercurium

Planetary machines

The cometarium proper

Variations on a theme

The forgotten empty focus

Transition

3. SOLVING KEPLER’S PROBLEM

The problem to be solved

Radau’s graphical method

Wren’s rolling circle

Rambout’s rolling protractor

Carlini’s wheel

A mysterious hybrid

Out with old, in with the new

Coda: a modern cometarium

4. THE RISE AND FALL OF THE COMETARIUM

Changing times

In the public eye

In the eye of the student

Patents

Catalogs, inventories and auctions

What the literature reveals

Ngram Viewer analysis

Lost and found again

The machine is dead; long live the machine

APPENDICES

I. A brief history of comets

II. Mathematical details

BIBLIOGRAPHY AND SUGGESTED FURTHER READING

NOTES AND REFERENCES

INDEX