When the Earth Was Flat: Studies in Ancient Greek and Chinese Cosmology

Spherical versus Flat

Foreword

Acknowledgements

References

Introduction                                                                                                                    

Chapter 1        Preliminaries on Sources and Methodology

          Sources

          Methodology

          References

Part One     Ancient Greece

Chapter 2        Peculiarities of Presocratic Flat Earth Cosmology

          The shape of the earth

Arguments concerning the shape of the earth

          Geographical issues

          The tilt of the celestial axis

          The alleged tilt of the earth

          Climatological issues

             Falling on a flat earth

          Distance of the heavens

          Temporal issues

          References

Chapter 3        Anaximander's Images

          Introduction

          The cosmic tree

          The tilted tree

          The reversal in the relationship between air and fire

          Tamed fire

          Turning wheels

          Two images for escaping fire

          Tilted wheels

          References

Chapter 4        Anaximander's Phenomenological Astronomy

          Closing fire spots

          Phases of the moon

Lunar eclipses

          Solar eclipses

          References

Chapter 5        Anaximander's Numbers

          Introduction

          An ordered universe

          Anaximander's numbers of the heavenly bodies

          Tannery and the standard interpretation

          The problem of the sun's distance

          Attempts to explain the origin of Anaximander's cosmological numbers

          An interpretation dating from before Tannery

          The sun's angular diameter

          Skeptical conclusions and a possible way out

          A new interpretation: the numbers as a calculator for the lunar cycle

          Conclusions

          References

Chapter 6        Anaximenes' Cosmology

          The cap simile; Graham and the top hat

          The tilted earth interpretation of the cap simile

          Bicknell's interpretation of the cap simile

          McKirahan's interpretation of the cap simile

          Fehling and the flat heaven

          A fresh look at the doxography

          Anonymous texts and Kirk's interpretation

          Towards an interpretation of Anaximenes' cosmology

          Concluding remarks

          References

          A cosmological quotation from Xenophanes' poem

Xenophanes' text in the interpretation of Aristotle, Achilles Tatius, Empedocles, pseudo-Aristotle, and Simplicius

          Xenophanes' text in the interpretation of Aëtius, Strabo, and Cicero

Xenophanes' text in the interpretation of Diogenes of Oinoanda, Hippolytus, and pseudo-Plutarch

          Xenophanes' text in the interpretation of Mourelatos

          The nature and movements of the celestial bodies

          The interpretation of an enigmatic text: Drozdek and Mourelatos

          Mourelatos' interpretation illustrated by Graham

A cosmic railway system and a cosmic ballet

          The different paths of the heavenly bodies according to Mourelatos and Graham

          Some more textual and conceptual problems

          The earth not infinitely extended, neither in surface nor in depth

The two meanings of pi

          A spherical cosmos and a hemispherical heaven

          The "many suns"

          The curved paths of the celestial bodies

          All disappearances of heavenly bodies are quenchings

          Final remarks

          References

          Introduction

          The Milky Way

          Anaxagoras on the Milky Way

Introductory remarks on eclipses

          Anaxagoras' alleged explanation of lunar eclipses

The incompatibility of Anaxagoras' theory of the Milky Way with his alleged explanation of lunar eclipses

          Invisible heavenly bodies below the moon

Attempts to understand the invisible bodies as an additional cause of lunar eclipses

          Invisible bodies as Anaxagoras' only theory of lunar eclipses

          The possible origin of a misunderstanding

          Concluding remarks

          References

Addendum to Chapter 8: "Crepuscular" Lunar Eclipses During Anaxagoras' Lifetime

          References

Chapter 9        Anaxagoras on The Light and Phases of the Moon

Introduction

Could Anaxagoras have given the correct explanation of the moon's phases?

Anaxagoras on the light of the moon in Aëtius 2.25 and analogous texts

Anaxagoras on the light of the moon in Aëtius 2.28 and analogous texts

Anaxagoras on the light of the moon in Aëtius 2.29 and analogous texts

Anaxagoras on the light of the moon in Aëtius 2.30 and analogous texts

Problems and past suggestions to solve them

The ambiguity of "received light"

The moon's light and phases according to Anaxagoras' suggestions for a new interpretation

Conclusion

          References

Chapter 10      Anaxagoras and the Measurement of the Sun and Moon

The doxographical evidence

Did Anaxagoras measure the size of the sun and moon with the help of a solar eclipse?

Solar eclipses; umbra, penumbra, and antumbra

Graham and Hintz on the eclipse of February 17, 478 BC

Further critical remarks on Graham and Hintz' attempt

Fehling's attempt

An extrapolation of Thales' method to measure the height of a pyramid

          References

Chapter 11      Aristotle's Arguments for the Sphericity of the Earth

Introduction

The first empirical argument

The second empirical argument

The third empirical argument

Empirical arguments that Aristotle did not use

Aristotle on empirical arguments for a flat earth

Theoretical arguments for a spherical earth

Final remarks

          References

Part Two    Ancient China

Chapter 12      An Ancient Chinese Flat Earth Cosmology. Main Features

The gai tian model of a flat earth and a flat heaven

The movements of the heavenly bodies and the location of Zhou

The shadow rule and the fundamental cosmic measurements

Some more calculations

The incorrectness of the shadow rule

The horizon and the rising and setting sun as optical illusions

Questionable interpretations of the heavens as an optical illusion

The heaven as an optical illusion and the range of visibility

The interrelation of the range of visibility and the area of sunlight

Another interpretation of the three-dimensional shape of sunlight

The size of the area of sunlight (first approach); the circle of the equinox

The size of the area of sunlight (second approach); the xuan ji

How we see the sun; the shadow rule once again

The limited applicability of the shadow rule

The cardinal directions

          References

Chapter 13      An Ancient Chinese Flat Earth Cosmology. Details and Calculations

The location of Zhou

Measuring the sun's diameter

The extension of the solar illumination

Geographical measurements

Sunrise and sunset seen from Zhou

The seven heng and the limit of the cosmos

An extrapolation: the southern pole

The heaven shaped like a truncated conical rain hat?

A short evaluation of the gai tian system in the Zhou bi

          References

Chapter 14      Ancient Chinese Versus Greek Flat Earth Cosmology

 Two kinds of flat earth cosmology compared

Greek influence on the gai tian flat earth cosmology?

          References

Chapter 15      Two Appendices: Cosmas Indicopleustes and Samuel Birley Rowbotham

Cosmas Indicopleustes and the shadow rule

Rowbotham: the world not a globe

          References

List of Abbreviations

List of Illustrations

Quotations from Ancient Greek and Roman Authors

Quotations from the Zhou bi and Ancient Chinese Authors

Bibliography