When the Earth Was Flat

<p>Spherical versus Flat </p><p>Foreword </p><p>Acknowledgements</p><p>References</p><p>Introduction&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </p><p>Chapter 1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Preliminaries on Sources and Methodology</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Sources</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Methodology</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Part One&nbsp;&nbsp;&nbsp;&nbsp; Ancient Greece </p><p>Chapter 2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Peculiarities of Presocratic Flat Earth Cosmology </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The shape of the earth </p><p>Arguments concerning the shape of the earth</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Geographical issues</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The tilt of the celestial axis</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The alleged tilt of the earth</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Climatological issues</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Falling on a flat earth</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Distance of the heavens</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Temporal issues</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 3 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaximander’s Images</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Introduction</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The cosmic tree</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The tilted tree</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The reversal in the relationship between air and fire</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Tamed fire</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Turning wheels</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Two images for escaping fire</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Tilted wheels</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaximander’s Phenomenological Astronomy</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Closing fire spots</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Phases of the moon </p><p>Lunar eclipses</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Solar eclipses</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaximander’s Numbers</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Introduction</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; An ordered universe</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaximander’s numbers of the heavenly bodies</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Tannery and the standard interpretation</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The problem of the sun’s distance </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Attempts to explain the origin of Anaximander’s cosmological numbers</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; An interpretation dating from before Tannery</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The sun’s angular diameter</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Skeptical conclusions and a possible way out</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A new interpretation: the numbers as a calculator for the lunar cycle</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Conclusions</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaximenes’ Cosmology</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The cap simile; Graham and the top hat</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The tilted earth interpretation of the cap simile</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Bicknell’s interpretation of the cap simile</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; McKirahan’s interpretation of the cap simile</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Fehling and the flat heaven</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A fresh look at the doxography</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anonymous texts and Kirk’s interpretation</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Towards an interpretation of Anaximenes’ cosmology</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Concluding remarks </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p>Chapter 7 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Xenophanes’ Cosmology<p></p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A cosmological quotation from Xenophanes’ poem</p><p>Xenophanes’ text in the interpretation of Aristotle, Achilles Tatius, Empedocles, pseudo-Aristotle, and Simplicius</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Xenophanes’ text in the interpretation of Aëtius, Strabo, and Cicero</p><p>Xenophanes’ text in the interpretation of Diogenes of Oinoanda, Hippolytus, and pseudo-Plutarch</p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Xenophanes’ text in the interpretation of some recent authors <p></p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Xenophanes’ text in the interpretation of Mourelatos</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The nature and movements of the celestial bodies</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The interpretation of an enigmatic text: Drozdek and Mourelatos</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Mourelatos’ interpretation illustrated by Graham</p><p>A cosmic railway system and a cosmic ballet</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The different paths of the heavenly bodies according to Mourelatos and Graham</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Some more textual and conceptual problems</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The earth not infinitely extended, neither in surface nor in depth</p><p>The two meanings of ἄπειρος</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A spherical cosmos and a hemispherical heaven</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The “many suns”</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The curved paths of the celestial bodies </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; All disappearances of heavenly bodies are quenchings</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Final remarks</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p>Chapter 8&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaxagoras on The Milky Way and Lunar Eclipses<p></p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Introduction</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Milky Way </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaxagoras on the Milky Way</p><p>Introductory remarks on eclipses</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaxagoras’ alleged explanation of lunar eclipses </p><p>The incompatibility of Anaxagoras’ theory of the Milky Way with his alleged explanation of lunar eclipses </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Invisible heavenly bodies below the moon</p><p>Attempts to understand the invisible bodies as an additional cause of lunar eclipses</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Invisible bodies as Anaxagoras’ only theory of lunar eclipses</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The possible origin of a misunderstanding</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Concluding remarks</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Addendum to Chapter 8: “Crepuscular” Lunar Eclipses During Anaxagoras’ Lifetime</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaxagoras on The Light and Phases of the Moon</p><p>Introduction</p><p>Could Anaxagoras have given the correct explanation of the moon’s phases?</p><p>Anaxagoras on the light of the moon in Aëtius 2.25 and analogous texts</p><p>Anaxagoras on the light of the moon in Aëtius 2.28 and analogous texts</p><p>Anaxagoras on the light of the moon in Aëtius 2.29 and analogous texts</p><p>Anaxagoras on the light of the moon in Aëtius 2.30 and analogous texts</p><p>Problems and past suggestions to solve them</p><p>The ambiguity of “received light”</p><p>The moon’s light and phases according to Anaxagoras’ suggestions for a new interpretation</p><p>Conclusion</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 10&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Anaxagoras and the Measurement of the Sun and Moon</p><p>The doxographical evidence </p><p>Did Anaxagoras measure the size of the sun and moon with the help of a solar eclipse?</p><p>Solar eclipses; umbra, penumbra, and antumbra </p><p>Graham and Hintz on the eclipse of February 17, 478 BC</p><p>Further critical remarks on Graham and Hintz’ attempt</p><p>Fehling’s attempt</p><p>An extrapolation of Thales’ method to measure the height of a pyramid</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 11&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Aristotle’s Arguments for the Sphericity of the Earth</p><p>Introduction </p><p>The first empirical argument</p><p>The second empirical argument</p><p>The third empirical argument</p><p>Empirical arguments that Aristotle did not use</p><p>Aristotle on empirical arguments for a flat earth </p><p>Theoretical arguments for a spherical earth</p><p>Final remarks</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Part Two&nbsp;&nbsp;&nbsp; Ancient China</p><p>Chapter 12&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; An Ancient Chinese Flat Earth Cosmology. Main Features</p><p>The gai tian model of a flat earth and a flat heaven</p><p>The movements of the heavenly bodies and the location of Zhou</p><p>The shadow rule and the fundamental cosmic measurements</p><p>Some more calculations</p><p>The incorrectness of the shadow rule</p><p>The horizon and the rising and setting sun as optical illusions</p><p>Questionable interpretations of the heavens as an optical illusion</p><p>The heaven as an optical illusion and the range of visibility</p><p>The interrelation of the range of visibility and the area of sunlight</p><p>Another interpretation of the three-dimensional shape of sunlight</p><p>The size of the area of sunlight (first approach); the circle of the equinox</p><p>The size of the area of sunlight (second approach); the xuan ji</p><p>How we see the sun; the shadow rule once again </p><p>The limited applicability of the shadow rule</p><p>The cardinal directions</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 13&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; An Ancient Chinese Flat Earth Cosmology. Details and Calculations</p><p>The location of Zhou</p><p>Measuring the sun’s diameter</p><p>The extension of the solar illumination</p><p>Geographical measurements</p><p>Sunrise and sunset seen from Zhou</p><p>The seven heng and the limit of the cosmos</p><p>An extrapolation: the southern pole</p><p>The heaven shaped like a truncated conical rain hat?</p><p>A short evaluation of the gai tian system in the Zhou bi</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 14&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ancient Chinese Versus Greek Flat Earth Cosmology</p><p>&nbsp;Two kinds of flat earth cosmology compared</p><p>Greek influence on the gai tian flat earth cosmology?</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>Chapter 15&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Two Appendices: Cosmas Indicopleustes and Samuel Birley Rowbotham </p><p>Cosmas Indicopleustes and the shadow rule</p><p>Rowbotham: the world not a globe</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; References</p><p>List of Abbreviations</p><p>List of Illustrations</p><p>Quotations from Ancient Greek and Roman Authors</p><p>Quotations from the Zhou bi and Ancient Chinese Authors</p><p> Bibliography<br></p>