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When the Earth Was Flat pp 221–240Cite as

Anaxagoras and the Measurement of the Sun and Moon

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Part of the book series: Historical & Cultural Astronomy ((HCA))

Abstract

According to the available sources, Anaxagoras compared the size of the sun and moon with that of the Peloponnesus. The relevant texts are the following:

  1. 11.1

    The sun is much bigger than (πολλαπλάσιον) the Peloponnesus.

  2. 11.2

    The sun exceeds (ὑπερέχειν) the Peloponnesus in size.

  3. 11.3

    The sun is bigger (μείζω) than the Peloponnesus.

  4. 11.4

    Anaxagoras says that it (sc. the sun) is larger than (μείζονα) the Peloponnesus.

  5. 11.5

    The moon is as big as (ὅση) the Peloponnesus.

  6. 11.6

    Anaxagoras says that the sun is 18 times the earth.

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Notes

  1. 1.

    P 2.21.3 (not in S) = DK 59A72 = GG 169 = MR 535; not in LM, Gr, and KRS.

  2. 2.

    Hippolytus, Refutatio Omnium Haeresium 1.8.8 = DK 59A42(8) = LM ANAXAG. D4 (8) = Gr. Axg38(8) = GG 270 = KRS 502(8).

  3. 3.

    Diogenes Laërtius, Vitae Philosophorum 2.8 = DK 59A1(8) = GG 340, not in Gr, LM, and KRS.

  4. 4.

    Theodoretus, Curatio affectionum Graecarum 1.97 and 4.22 = GG 445 and 453 = MR 536; not in DK, LM, Gr, and KRS.

  5. 5.

    Plutarch, The Face on the Moon 932a = Gr. Axg41 = GG 189; not in DK and KRS.

  6. 6.

    Isagoge bis excerpta 17 = MR 525 (see also 538).

  7. 7.

    The reason for the difference is that the AD–BC year numbering does not have a year 0; this is best illustrated with a small picture of the timeline around the beginning of our era (Fig. 11.1).

  8. 8.

    See Graham (2013a, 149; 2013b, 4); Graham and Hintz (2007, 324).

  9. 9.

    Cf. West (1971, 233, n. 1); Sider (1973).

  10. 10.

    West (1971, 233, n. 1).

  11. 11.

    Cf. Graham (2013a, 147–148); Graham and Hintz (2007, 322–324).

  12. 12.

    Fehling (1985, 209–210).

  13. 13.

    Cf. Graham (2013a, 150): “(…) he could see that the sun was larger, for the moon failed to block the periphery of the sun.”

  14. 14.

    Sider (1973, 129, n. 10, my italics).

  15. 15.

    Graham and Hintz (2007, 327 and n. 24).

  16. 16.

    Sider (1973, 129, n. 10).

  17. 17.

    Graham and Hintz (2007, 327, n. 21, my italics).

  18. 18.

    Graham and Hintz (2007, 324 and 336, my italics).

  19. 19.

    Graham (2013a, 149 and 144 n. 17, my italics).

  20. 20.

    Graham (2013a, 149 n. 25).

  21. 21.

    Graham (2013a, 152, Fig. 5.2).

  22. 22.

    Graham and Hintz (2007, 330).

  23. 23.

    Graham (2013a, 153).

  24. 24.

    Graham and Hintz (2007, 327, n. 25), and 328 Fig. 4.

  25. 25.

    Perhaps they forgot to use the day light vision button of their computer program.

  26. 26.

    Graham (2013a, 151, 148).

  27. 27.

    Graham and Hintz (2007, 321).

  28. 28.

    That Anaxagoras believed that the earth is flat is reported by several sources: Diogenes Laërtius, Vitae Philosophorum 2.8 = DK 59 A1(8) = Gr Axg32(8) = GG 340, not in LM and KRS; Hippolytus, Refutatio Omnium Haeresium 1.8.3 = DK 59A42(3) = LM ANAXAG. D4 (3) = Gr Axg38(3) = GG 271= KRS 502(3); Plato, Phaedo 97B = DK 59A47 = LM ANAXAG. R5 = GG3, not in Gr and KRS. He even put forward a proof of its flatness, as is shown by Panchenko (1997) and will be discussed below, in Chap. 12, section Aristotle on Empirical Arguments for a Flat Earth.

  29. 29.

    Diogenes Laërtius, Vitae Philosophorum 1.23 = DK 11A1(23) = LM THAL. R6 = Gr Ths12 = TP1 Th237(23).

  30. 30.

    Graham (2013a, 120).

  31. 31.

    Empedocles, quoted by Plutarch, The Face on the Moon 929c–d = DK 31B42 = LM EMP. D132 = Gr Emp87. The same quotation in West (1971, 233, n. 1).

  32. 32.

    Graham and Hintz (2007, 322), cf. West (1971, 233 n. 1).

  33. 33.

    Graham (2013c, 139, my italics).

  34. 34.

    Stephenson (1997, 345–346).

  35. 35.

    Graham and Hintz (2007, 327, n. 24); Thucydides, Peloponnesian War 4.52.

  36. 36.

    Graham (2013a, 149).

  37. 37.

    Britton (1989, 5). See also Steele (2000, 423); Aveni (1993, 47); O’Grady (2002, 139).

  38. 38.

    Graham and Hintz (2007, 327).

  39. 39.

    Graham (2013c, 139); cf. Graham (2013a, 149–150).

  40. 40.

    Graham (2013a, 149 n. 26).

  41. 41.

    Graham (2013a, 150)

  42. 42.

    Graham (2013c, 139–140). See also Graham and Hintz (2007, 339) and Graham (2013a, 153–154), where he adds: “he could have also sent letters to stargazers in other cities seeking information.”

  43. 43.

    Graham (2013c, 151).

  44. 44.

    Graham and Hintz (2007, 327 n. 24) refer to Stephenson (1997, 345–346) and Sider (1973, 129, n. 10). They object that Stephenson “attributes to a non-astronomer, Thucydides, the ability to discern a ‘small’ eclipse of 0.72 in 424 BC” (ibid.). However, in Peloponnesian War 4.52, Thucydides does not imply to have observed this eclipse, but probably refers to observations of astronomers. In the same sentence, he reports that there was an earthquake, which also does not imply that he himself has felt it.

  45. 45.

    Graham (2013b, 5, n. 18).

  46. 46.

    According to Casson (1995, 48 and 234), sails were generally made of linen patches sewn together. Perhaps they proffered a tool for observing solar eclipses with the naked eye, but one might wonder how accurate those observations could have been.

  47. 47.

    Graham (2013a, 155, n. 35).

  48. 48.

    Graham and Hintz (2007, 330–331).

  49. 49.

    Graham (2013a, 155; 2013c, 139).

  50. 50.

    Graham and Hintz (2007, 327).

  51. 51.

    See Herodotus, Historiae 7.37.2, Thucydides, Peloponnesian War 2.28.1 and 4.52.1, mentioned in Graham (2013a, 150, n. 30). To these, we might add (perhaps) April 16, 1178 BC (Homer’s eclipse, Odyssea 20.345), May 28, 565 BC (Thales’ eclipse, cf. Herodotus, Historiae 1.74), April 6, 648 BC (Archilochus’ eclipse, cf. S 4.46.10), and May 19, 557 BC (eclipse of the Siege of Larissa, cf. Xenophon, Hellenica 2.3.4).

  52. 52.

    Graham (2013a, 154).

  53. 53.

    See Graham (2013a, 154–155).

  54. 54.

    Mansfeld (1979).

  55. 55.

    Cf. Graham and Hintz (2007, 330, my italics).

  56. 56.

    Fehling (1985, 209).

  57. 57.

    Fehling (1985, 209).

  58. 58.

    Fehling (1985, 210).

  59. 59.

    Fehling (1985, 210). The (right) value of 0.5 degrees is attributed to Thales by Diogenes Laërtius, Vitae Philosophorum 1.24 = DK 11A1(24) = LM THAL. R14 = Gr Ths1(24) = TP1 Th237(24); not in KRS, but see p. 83. See also Apuleius, Florida 18.32 = DK 11A19 = LM THAL. R13 = TP1 Th178; not in Gr and KRS. The (wrong) value of 2 degrees (1/15 of a sign of the zodiac) is, surprisingly, used by Aristarchus, see Heath (1913, 352–355) (Hypothesis 6 for the moon and Proposition 2 for the sun).

  60. 60.

    This calculation presupposes that it was done from or near the center of the flat earth’s surface. Since on a flat earth the sun is not far away, its angular diameter must be greater if an observer was situated at the edge of the earth. The ancient Greeks believed, however, that their land and especially Delphi, was the middle of the earth.

  61. 61.

    This remark is intended to overcome Graham’s objection (2013a, 147) that with this method it is the sun, not the moon, that is measured.

  62. 62.

    Graham (2013a, 146).

  63. 63.

    Graham and Hintz (2007, 323).

  64. 64.

    Graham and Hintz (2007, 324).

  65. 65.

    • P = Aëtius in pseudo-Plutarch, Placita (numbering according to Dox).

    • S = Aëtius in Stobaeus, Anthologium (numbering according to Wachsmuth and Hense).

References

  • P = Aëtius in pseudo-Plutarch, Placita (numbering according to Dox).

  • S = Aëtius in Stobaeus, Anthologium (numbering according to Wachsmuth and Hense).

  • Aveni, A.F., Ancient Astronomers, Washington DC: Smithsonian Books 1993.

    Google Scholar 

  • Britton, J.P., An Early Function for Eclipse Magnitudes in Babylonian Astronomy. Centaurus 39 (1989) 1–52.

    Article  ADS  MathSciNet  Google Scholar 

  • Casson, L. Ships and Seamanship in the Ancient World. Baltimore and London: The John Hopkins University Press 1995 (repr. of 1971).

    Google Scholar 

  • Diels, H. and W. Kranz, Die Fragmente der Vorsokratiker. Zürich/Hildesheim: Weidmann 19516 (=DK).

    Google Scholar 

  • Fehling, D., Das Problem der Geschichte des griechischen Weltmodells vor Aristoteles. Rheinisches Museum für Philologie 128 (1985), 195–231.

    Google Scholar 

  • Gershenson, D.E. and D.A. Greenberg, Anaxagoras and the Birth of Physics. New York: Blaisdell Publishing Company 1964 (=GG).

    Google Scholar 

  • Graham, D.W., The Texts of Early Greek Philosophy. Cambridge: Cambridge University Press 2010 (=Gr).

    Google Scholar 

  • ―, Science Before Socrates. Oxford: University Press 2013a.

    Google Scholar 

  • ―, Anaxagoras and the Comet. Ancient Philosophy 33 (2013b), 1–18.

    Article  Google Scholar 

  • ―, Anaxagoras: Science and Speculation in the Golden Age. In: J. McCoy (ed.), Early Greek Philosophy. The Presocratics and the Emergence of Reason. Washington DC: The Catholic University of America Press 2013c, 139–156.

    Google Scholar 

  • Graham, D.W. and E. Hintz, Anaxagoras and the Solar Eclipse of 478 BC Apeiron 40 (2007), 319–344.

    Article  Google Scholar 

  • Kirk, G.S., J.E. Raven and M. Schofield, The Presocratic Philosophers. Cambridge: Cambridge University Press 2009 (=KRS).

    Google Scholar 

  • Laks, A. and G.W. Most, Early Greek Philosophy VI, Cambridge MA. 2016.

    Google Scholar 

  • Mansfeld, J, The Chronology of Anaxagoras’ Athenian Period and the Date of his Trial I. Mnemosyne, 4th ser., 32 (1979), 39–69 (reprinted in: J. Mansfeld, Studies in the Historiography of Greek Philosophy. Assen: Van Gorcum 1990. 264–294).

    Google Scholar 

  • Mansfeld, J. and D.T. Runia, Aëtiana. The Method and Intellectual Context of a Doxographer, Volume Two, Part Two. Leiden: Brill 2009 (=MR).

    Google Scholar 

  • O’Grady, P. Thales of Miletus: The Beginnings of Western Science and Philosophy, Aldershot: Ashgate 2002.

    Google Scholar 

  • Panchenko, D., Anaxagoras’ Argument Against the Sphericity of the Earth. Hyperboreus 3 (1997), 175–178.

    Google Scholar 

  • Sider, D., Anaxagoras on the Size of the Sun. Classical Philology 68 (1973), 128–129.

    Article  Google Scholar 

  • Steele, J.M., Eclipse Prediction in Mesopotamia. Archive for History of Exact Science 54 (2000), 421–454.

    Article  ADS  MathSciNet  Google Scholar 

  • Stephenson, F.R., Historical Eclipses and Earth’s Rotation. Cambridge: Cambridge University Press 1997.

    Book  Google Scholar 

  • West, M.L., Early Greek Philosophy and the Orient. Oxford: Clarendon Press 1971.

    Google Scholar 

  • Wöhrle, G., Traditio Praesocratica. Die Milesier: Thales. Berlin: Walter de Gruyter 2009 (=TP1).

    Google Scholar 

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  1. Philosophy, University of West Bohemia, Amsterdam, The Netherlands

    Dirk L. Couprie

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Couprie, D.L. (2018). Anaxagoras and the Measurement of the Sun and Moon. In: When the Earth Was Flat. Historical & Cultural Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-97052-3_11

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