Abstract
Plutarch, Hippolytus, and Diogenes Laertius report that Anaxagoras compared the size of the sun with the Peloponnesus (see Fig. 16.1). The aim of this chapter is to show that Anaxagoras was not crazy when he said this but that it was a fair estimate, from his point of view, which was that of a flat earth. More precisely, I show that with the instruments (gnomon, clepsydra, sighting tube) and with the geometrical knowledge (the properties of similar triangles, simple equations, Pythagoras’ theorem) available, he must have been able to use the procedures and perform the calculations needed to reach approximately his result.
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- 1.
E.g., Dreyer: “the sun (…) greater than the Peloponnesus, and therefore not at a great distance from the earth” (my italics), which implies that the sun must be rather small, see Fig. 9.9 in Chap. 9 (1953: 31). Fehling: “vielfach so groβ nach Aëtius (to whom Plutarch’s text goes back, according to Diels, D.C.), ihm war das Richtige nicht groβ genug” (1985b: 209, my italics). O’Brien: “For if the sun is smaller than the earth” (1968: 124).
- 2.
- 3.
For Fig. 16.2, I consulted NASA’s Five Millennium Catalog of Solar Eclipses on the internet. More specifically http://eclipse.gsfc.nasa.gov/SEsearch/SEsearchmap.php?Ecl=04620430.
- 4.
Usually, 1 li is said to equal about 500 m, but Dubs has calculated the li of the Han dynasty to be 415.8 m (1955: 160 n. 7).
- 5.
The final redaction of the Zhou bi, a collection of ancient Chinese texts on astronomy and mathematics, was probably in the first century B.C., but contains older material.
- 6.
In the Zhou bi, the gnomon has a length of 8 chi, its shadow 6 chi, which is also said to shorten 1 cun for every 1,000 li southward. In this text, BT = 60,000 li, and ST (the distance of the sun to the earth) = 80,000 li (see Cullen 1996: 78 and 178).
- 7.
See http://www-history.mcs.st-andrews.ac.uk/HistTopics/Greek_numbers.html. Cf. also Boyer: “It was in the use of fractions that the (Greek notation) systems were weak” (1968: 11).
- 8.
Anaxagoras could have observed this. We, however, can also calculate it with the help of trigonometry, knowing that the angle at the top of the gnomon at the summer solstice at Delphi is 38.5 − 23.5 = 15°, and hence the shadow at the bottom of the gnomon 75°. The length of the shadow is then 200:tan 75 = 53.6 cm, and at Sparta 200:tan 76.4 = 48.4 cm. If one might think that Sparta is not far enough to the south to discern any significant difference between the shadows of the gnomons at Delphi and Sparta, because of the range of uncertainty that is inherent to measuring the shadow of a gnomon, one could imagine the second measuring point at Cape Tainaron in the farthermost south of the Peloponnesus, at 36.4°N and 22.5°E, where the shadow of the gnomon is 45.8 cm (a learned man like Anaxagoras would not have been afraid as the Greeks thought there to be one of the entrances to Hades).
- 9.
As the circumference of the earth, measured over the poles, is about 40,000 km, the difference between two successive grades of latitude = about 111.13 km. The distance between Delphi and Sparta is 1.4 × 111.13 = about 156 km.
- 10.
The real distance between Delphi and the tropic of Cancer is 1,670 km.
- 11.
Cf. Fehling: “Nun betrug die gröβte Entfernung innerhalb der damals bekannten Erde (von den Säulen des Herakles bis Babylon) ca. 5000 km” (1985b: 210).
- 12.
In an analogous way, one could imagine Anaxagoras to have estimated the distance and size of the moon. The moon at its highest point due south is about 5° higher than the sun. Accordingly, the point on earth where the moon at its highest stands in the zenith is at 28.5°N. If we take S in Fig. 16.6 to be the moon at its highest point due south, then the angle XST = 10°. Let us suppose that Anaxagoras estimated the distance XT from Delphi (at 38.5°N) to the point on earth where the moon stands in the zenith to be 1,000 km. Then XS = 5,817 km, and the size of the moon = 51 km. However, as far as I know, there exist no reports of the use of the gnomon for measuring the shadow of the moon, although this may be done, especially at full moon.
- 13.
For this and other variations in the methods and results of calculations concerning the size of the sun, see Heath (1913: 311–113).
- 14.
The article by D.W. Graham and E. Hintz, “Anaxagoras and the Solar Eclipse of 478 B.C.”, Apeiron 40 (2007) 319–344, came to my attention after I had finished the manuscript of this book. I intend to devote a separate article to it, but essentially Sider was already right when he wrote: “The eclipse of 478 B.C. was annular (i.e. there would be no umbra)” (1973: 129, n. 10).
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Couprie, D.L. (2011). The Sun Is as Big as the Peloponnesus. In: Heaven and Earth in Ancient Greek Cosmology. Astrophysics and Space Science Library, vol 374. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8116-5_16
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