The Graeco-Roman World

Boccaletti, Dino

doi:10.1007/978-3-319-90593-8_1

The Graeco-Roman World

Dino Boccaletti²

Chapter
First Online: 14 July 2018

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Abstract

Today, the earth, on which we move every day from one way to another and build our houses, can be nominally transformed, by ourselves, with a simple change of type (lower-case → upper-case) into something more important and greater: the Earth.

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Notes

1.
From now on we shall always use the upper case (except in the quoted excerpts, respecting their original form).
2.
It seems that the Babylonians had conceived the Earth as a disc with a central mountain encircled by the ocean and with a system of mountains which supported a solid hemispheric sky.
3.
As the great German scholar Bruno Snell says in the introduction of his fundamental work Die Entdeckung des Geistes. Studien zur Entstehung des europäischen Denkens bei den Griechen (1948), the thought in its logical forms common to us Europeans arose among the Greeks, and indeed since that time it has been considered the only possible form of thought.
4.
Strabo: Geography, vol. I (Eng. trans. Horace Leonard Jones) .
5.
Homer: Iliad, XVIII, 483–489, 606–607 ( trans. Samuel Butler) .
6.
Hesiod: Theogony 116–138 (Eng. trans. Hugh G. Evelyn-White) .
7.
The Shield of Heracles 314–316, trans. Hugh G. Evelyn-White .
8.
Among the numerous (incomplete) translations into English of Hermann Diels’s Die Fragmente der Vorsokratiker griechisch und deutsch (Berlin, 1903), one can refer to Kathleen Freeman : Ancilla to Pre-Socratic Philosophers (Harvard University Press, 1948; rpt. 1983).
9.
Diogenes Laertius: Lives of Eminent Philosophers, 2 vols. trans. R.D. Hicks , Loeb Classical Library (Cambridge, MA: Harvard University Press, 1925).
10.
B. Snell, op. cit., Chap. XI, 5.
11.
Aristotle: Metaphysics I, 983 b6 (Eng. trans. W. D. Ross).
12.
Aristotle: On the Heavens II, 294a: “Others say the Earth rests upon water. This, indeed, is the oldest theory that has been preserved, and is attributed to Thales of Miletus. It was supposed to stay still because it floated like wood and other similar substances, which are so constituted as to rest upon but not upon air. As if the same account had not to be given of the water which carries the Earth as of the Earth itself!” (Eng. trans. J. L. Stocks) .
13.
Aristotle: On the Heavens II, 13, 295b 10 (Eng. trans. J. L. Stocks).
14.
See: Giorgio de Santillana: The Origins of Scientific Thought: From Anaximander to Proclus (Chicago: The University of Chicago Press, 1961), chap. 1.
15.
This was told by Hippolytus of Rome (175–235 AD), a Christian writer, in his work Refutatio omnium haeresium, Chap. V (see Hippolytus Romanus: The Refutation Of All Heresies, trans. J. H. MacMahon) and, before him, by Aëtius in Placita Philosophorum (III, 10).
16.
Diogenes Laertius, Lives, op. cit. book II, 1: “Anaximander the son of Praxiades, was a native of Miletus. He laid down as his principle and element that which is unlimited without defining it as air or water or anything else. He held that the parts undergo change, but the whole is unchangeable; that the Earth, which is of spherical shape, lies in the midst, occupying the place of a centre; that the moon, shining with borrowed light, derives its illumination from the sun; further, that the sun is as large as the Earth and consists of the purest fire”.
17.
See in this regard F. Enriques , G. De Santillana: Storia del Pensiero Scientifico, vol. I (Treves: Tumminelli, 1932), pp 265–270.
18.
Herodotus: The Histories, book II, 109: “For as touching the sun-dial and gnomon and the twelve divisions of the day, they were learnt by Hellenes from Babylonians” (Eng. trans. G. C. Macaulay—Project Gutenberg, 97).
19.
Diogens Laertius, Lives, op. cit., ibidem.
20.
See Placita Philosophorum (I, 3) (Eng. trans. William W. Goodwin) ; see also Diels: Fragmente, op. cit., 2.
21.
Aristotle: On the Heavens II, 13, 294b (Eng. trans. J. L. Stocks) .
22.
It is handed down that he had written a work in prose (lost) entitled On Nature.
23.
Diogenes Laertius, Lives, op. cit., IX, 11.
24.
Aristotle: Metaphysics I, 5-985b 23–28 (Eng. trans. W. D. Ross).
25.
See Aëtius: Placita Philosophorum II, 16 (Eng. trans. William W. Goodwin) ; see also Diels’ Fragmente, op. cit., 24, 4).
26.
On this see: T. Heath, Aristarchus of Samos: The Ancient Copernicus (Oxford, Clarendon Press, 1913 (prt. Dover, 1981) and G. V. Schiaparelli , “I precursori di Copernico nell’antichità” in Scritti sulla Storia dell’Astronomia antica (Zanichelli, 1925, rpt. Milan, Mimesis, 1997).
27.
Diogenes Laertius, Lives, op. cit., VIII, 85.
28.
Aristotle: On the Heavens, II, 293a–293b (Eng. trans. J. L. Stocks) .
29.
On this, see T. Heath: Aristarchus of Samos, op. cit. and J. L. E. Dreyer: History of the Planetary Systems from Thales to Kepler (Cambridge University Press, 1906).
30.
Aëtius, Placita Philosophorum, III 10, 5 (Diels, op. cit., 68, 94): “Democritus [said] that it is like a quoit in its surface, and hollow in the middle” (Eng. trans. William W. Goodwin).
31.
Aëtius, Placita Philosophorum, III 15, 7 (Diels, op. cit. 28, 44): “Parmenides and Democritus, that the earth being so equally poised hath no sufficient cause why it should incline rather to one side than to the other; so that it may be shaken, but cannot be removed.” trans. William W. Goodwin) .
32.
G. de Santillana, op. cit, chap. 12.
33.
Plato: Phaedo 108–109 (Eng. trans. Sanderson Beck).
34.
Plato: Timeaus 39–40 (Eng. trans. B. Jowett) .
35.
J. L. E. Dreyer: History of the Planetary Systems from Thales to Kepler (Cambridge University Press, 1906), Chap. 3.
36.
Aristotle, On the Heavens II 17, 293b (Eng. trans. J. L. Stocks) .
37.
See P. Duhem: Le Système du Monde (Paris: Hermann, 1919), vol. 1, chap. II, XI.
38.
Aristotle gives knowledge of this system and of the corrections proposed by Callippus (370–300 BC) in the twelfth book of Metaphysics (XII, 8, 1073 b 17–1074 a 14). More information comes from the Commentary of Simplicius (sixth century AD) to On the Heavens of Aristotle. On that report Schiaparelli based his reconstruction of the “mathematical mechanism” imagined by Eudoxus. See G. V. Schiaparelli: “Le Sfere omocentriche di Eudosso, di Callippo e di Aristotele” in Scritti sulla storia dell’astronomia antica, op. cit., II, pp 5–112.
39.
See T. L. Heath: Aristarchus of Samos, op. cit., p. 193.
40.
Aristotle: On the Heavens, op. cit., II, 4, 286 b (Eng. trans. J. L. Stocks).
41.
See D. Boccaletti : “From the epicycles of the Greeks to Kepler’s ellipse. The breakdown of the circle paradigm in Cosmology through time”, in Cosmology Through Time: Ancient and Modern Cosmology in the Mediterranean Area (Conference proceedings, Monte Porzio Catone (Rome), Italy, June 18–20, 2001), eds. S. Colafrancesco and G. Giobbi (Milan: Mimesis) pp 99–112.
42.
Aristotle: On the Heavens op. cit., II, 4, 287 a (Eng. trans. J. L. Stocks) .
43.
Aristotle: On the Heavens II, 287 a–287 b (Eng. trans. J. L. Stocks).
44.
Aristotle: On the Heavens II, 13, 293 a.
45.
Aristotle: On the Heavens II, 14, 296 a–296 b (Eng. trans. J. L. Stocks).
46.
Aristotle: On the Heavens II, 14, 297 a (Eng. trans. J. L. Stocks) .
47.
P. Duhem: Le système du monde, op. cit., p. 213.
48.
Aristotle: On the Heavens II, 14, 297 b (Eng. trans. J. L. Stocks).
49.
See Paul Tannery: Recherches sur l’histoire de l’astronomie ancienne (Paris, 1893), p. 103.
50.
Aristotle: On the Heavens II, 14, 297b–298a (Eng. trans. J. L. Stocks).
51.
“And, see, the farm-roof chimneys smoke afar/ And from the hills the shadows lengthening fall!” (Eng. trans. John William Mackail) .
52.
Á. Szabó and E. Maula : Le début de l’astronomie de la géographie et de la trigonométrie chez les Grecs (Paris: Vrin, 1986), première partie.
53.
Here is the text: “Son of Praxiades, Milesian, philosopher, a relative and student and successor of Thales. He first discovered an equinox and solstices and hour-indicators, and that the Earth is situated in the middle [of the universe]. He also introduced a sundial and explained the basis of all geometry. He wrote On Nature, Circuit of the Earth, and Fixed Bodies and Globe and some other works” (Eng. trans. Jennifer Benedict , From Suda on Line: Byzantine Lexicography—http://www.stoa.org/sol).
54.
We refer the reader to Szabó and Maula, Le début de l’astronomie de la géographie, op. cit., for all the geometric treatment.
55.
On Pytheas and his travels we refer the reader to the thorough book (in Italian) of Stefano Magnani , Il viaggio di Pitea sull’oceano (Bologna: Patron editore, 2002).
56.
In the fourth century many voyages (even with non-military purposes) were performed by Greek navigators, but that of Pytheas is the most important both for the lands he visited and the detailed account he drew up of it.
57.
See Andreas Kleineberg , Christian Marx , Eberhard Knobloch , Dieter Leigemann , Germania und die Insel Thule (Darmstadt, 2010), Chap. 6.
58.
See the English translation in T. L. Heath’s Aristarchus of Samos, op.cit., ed. 1981, pp. 353–414.
59.
T. L. Heath (ed.): The Work of Archimedes (Cambridge University Press, 1897; rpt. Dover, 2002), pp. 221–222.
60.
Plutarch: De facie in orbe lunae, op. cit., p. 304 (see the translation by T. L. Heath in Aristarchus of Samos, op. cit.).
61.
Vitruvius: De architectura IX, 8, 1. According to Szabò , “Vitruve s’est trompé” (Szabò and Maula , Le début, op. cit., p. 60). On the basis of quotations from Aristophanes, he holds that the scaphe existed before Aristarchus.
62.
Regarding this, J. Dutka (“Eratosthenes’ measurement of the Earth reconsidered”, Arch. Hist. Exact Sci. 46 (1993): 55–66) points out that the method used by Eratosthenes, i.e. the use of the proportion
$$\frac{circumference\;of\;the\;Earth}{terrestrial\;distance} = \frac{angular\;measure\;of\;the\;meridian}{angular\;difference\;of\;latitude},$$
has remained the basis procedure for geodetic surveys, except some technical improvements notably in the seventeenth century, until the advent of geodesic satellites (ca. 1960).
63.
Little is known of the life of Cleomedes. He seems to have written his elementary astronomical textbook De motu circulari corporum caelestium between the time of Posidonius and Ptolemy (i.e., between the first century BC and the second century AD). The book was written in Greek; we have quoted the Latin title of the classical translation of H. Ziegler (Teubner, Leipzig, 1891). A partial English translation can be found in Heath’s Greek Astronomy (London, 1932; rpt. Dover, 1981). A recent French translation exists: Cléomède, Théorie Élementaire, trans. and comm. R. Goulét (Paris: Vrin, 1980). (We owe to this book Fig. 1.2.) We must consider that Cleomedes’ work was a popular work and that at that time Eratosthenes’ works Geography and The Measurement of the Earth were certainly still accessible to the scholars. Unfortunately, Cleomedes’ book is the only complete account of Eratosthenes’ measurements still extant, thus we must start from it.
64.
The translation of this passage is from T. L. Heath: Greek Astronomy, op. cit., pp 109–110.
65.
A measurement of this type, reported by Cleomedes as anonimous, is ascribed to Dicearchus of Messina (350–290 BC) and considers lying on the same meridian the two towns of Syene and Lysimachia (Gallipoli on the Dardanelles). Maybe Archimedes refers to this measurement when (in The sand-reckoner) he alludes to a few who tried to demonstrate that the perimeter of the Earth measures 300,000 stades.
66.
G. Pólya: Mathematical Methods in Science (Washington, 1977).
67.
See F. Hultsch: Griechische und römische Metrologie (Berlin: Weidman, 1882).
68.
L. Russo: “Ptolemy’s Longitudes and Eratosthenes’ measurement of the Earth circumference”, Mathematics and Mechanics of complex Systems 1(2013): 67–79.
69.
G. Dragoni, in his book Eratostene e l’apogeo della scienza greca (Bologna: CLUEB, 1979), which is one of the more thorough works about Eratosthenes, holds with sound arguments that the winter measurements of which Cleomedes does not mention the author must be credited to Eratosthenes. Dragoni rightly points out that most of the scholars neglect this part of the narration of Cleomedes. Maybe, one can suppose, that many, rather than to go back to the original work, are content with referring to quotations from others.
70.
L. Russo, loc. cit.
71.
Horace, Epistles, II, 1, 156.
72.
See L. Russo: The Forgotten Revolution: How Science was Born in 300 BC and Why It Had to Be Reborn (Berlin: Springer, 2004).
73.
See, for instance, W. H. Stall: Roman Science (The University of Wisconsin Press, 1952), First Part.
74.
Tusculanae Disputationes I, 5: “Geometry also was in the highest esteem among them, and none were more illustrious than the mathematicians; while in this art we go no farther than is needful for the purpose of measuring and calculating” (Eng. trans. Andrew P. Peabody ).
75.
See W. G. L. Randles: De la terre plate au globe terrestre (Une mutation épistémologique rapide, 1480-1520) (Paris: Librarie Armand Colin, 1980).
76.
We shall treat this subject in the Chap. 2.
77.
Strabo: Geography I, 1 (Eng. trans. H. Leonard Jones).
78.
See Francesco Prontera : “Sull’esegesi ellenistica della Geografia omerica” in Geografia e Storia nella Grecia antica (Florence: Leo S. Olschki Editore, 2011), pp 3–14.
79.
Strabo: Geography I, 1 (Eng. trans. H. Leonard Jones).
80.
Strabo: Geography I, 1 (Eng. trans. H. Leonard Jones).
81.
Strabo: Geography I, 1 (Eng. trans. H. Leonard Jones).
82.
Strabo: Geography II, 1 (Eng. trans. H. Leonard Jones).
83.
By the eminent Grecian scholar Giovanni Pugliese Carratelli .
84.
Strabo: Geography II, 1 (Eng. trans. H. Leonard Jones).
85.
Strabo: Geography II, 1 (Eng. trans. H. Leonard Jones).
86.
On this, see L. Russo: The forgotten revolution, op. cit.
87.
O. Neugebauer: A History of Ancient Mathematical Astronomy, Part two (Springer-Verlag, 1975), p. 934.
88.
Maximus Planudes also reconstructed the 27 maps included in the work (see later) following (it seems) the instructions contained in Ptolemy’s text. It is still under discussion if an original version of the 27 maps drawn by Ptolemy himself ever existed.
89.
See O. Neugebauer: “Ptolemy’s Geography, Book VII, Chaps. 6 and 7”. In: Astronomy and History Selected Essays (New York: Springer, 1983), p. 326.
90.
K. F. A. Nobbe: Claudii Ptolemaei Geographia, 3 vols. (Leipzig: Sumptibus et typis Caroli Tauchnitii, 1843–1945).
91.
C. Müller and C. T. Fisher (eds.): Claudius Ptolemaeus Geographia: Selections, 5 vols. (Paris: A. Firmin Didot, 1883–1901).
92.
Ptolemy’s Almagest, trans. and annotations G. J. Toomer (Princeton University Press, 1998).
93.
John L. Berggren and Alexander Jones: Ptolemy’s Geography, An annotated translation of the theoretical chapters (Princeton University Press, 2000).
94.
Ptolemy: Geography I, 1, 1–2 (Eng. trans. Louis Francis, who uses the term “Cartography” where we have substituted [Geography]).
95.
Ptolemy: Geography I, 1, 3 (Eng. trans. Louis Francis).
96.
Thomas S. Kuhn called this model “the two-sphere universe”; see The Copernican revolution. Planetary Astronomy in the development of Western Thought (Cambridge MA: Harvard University Press, 1957, Chap 1).
97.
Geography I, 2, 2 (Eng. trans. Louis Francis).
98.
Geography I, 6, 1 (Eng. trans. Louis Francis).
99.
Geography I, 6, 3 (Eng. trans. Louis Francis).
100.
L. Russo: Ptolemy’s longitudes, loc. cit.
101.
O. Neugebauer: A History of the ancient mathematical Astronomy, op. cit., p. 934.
102.
For this and the other discussion regarding De Chorographia, we refer the reader to Pomponii Melae De Chorographia libri tres. Introduction, critical edition and commentary by Piergiorgio Parroni (in Italian) (Rome: Edizioni di Storia e Letteratura, 1984).
103.
Pomponii Melae De Chorographia libri tres, ed. C. Frick (Leipzig: Teubner, 1880), p.1 (rpt. Stuttgart: W. Schaub, 1967), p. 1. Eng. trans: “I should, however, say more elsewhere and with greater preciseness” (Pomponius Mela’s Description of the World, trans. Frank E, Romer (University of Michigan Press, 1998, p. 33).
104.
De Chorographia, op. cit., p. 1: “A description of the known world is what I set out to give, a difficult task and one hardly suited to eloquence…” (ibidem).
105.
De Chorographia, op. cit., pp 1–2: “Omne igitur hoc, quidquid est cui mundi caelique nomen indidimus, unum id est et uno ambitu se cunctaque amplectitur. partibus differt; unde sol oritur oriens nuncupatur aut ortus, quo demergitur occidens vel occasus, qua decurrit meridies, ab adversa parte septentrio. huius medio terra sublimis cingitur undique mari, eodemque in duo latera quae hemisphaeria nominant ab oriente divisa ad occasum zonis quinque distinguitur. mediam aestus infestat, frigus ultimas; reliquae habitabiles paria agunt anni tempora verum non pariter. antichthones alteram, nos alteran incolimus. illius situs ob ardorem intercedentis plagae incognitus, huius dicendus est” (Eng. trans. Pomponius Mela’s Description of the World, trans. Frank E. Romer (University of Michigan Press, 1998, p. 34).

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Boccaletti, D. (2019). The Graeco-Roman World. In: The Shape and Size of the Earth. Springer, Cham. https://doi.org/10.1007/978-3-319-90593-8_1

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