Having a Knack for the Non-Intuitive: Aristarchus's Heliocentrism through Archimedes's Geocentrism

Ptolemy , Almagest, translated and annotated by Toomer G. J. (Princeton, 1998), 44–45.

Heath T. L. , Aristarchus of Samos: The ancient Copernicus (Oxford, 1913), 301.

Fowler David talks of arithmetized geometry as follows: “Arithmetized geometry is how we tend to think of geometry today; a line has a length, a number; a rectangle has an area, again a number which is equal to the product of the lengths of its sides; ratios are defined arithmetically, as quotients of numbers; and so on. So the geometry becomes translated into the arithmetical manipulation of numbers … addition, subtraction, multiplication, division, taking roots, etc. … and then this arithmetic is later abstracted into algebra.” See Fowler D. H. , “The story of the discovery of incommensurability, revisited”, in Trends in the historiography of science , ed. by Gavroglu K. Christianidis J. Nicolaidis E. (Dordrecht, 1994), 221–35, p. 229. But he also insists that “early Greek mathematics and astronomy, up to and including Archimedes, was not arithmetized” ( Fowler D. H. , “Logistic and fractions in early Greek mathematics: A new interpretation”, in Histoire des fractions, fraction d'histoire , ed. by Benoit P. Chemla K. Ritter J. (Basel, 1992), 133–47, p. 133). Fowler's view, as expressed in many of his publications, is that the arithmetization of Greek mathematics came later as a result of the introduction of some form of the Babylonian number system in Greek astronomy, after the second century b.c., and that these developments were connected with the works of Hypsicles and Hipparchus. See for example Fowler D. H. , The mathematics of Plato's Academy: A new reconstruction (Oxford, 1990), 222. We shall add some comments to these views later in this paper.

See for example Martin T. H. , Mémoires sur l'histoire des hypothèses astronomiques chez les Grecs et les Romains (Mémoires de l'Académie des Inscriptions et des Belles-Lettres , xxx/2 (1881)); Schiaparelli G. , Origine del sistema planetario eliocentrico presso i Greci (Memorie del R. Instituto Lombardo di Scienze e Lettere: Classe di scienze matematiche e naturali , xviii (1898)); Tannery P. , Recherches sur l'histoire de l'astronomie ancienne (Mémoires de la Société des Sciences Physiques et Naturelles de Bordeaux, 4th ser., i (1893)); Dreyer J. L. E. , History of the planetary systems from Thales to Kepler (Cambridge, 1906; reprinted as A history of astronomy from Thales to Kepler (New York, 1953)); Heath , op. cit. (ref. 2); Duhem P. , Le système du monde: Histoire des doctrines cosmologiques de Platon à Copernique, i (Paris, 1913); v. Erhardt R. v. Erchardt-Siebold E. , “Archimedes' Sand-reckoner: Aristarchos and Copernicus”, Isis, xxxiii (1942), 578–602; Neugebauer O. , “Archimedes and Aristarchus”, Isis, xxxv (1942), 4–6.

Plutarch (Platonicae quaestiones, viii, 1); Sextus Empiricus ( Adversus mathematicos , x, 174); Ps-Plutarch ( De placita philosophorum , ii, 24). The only passage where Aristarchus's heliocentrism is said to have been considered critically is in Plutarch's De facie in orbe lunae, c. 6.

E.g.: “This [the Archimedes account of Aristarchus's heliocentrism] is stupendous, and would be incredible if we had it from another source” ( Sarton G. , Hellenistic science and culture in the last three centuries b.c. (New York, 1993), 57); “Mais, dans le courant du IIIe siècle, parut un ouvrage qui bouleversait les opinions reçues …; bien qu'il ne resât pas ignoré même du grand public, le système héliocentrique d'Aristarque n'eut pour ainsi dire aucun succès; seul un astronome du IIe siècle avant J.C. nommé Séleucus … passe pour l'avoir adopé” (our emphasis) ( Beaujeu J. , “Astronomie et géographie mathématique”, in Taton R. (ed.), Histoire générale des sciences, i: La science antique et médiévale des origines à 1450 (Paris, 1994), 356 and 358).

Cicero , Quaestiones academicae priores, II, 39.

Goldstein B. R. Bowen A. C. , “A new view of early Greek astronomy”, Isis, lxxiv (1983), 330–40.

Heath's translation, op. cit. (ref. 2), 276.

A systematic discussion of the views expressed about this passage can be found in Duhem, op. cit. (ref. 4), 410–18.

Platonicae quaestiones , viii, 1. See Heath , op. cit. (ref. 2), 183.

Ibid. See Heath , op. cit. (ref. 2), 305.

On the heavens , ii, 13. See Heath , op. cit. (ref. 2), 186.

See Boeckh A. , Untersuchungen über das kosmische System des Platon (Berlin, 1852), 148.

See Quaestiones naturales, vii, 2.

See Goldstein Bowen , op. cit. (ref. 8), 332.

Gelon was the son of the king of Syracuse, Hieron II. He co-ruled with his father beginning about 240 b.c. until his death c. 216, when he was over fifty years old.

Knorr W. R. , “Archimedes and the Elements: Proposal for a revised chronological ordering of the Archimedean corpus”, Archive for history of exact sciences, x/3 (1978), 211–90.

Archimedes's lifetime extended from c. 287 to 212 b.c.

On Aristarchus's dates see: Heath , op. cit. (ref. 2), 299; Stahl W. H. , “Aristarchus of Samos”, Dictionary of scientific biography, i, 246–50, p. 246; Wall B. E. , “Anatomy of a precursor: The historiography of Aristarchos of Samos”, Studies in history and philosophy of science, vi (1975), 201–28, pp. 210 seq.

Our knowledge of Aristarchus's extant On the sizes and distances of the sun and moon is derived from a collection of about twenty manuscripts. These manuscripts include a number of works that are presumed to have made up a unified collection, referred to by Pappus of Alexandria in the sixth book of his Mathematical collection under the name of Treasury of astronomy. The oldest and best of these manuscripts is from the tenth century and it seems to be the source from which all the other extant manuscripts are derived. See Heath , op. cit. (ref. 2), 325. The extant text of the Sand-reckoner is also based on a manuscript of the same period. This manuscript (known as Codex A, a name given by Heiberg) had been written in Constantinople in the ninth century; it was then transported to the West and became the archetype of most of the extant works of Archimedes, including the Sand-reckoner. This codex disappeared sometime after 1564, but we have various copies of it, made between 1450 and 1550.

For the Greek text see Heiberg J. L. , Archimedes, Opera omnia, ii (Leipzig, 1913), 218. There have been numerous translations of this passage. See, e.g., Dreyer , op. cit. (ref. 4), 136–7; Heath , op. cit. (ref. 2), 302; Duhem , op. cit. (ref. 4), 420–1; Dijksterhuis E. J. , Archimedes (Princeton, 1987), 362–3; Erhardt Erhardt-Siebold , op. cit. (ref. 4), 579. Our translation differs from these in a number of (minor) points. Though these differences have some philological interest, they are not important for the arguments developed in this paper.

See ref. 5. Some other evidence about Aristarchus's heliocentrism comes from Plutarch, Aëtius, Sextus Empiricus and Ps-Plutarch. The corresponding passages, which are of minor importance for our purpose, are translated and discussed in Heath's op. cit. (ref. 2), 304 seq.

Netz R. , The shaping of deduction in Greek mathematics: A study in cognitive history (Cambridge, 1999), 284 seq.

Erhardt Erchardt-Siebold , op. cit. (ref. 4), 588 seq.

The relevant passage is quoted by Heath, op. cit. (ref. 2), 221–3.

See Goldstein Bowen , op. cit. (ref. 8), 339.

Fowler , The mathematics of Plato's Academy (ref. 3), 54.

Huxley G. , “Aristarchus of Samos and Graeco-Babylonian astronomy”, Greek, Roman and Byzantine studies, v (1964), 123–31.

Bowen A. C. Goldstein B. R. , “Meton of Athens and astronomy in the late fifth century b.c.”, in A scientific humanist: Studies in memory of Abraham Sachs, ed. by Leichty E. Ellis M. deJ. Gerardi P. (Philadelphia, 1988), 39–81.

Netz R. , op. cit. (ref. 24), 292 seq.

Goldstein Bowen , op. cit. (ref. 8).

Heath's translation, op. cit. (ref. 2), 275–6.

Dreyer , op. cit. (ref. 4), 131 seq.

Heath , op. cit. (ref. 2), 312.

Heath , op. cit. (ref. 2), 276.