Heraclides and Heliocentrism: Texts,Diagrams,and Interpretations

The standard work on Aristarchus remains Heath Thomas L. , Arislarchus of Samos, the ancient Copernicus (Oxford, 1913, repr. 1959); see chap. 18 for Heraclides of Pontus. For Copernicus's awareness that Aristarchus conceived of a mobile Earth, see Nikolaus Kopernikus Gesamtausgabe, ed. by Kubach Fritz (Munich, 1944), i, fol. llv, lines 15–17.

Kepler , who made a determined search to find an ancient Platonic school of heliocentrism, was quite ready to discover limited heliocentrism, for Mercury and Venus, in Plato as well as in Vitruvius Pliny MacRobius , and Capella Martianus , but never mentioned Heraclides of Pontus. See Kepler's Apologia contra Ursum in sect. II of Jardine Nicholas , The birth of history and philosophy of science (Cambridge, 1984), and the discussion of Kepler's presumed precursors of Copernicus according to Apologia contra Ursum, Part 4, in Eastwood Bruce , “Kepler as historian of science: Precursors of Copernican heliocentrism …”, Proceedings of the American Philosophical Society, cxxvi (1982), 367–94.

Ibid., 373–81, 383–91.

Duhem Pierre , Le système du monde (Paris, 1915), iii, 44–162; Dicks D. R. , Early Greek astronomy to Aristotle (Ithaca, 1970), 136–7, 218–19.

Wehrli Fritz (ed.), Die Schule von Aristoteles. Texte und Kommentar, vii: Herakleides Pontikos (Basel, 1953), 35–38. 94–101, presents the astronomical fragments and brief commentary. See also idem, “Herakleides der Pontiker”, Paulys Realencyclopädie der Altertumswissenschaft , Suppl. II (1968), 675–86, esp. pp. 685–6. Gottschalk H. B. , Heraclides of Pontus (Oxford, 1980), 58–87, discusses very competently the astronomical fragments but I differ with his interpretations of the two crucial texts for any so-called Heraclidean heliocentrism.

The text appears in Diels Hermann (ed.), Commentaria in Aristotelem graeca, ix: Simplicii in Aristotelis Physicorum libros quattuor priores commentaria (Berlin, 1882), 291–2; also in Posidonius , The fragments , ed. by Edelstein L. and Kidd I. G. (Cambridge, 1972), 44–45. A translation appears in Heath, Aristarchus (ref. 1), 275–6, reprinted in Cohen M. R. and Drabkin I. E. (eds), A source book in Greek science (Cambridge, Mass., 1958), 90–91. On ‘saving the phenomena’ a useful introduction is Mittelstrass Jürgen , Die Rettung der Phänomene, Ursprung und Geschichte eines antiken Forschungsprinzips (Berlin, 1962), 140–221, on astronomy; and Lloyd G. E. R. , “Saving the appearances”, Classical quarterly, n.s. xxviii (1978), 202–22.

The text is in Waszink J. H. (ed.), Timaeus a Calcidio translatus commentarioque instructus (London, 1962/1975), 156–9 (cc. 108–12). A translation of cc. 109–11 can be found in Gottschalk , Heraclides (ref. 5), 69–70.

See above, ref. 5.

The leading figures in this nineteenth-century group were Schiaparelli Giovanni V. , I precursori di Copernico nell'antichità (Memorie del Reale Istituto Lombardo di Scienze e Lettere , xii; Milan, 1873), 416–20; Origine del sistema planetario eliocentrico presso i Greci (Memorie del Reale Istituto Lombardo, classe di scienze mathematiche e naturali , xviii; Milan, 1898), 151–67, under the heading, “The heliocentric planetary system considered as a possible geometrical hypothesis”; and Staigmüller Hermann , “Beiträge zur Geschichte der Naturwissenschaften in Klassischen Altertume”, Programm des königlichen Realgymnasiums in Stuttgart (Stuttgart, 1899), 33–35 and “Herakleides Pontikos und das heliokentrisches System”, Archiv für Geschichte der Philosophie, xv (1902), 141–65. Both Schiaparelli and Staigmüller argued vigorously, even over-enthusiastically, that the text in question must assign the hypothesis of a heliocentric mobile Earth to Heraclides. Cautions and alternatives of various sorts were issued by August Böckh, Untersuchungen über das kosmische System des Piatons (Berlin, 1852), 133–40; Martin Thomas H. , “Mémoires sur l'histoire des hypothèses astronomiques chez les grecs et les romains I, v, 2–4”, Mémoires de l'Institut National de France, Académie des Inscriptions et Belles-lettres, xxx, Part 2 (1883), 1–43, pp. 25–43; and Tannery Paul , “Sur Héraclide du Pont”, Revue des études grecques, xii (1899), 307–10.

This translation is primarily that of Heath, Aristarchus (ref. 1), 275–6, emended in part according to Gottschalk , Heraclides (ref. 5), 63, replacing much of lines 20–35 of Heath's p. 276.

The closeness of Geminus to Posidonius is of some interest here but remains uncertain. Germaine Aujac's introduction to her edition of Geminus, Introduction aux phénomènes (Paris, 1975), p. xxii, bases a reconstructed biography of Geminus on a letter of c. 15 b.c. by Dionysius of Halicarnassus to one Cn. Pompeios Geminos, while admitting that her identification of this addressee with our astronomer Geminus is a hypothesis recommended primarily by its lack of explicit contradiction. Neugebauer Otto , History of ancient mathematical astronomy (New York, 1975), ii, 579–80, dates Geminus to the first half of the first century a.d., but some latitude exists in the bases for the calculation, placing Geminus's writing (in his later years?) perhaps at the turn of the b.c. — a.d. eras. Aujac puts his Introduction to the phaenomena at c. 50 b.c., clearly too early. The upshot allows us to consider Geminus as a follower of Posidonius but probably not as one of his students.

Posidonius , The fragments (ref. 6), 44–45. Kidd Ian G. , “Philosophy and science in Posidonius”, Antike und Abendland, xxiv (1978), 7–15, p. 11, shows the Posidonian elements, placing astronomy in the service of philosophy rather than in the position of peer.

Ibid., II: Kidd paraphrases and partly reiterates the quotation, saying, “You might even have a hypothesis put forward which violates the <image> or postulates, with a guy (<image>) like Heraclides Ponticus assuming the Earth to be in motion in some way”.

Gottschalk , Heraclides (ref. 5), chaps. 1, 7, points to the generally Platonic cast of Heraclides's thought as well as the literary, especially rhetorical, manner in which he presented arguments. Heraclides's polemical attitude is remarked by, among others, Wehrli , Schule (ref. 5), 99; Wehrli , “Herakleides” (ref. 5), 685.

Gottschalk , Heraclides (ref. 5), 64–66.

Ibid., 66–69.

Ibid., 68–69.

Dreyer J. L. E. , History of the planetary systems from Thales to Kepler (Cambridge, 1906), 87–107.

Ibid., 92–95.

Neugebauer , op. cit. (ref. 11), 627–8, explains this succinctly. Here I would not agree with Gaiser Konrad , Platons ungeschriebene Lehre (Stuggart, 1963), 383–4, in the view that Heraclides has referred to a Eudoxan motion that is equivalent to nutation.

Gottschalk , Heraclides (ref. 5), 69–82, presents his arguments for this interpretation.

The text here (dividantur in quinquaginta momenta) is corrupt, as Gottschalk , Heraclides (ref. 5), 70, n. 38, following Commentarius Calcidii, ed. by Waszink (ref. 7), 157, apparatus ad lin. 27, observes. While agreeing on the sense of the passage, I would emend it a bit differently.

The text here (ed. by Waszink , 158, line 11) reads KA and KΓ, rather than XA and XΓ, but the text is surely corrupt here as my subsequent analysis of the diagrams will show.

See Commentarius Calcidii , ed. by Waszink (ref. 7), 156–9 for the Latin texts of cc. 108–12. A translation of c. 112 can be found in van der Waerden B. L. , “The motion of Venus, Mercury and the Sun in early Greek astronomy”, Archive for history of exact sciences, xxvi (1982), 99–113, p. 103.

Commentarius Calcidii, ed. by Waszink (ref. 7), 157, lines 3–5: “Quod his usu accidit ex eo quod una medietas atque punctum unum est tam solstitialis circuli quam cuiuslibet alterius stellarum harum”.

See ibid. , 108, line 15 (c. 61); 111, line 14 (c. 64); 127, line 23–128, line 1 (c. 79); 130, lines 8–9 (c. 80); cf. 131, line 7 (c. 81), where punctum alone describes a geometrical centre in an epicyclic arrangement.

Taylor Alfred E. , A commentary on Plato's Timaeus (Oxford, 1928), 200–1. Evans Godfrey , “The astronomy of Heraclides Ponticus”, Classical quarterly, lxiv (1970), 102–11, p. 110; Evans's article proposes (p. 108) three theories in the text of cc. 108–12 of Calcidius, but I find such a proposition quite incredible.

Neugebauer Otto , “On the allegedly heliocentric theory of Venus by Heraclides Ponticus”, American journal of philology, xciii (1972), 600–1.

Commentarius Calcidii, ed. by Waszink (ref. 7), 158; see p. clxxxx on the source of the published diagrams, a ms. of the tenth century from northern France.

In Waszink's edition at 110, line 14; 111, line 17 (globus solis); 128, line 3 (globus solis); 142, line 9; 147, line 3.

At 116, line 7; 116, line 11; 119, line 11; 119, line 13; 119, line 15; 121, line 2; 122, line 16; 125, line 16; 127, line 22; 134, line 9; 138, line 12; 145, line 12; 145, line 14; 150, line 17; 151, line 3; 151, line 6; 154, line 7; 159, line 19; 161, line 25. At the three points on p. 119, globus = orbis. Cicero , De natura deorum, II, xviii, 47, defines globus as spherical.

At 128, line 9; 131, lines 2–3, 131; lines 4–5.

See above ref. 23.

Diagrams at Commentarius Calcidii, ed. by Waszink (ref. 7), 158; also see above, ref. 29.

van der Waerden B. L. , “Die Astronomie des Heraklides von Pontos”, Berichte der mathematisch-naturwissenschaftlichen Klasse der sächsischen Akademie der Wissenschaften zu Leipzig, xcvi (1944), 47–56; Die Astronomie der Pythagoreer (Verhandelingen der Koninklijke Nederlandse Akademie van Wettenschappen Afdeeling Naturkunde, sect. 1, vol. xx, no. 1; Amsterdam, 1951), 62–73.

van der Tak Johannes G. , “Calcidius' illustration of the astronomy of Heracleides of Pontos”, Philologus, cxvi (1972), 129–36.

I have been unable to inspect Napoli Biblioteca Oratoriana ms. XVI.XVIII (a.d. 1507).

The dating of the mss. comes with very few exceptions from Waszink's edition (ref. 7), pp. cvii–cxxx.

Van der Waerden , “Heraklides” (ref. 35), 52, uses 13 mss.; in Astronomie der Pythagoreer (ref. 35), 70, he adds two, from Bamberg and Leiden, to the earlier list.

While it is not my concern to dispute van der Waerden's approach point by point, it should be recognized that he has continually argued for a Heraclidean heliocentrism in an extreme form which involves the Earth as well as Mercury and Venus. This position appears in his essays of 1944 and 1951 and can be found in his more recent works: Das heliozentrische System in der griechischen, persischen und indischen Astronomie (Zürich, 1970), 51; “On the motion of the planets according to Heraclides of Pontus”, Archives internationales d'histoire des sciences, xxviii (1978), 167–82. The last of these I consider highly tendentious, arguing for possibilities not historical plausibilities.

Van der Waerden , “Heraklides” (ref. 35), 53; Astronomie (ref. 35), 71.

Van der Waerden , “Heraklides” (ref. 35), 54.

Van der Tak , “Calcidius' illustration” (ref. 36), 135, for the three groups of diagrams (Figs 1–3), 136 for the four hypothesized stages of devolution from Group III (similar to our Figure 2). He surveyed 20 manuscripts with diagrams and noted more of the pertinent characteristics than van der Waerden.

London BL ms. Roy. 12.B.XXII, f. 33v (s. XII in.); Napoli BN ms. VIII.F.11, ff. 23v-24r (s. XII); Paris BN ms. lat. 10195, ff. 105v-106r (s. XI). I shall return to these three later.

He found the lines XA and XΓ always tangents to the inner circle; this is not the case in one example, Vat. Regin. lat. 1114, f. 45v (s. XIV). He said the letters EZH, unexplained by Calcidius, appear; this is not precisely correct in seven examples, of which three have only EH, one has EZ, three have ΔEZH.

Bruxelles BR 9625–9626 (s. X), London BL Add. 15293 (s. XI ex.-XII in.), Lyon BM 324 (s. IX), Milano Ambr. 1.95 inf. (s. XI ex.), München CLM 13021 (s. XII²−XIII in.), Napoli BN VIII. E.30 (s. XV), Oxford Bodl. Canon. class. lat. 175 (a.d. 1459), Paris BN 2164 (s. XI¹), Paris BN 6281 (s. XII in.), Paris BN 6282 (s. XI m.), Valenciennes BM 293 (s. IX), Vat. lat. 1544 (c. 1470), Vat. Barb. 22 (s. XI in.), Vat. Regin. 123 (a.d. 1056), Vat. Regin. 1114 (s. XIV), as well as the earliest printed edition (Paris, 1520).

Arezzo BC 431 (s. XV), Bamberg SB M.V.15 (s. XI), Firenze Laur. Plut. 84.24 (s. XV), Firenze Laur. Plut. 89 sup. 51 (s. XI), Firenze BN S. Marco I.IV.28 (s. XI), Firenze BN S. Marco I.IX.40 (s. XII), Köln DB 192 (s. XI), Kraków Jagiel. 529 (s. X), Leiden UB BPL 64 (s. XI), Leipzig UB Rep. 1.84 (s. XII ex.-XIII in.), London BL Add. 19968 (s. XI), Milano Ambr. S. 14 sup. (a.d. 1454), München CLM 6365 (s. XI), Napoli BN VIII.E.29 (s. XV), Oxford Bodl. Canon. class. lat. 176 (s. XV), Paris BN 6280 (s. XI), Paris BN 6570 (s. XII), Philadelphia U. Penn. 13 (c. 1500), Praha SK III.A.13 (s. XIV), Trier Bist. Arch. 28 (s. XII), Vat. Barb. 21 (s. XI), Vat. Chigi E.VI.194 (s. XV), Vat. Regin. 1308 (s. XI in.), Vat. Regin. 1861 (s. XI), Vat. Urb. 203 (s. XV), Wien NB 176 (s. XII), Wolfenbüttel 116 Gud. lat. 2° (s. XI).

Though van der Tak did not notice it, the letter A of ΔEZH appears very frequently (in 17 mss).

This occurs in Arezzo 431, f. 34v; Leiden BPL 64, f. 85v; Praha III.A.13, f. 99ra; Vat. Barb. 21, f. 59v; Wolfenbüttel 116 Gud. lat. 2°, f. 39v. Paris 6570, f. 21r, has none of the four letters.

Of Group II the six with tangents are the Bamberg, Köln, Trier, Leiden, Barberini, and Arezzo mss. The Praha and Wolfenbüttel mss. have the lines XA and XΓ slightly apart from the circle.

Cambridge Fitzwilliam Museum McClean 169 (s. XV), Cambridge UL Sidney Sussex 31 (s. XIV), Kraków Jagiel. 665 (s. XV), Paris BN 7188 (s. XII in.), Wien NB 443 (s. XI). It should be noted that the two early mss. reverse positions of A and Γ.

Vat. Regin. 1114, f. 45v (s. XIV).

Leiden BPL 64, f. 85v (s. XI); [Paris 6280, f. 28r (s. XI)]; Paris 6570, f. 21r (s. XII); [Vat. Chigi E.VI.194, f. 52v (s. XV)]. I enclose Paris 6280 and Chigi E.VI.194 in brackets because in these the Group III diagram is both marginal and joined to a more common version of the diagram for c. 112, making it very likely that this example of a Group III diagram should be ignored in any discussion of the diagrams for cc. 110–11. In Paris 6280 the Group III diagram seems to be intended only for c. 112, and in Chigi, E.VI.194 the Group III diagram, apparently illustrating only c. 112, is almost certainly copied from Paris 6280; van der Tak does not record any of this. He continues to confuse this important point by claiming that Paris 6570 has “two varieties of class III” (p. 132), whereas the second of these is definitely an illustration for c. 112, not c. 111; also, the second is clearly a marginal addition, while the first was apparently intended to accompany the text when it was written.

Commentarius Calcidii, ed. by Waszink (ref. 7), unnumbered page following p. clxvi.

That the marginal diagrams in P3 definitely pertain only to c. 112, not c. 111, seems proven by the position of these marginal diagrams in Ch3 (Chigi E.VI.194), where they are even farther removed from c. 111.

This inventiveness of eleventh- (or late tenth)-century scribes with regard to Calcidian diagrams is neither unique nor unusual. The manuscripts of Martianus Capella, Macrobius, Bede, and the Plinian astronomical excerpts all had diagrams added or consciously altered to accord with the sense made by the readers, and such inventiveness appeared especially in the ninth- to eleventh-century period, earlier for some texts than for others.

The details of this Capellan diagram are to be discussed in a separate study. In BPL 64 it occurs at f. 46v.

There are 28 such mss. of Plato's Timaeus before s. XII, including Phillipps 816, once thought lost, which is now: Austin (U.S.A.), University of Texas, Ransom Humanities Center Library, ms. 29 (the library will not microfilm this manuscript); the Timaeus appears at ff. 12r-24r with no diagrams and virtually no glosses.

These two pairs of diagrams for 110–11 and 112 appear respectively on ff. 85v-86r.

The label is lacking only in Köln 192 and Wolfenbüttel 116 Gud. lat. 2°, both in Group II.

Leiden BPL 64, f. 85v; Paris 6280, f. 28r; Paris 6570, f. 21r; Vat. Chigi E.VI.194, f. 52v; Vat. Regin. 1114, f. 45v.

The details, conceived in order to advance a Heraclidean heliocentrism, have no support from the diagrams and none I find plausible in the text. See van der Waerden , Astronomie (ref. 35), 70–73.

Vat. Regin, 1114, ff. 45v–46r.

Leiden BPL 64, f. 86r; Paris 6280, f. 28r; Paris 6570, f. 21v; Vat. Chigi E.VI.194, f. 53r. Each of these references is to the page with diagrams for c. 112.

This revision appears in Napoli BN VIII.E.30, f. 34v (s. XV), and Vat. lat. 1544, f. 78r (c. 1470); both mss. have diagrams for cc. 110–11 in Group I. This revised form also appears in the 1520 Paris edition, f. 33v, and can be conveniently seen in van der Waerden , “The motion of Venus, Mercury, and the Sun …” (ref. 24), 103 (his Fig. 2). Van der Waerden's article is ingenious but fails completely to establish that the theory he has in mind was Plato's or that it would not have come from one of many Hellenistic sources.

Napoli BN VIII.F.11, ff. 23v–24r (s. XII).

The scribe seems to have followed the defective text for 112 in this ms. in locating the circle. The ms. says that the circle touches A and Γ rather than the lines XA (KA) and XΓ (KΓ).

London BL Roy. 12.B.XXII, f. 33v, 5–6: “affirmant aliquanto quam solis esse elacionem luciferi globum qui limitatur notis ΔEZH contingens A …”.

This ms., R1 in Waszink's stemma, is closely related only to extant mss. with the Timaeus alone, not Calcidius's commentary.

Hiller Edward , “De Adrasti Peripatetici in Platonis Timaeum commentario”, Rheinisches Museum für Philologie, N. F. xxvi (1871), 582–9. Followed by Switalski Wladislaus Bruno , Des Chalcidius Kommentar zu Plato 's Timaeus (Beiträge zur Geschichte der Philosophie des Mittelalters, Bd iii, Heft 6; Münster, 1902), 71–91, who argues that Adrastus and Posidonius, rather than Theon, are Calcidius's sources.

Huxley G. L. , “Theon of Smyrna”, Dictionary of scientific biography , ed. by Gillispie C. C. , xiii (1976), 325–6; and especially von Fritz Kurt , “Theon aus Smyrna”, Realencyclopädie der Altertumswissenschaft, ser. 2, x (1934), 2067–8, 2071.

Hiller , “De Adrasti” (ref. 70), 588–9, with reference explicitly to cc. 107–11 (?!). Martin also remarked that the opinions and wording here are very much like those which Theon derived from Adrastus, but this seems to beg the question when we do not have Adrastus. Waszink Hendrik Jan , Studien zum Timaioskommentar des Calcidius, i: Die erste Hälfte des Kommentars (Leiden, 1964), 31–33, does not add much strength to Hiller's argument.

For example, the 50° elongation of Venus from the Sun: See Smyrnaeus Theon , Expositio rerum mathematicarum ad legendum Platonem utilium , ed. by Hiller E. (Leipzig, 1878), 137 (c. 13), 187 (c. 33).

Switalski Bruno (op. cit. (ref. 70)) argued with insufficient evidence that Posidonius (along with Adrastus) was a source for Calcidius. If we wish to hypothesize on the basis of this unfortunately unsubstantiated claim, we can at least remind ourselves that Posidonius was the author of the reference to Heraclides in the text of Simplicius's commentary on Aristotle's Physics. Perhaps Calcidius's reference to Heraclides also derived ultimately from Posidonius (with neither reference being demonstrably heliocentrical)? There is, of course, no way to answer this question.

Cornford F. M. , Plato's cosmology: The Timaeus of Plato (London, 1937), 105, n. 2; Taylor , Commentary (ref. 27), 196, comm. ad 38D, 3. Both agree that the text should not contain the <image>, thereby establishing that each of the three planets has an independent geocentric circle. See also Taylor , 154 (ad 36D, 3–4), 155 (ad 36D, 5–6).

Theon , Expositio, ed. by Hiller (ref. 73), 188–9 (c. 34).

Commentarius Calcidii, ed. by Waszink (ref. 7), 156, 19: “Ait [Plato] tamen hos ignes contrariam quoque habere vim”.