^{page 423 note 1} Aet. 2. 20. 1, 24. 2, 25. 1. (A 21 and 22. References in parentheses are to Diels-Kranz, Die Fragmente der Vorsokratiker, 6th edn. on wards.) Achilles, Isag. 19 (A 21), places the sun at the centre of its wheel, instead of on the rim of a wheel concentric with the earth. This version is accepted by Martin, ‘Mémoir sur les hypothèses astronomiques des plus anciens philosophes de la Grèce étrangers à la notion de la sphéricité de la terre’, Mémoires de I'Institut national de France, Académic des Inscriptions et Belles- Lettres, 29, ^ème partie (1879), 72–86, and in his earlier days by Zeller: for Zeller's motive and his change of mind see p. 426 n. 4 below. Achilles' version is rightly rejected by Teichmüller, , Studien zur Geschichte der Begriffe (Berlin, 1874), pp. 18–21Google Scholar and 550–2, and by Neuhäuser, , Anaximander Milesius, etc. (Bonnae, 1883), pp. 373–6,Google Scholar and by all more recent scholars. (After the first reference, modern works will usually be cited by the author's name alone.)

^{page 423 note 2} Aet. 2. 21. 1 (A 21). Hippol. Ref. 1. 6. 5 (A 11). Hippolytus' text makes the wheel of the sun 27 times the size of the moon. Diels' lacuna seems the best correction of this, Doxographi Graeci, 560. 5.Google Scholar Earlier it was thought that was simply an error for , by Gruppe, , Die kosmischen Systeme der Griechen (Berlin, 1851), p. 45Google Scholar note, followed by Roeper, , Philologus vii (1852), 608–9.Google Scholar Acceptance of the unamended text of Hippolytus largely vitiates Zeller's later re construction, Die Philosophie der Griechen, etc. 6th edn. by Nestle, Teil 1, Abteilung 1, p. 300 n. 2: for Zeller's motive here and his earlier view see p. 426 n. 4 below.

^{page 423 note 3} Aet. 2. 20. 1 (A 21).

^{page 423 note 4} Tannery, Pour l'hisloire de la science Hellene, etc., 2nd edn. by Diès, p. 94; Burnet, Early Greek Philosophy, 4th edn., p. 68; Diels, ‘Ueber Anaximanders Kosmos’, A.G.Ph. N.F. iii (1897), 231; Mieli, , I Prearistotelici (Firenze, 1916), p. 46;Google ScholarHeath, , Aristarchus of Samos, etc., p. 37.Google Scholar

Earlier it had been suggested that the smaller figure represented the circumference minus the size of the hole for the sun, by Forbiger, , Handbuch der alten Geographic, etc., Band i (Leipzig, 1842 ═ 2nd. edn. Hamburg, 1877), p. 523 n. 57,Google Scholar and by Roeper, op. cit., p. 608, repeated in Zeitschrift fur die Alter-tumswissenschaft, 1852, col. 442.Google Scholar This in effect confuses circumference and diameter, for it makes the circumference of the sun's orbit 27 or 28 times the diameter of the earth. Cf. p. 425 below.

Neuhäuser, p. 398 n. 4, had suggested that the two figures might represent the different distances from the centre and from the edge of the earth. The same reconstruction appears to be intended by Freeman, who writes that ‘27+1 and 18+1 express sun plus earth-ring, and moon plus earth-ring, respectively’, The Pre-Socratic Philosophers: A Companion to Diels, Fragmente der Vorsokratiker, p. 59.

^{page 423 note 5} The Presocratic Philosophers, p. 136 n. 1.Google Scholar Kirk's reasoning is accepted by Guthrie, who suggests that ‘the larger figures are likely to have been some commentator's refinement’, A History of Greek Philosophy, vol. i, p. 95. Kahn likewise suggests that the figure 28 is ‘a corrupt reading’, Anaximander and the Origins of Greek Cosmology, p. 62. We may observe, however, that Anaximander's dealing was recorded by Eudemus, ap. Simpl. De caelo 471. 2–6 (A 19) ═ fr. 146 Wehrli.Google Scholar

At one point Burch also supposes, as Kirk does, that the thickness or width of the rim of the sun wheel would equal the diameter of the earth; and he suggests therefore that the inner and outer radius of the sun wheel is 27 and 28 times the diameter of the earth, ‘Anaximander, the First Metaphysician’, Rev. of Met. iii (1949), 155 n. 41. But the comparison of radius and diameter is implausible.

^{page 424 note 1} This was in fact the intention of Tannery, p. 94, and of Diels, p. 232. It is also the lesson to be drawn from Diels' diagram, p. 236; and the same conclusion could be inferred from some remarks in Burch, p. 155 n. 41.

In fact, of the authors cited above, p. 423 n. 4, Kirk's criticism, that there should be a difference of two units between the inner and the outer diameter, would apply with certainty only to Mieli; for Mieli alone, p. 46 n. 10, explicitly shares Kirk's assumption that the thickness or width of the rim of the sun wheel would be the same as the diameter of the earth. Heath has quite likely fallen into the same error, p. 37, although he is not so explicit as Mieli. Burnet is noncommittal, p. 68.

^{page 424 note 2} Pseudo-Plutarch, Strom. 2 (A 10). Cf. Hippol. Ref. 1. 6. 4 (A 11).

^{page 424 note 3} Aet. 2. 20. 1. There are similar phrases in other passages cited by Diels-Kranz, A 21 and 22.

^{page 424 note 4} Hippol. Ref. 1. 6. 3 (A 11), partly re peated in Aet. 3. 10. 2 (A 25). is Roeper's emendation, p. 609, for . The emendation has been widely, and probably rightly, accepted; but not by Kahn, pp. 55–56 and 81 n. 3.

^{page 424 note 5} Aet. 2. 21. 1 (A 21).

^{page 424 note 6} For example by Kirk, p. 134, and Guthrie, p. 95 (which is inconsistent with the translation on p. 98).

^{page 424 note 7} Strom. 2 (A 10).

^{page 425 note 1} p. 66.

^{page 425 note 2} Hippol. Ref. i. 6. 3 (A II). Cf. Diels-Kranz A 26, and Plato, Phaedo 108 e 4–109 a 8, Tim. 62d 12–63 a 2.

^{page 425 note 3} For Anaximenes, see the passages quoted by Diels-Kranz, 13 A 6, 7, and 20. For Anaxagoras, see 59 A 42 and 88. Cf. Plato, Phaedo 99 b 8 and 108 e 5–109 a 2. Gomperz seems to me wrong to try to associate the explanation of the earth's stability with the idea of a necessarily thin earth. He writes that the earth ‘nur dann ein sicheres Gleichgewicht besitzen konnte, wenn der Durchmesser seiner Grundfläche beträchtlich gröβer war als seine Höhe’, Griechische Denker, vol. i, p. 42.Google Scholar

^{page 425 note 4} p. 136 n. 1.

^{page 425 note 5} Diameters are spoken of by Diels, p. 231, Dreyer, History of the Planetary Systems from Thales to Kepler, pp. 14–15,Google Scholar Mieli, p. 46, Burch, p. 154 (but cf. above p. 423 n. 5), Kahn, p. 62, and Guthrie, p. 95. Circumferences are spoken of by Zeller, 6th edn., p. 300 n. 2, and Burnet, 4th edn., p. 68, although in his first edition, p. 70 n. 92, Burnet spoke of diameters. Radii are spoken of by Taylor, , A Commentary on Plato's Timaeus, p. 163,Google Scholar and by Tannery, , Recherches sur I'histoire de I'astro-nomie ancienne, p. 323, although in Science hellène, p. 94, Tannery speaks of diameters.Google Scholar

^{page 425 note 6} ‘Innumerable Worlds in Presocratic Philosophy’, C.Q..xxviii (1934), 12, cf. p. 15. There is a more deliberate comparison of radius and diameter by Burch, see p. 423 n. 5 above.

^{page 425 note 7} p. 114.

^{page 425 note 8} P. 38.

^{page 425 note 9} 3rd edn., Theil 1, p. 195 n. 3.

^{page 426 note 1} Teichmüller, pp. 16–17; Neuhäuser, pp. 370–1; Zeller, 4th edn., Theil 1, p. 206 n. 4; 5th edn., Theil 1, Hälfte 1, p. 224 n. 2; 6th edn., Teil 1, Abteilung 1, p. 300 n. 2.

^{page 426 note 2} Heath, p. 32.

^{page 426 note 3} p. 90.

^{page 426 note 4} Baccou, , Histoire de la science grecque de Thales a Socrate (Paris, 1951), pp. 76–77. Baccou explicitly rejects the notion that Anaximander's measurements ‘ont … été proposes … de façon purement arbitraire’. He argues also that from the measurement of the angular diameter of the sun and the moon, and from an estimation of the size of the earth, were derived the figures for the distances of the sun and the moon. He adds, however: ‘Certes, je ne me hasarderai pas à reconstituer le procédé employé.’Google Scholar

^{page 426 note 5} Zeller, for example, to avoid this dis crepancy, adopts the reading in Hippolytus (cf. p. 432 n. 2 above). But this would make the sun's orbit 1g X 27 x 3 times the size of the earth's, and the sun's, diameter; which would make the sun ap pear only half the size it does. Earlier, Zeller had dismissed the reading in Hippolytus as ‘wohl ein Miβverstandnis oder ein Schreibfehler’, 3rd edn., Theil 1, p. 195 n. 3 But at the same time, in order not to violate the sun's angular diameter, Zeller had adopted Achilles' account of the sun at the centre of its wheel (see p. 431 n. 1 above). Sartorius complicated and implausible reconstruction is also in part designed to avoid too great a discrepancy between Anaximander's system and the sun's angular diameter, 'Die Entwicklung der Astronomie bei den Griechen bis Anaxagoras und Empedokles, in besonderem Anschluβ an Theophrast, Zeitschrift für Philosophic und philosophische Kritik, N.F. lxxxii (1883), 217–24, especially pp. 221–2.Google Scholar

^{page 426 note 6} Aet. 2.2 5. 1, 29. 1 (A 22). 2. 13. 7 (A 18).

^{page 426 note 7} Aet. 2. 25. 1 (A 22).

^{page 426 note 8} Tannery, Science hellène, pp. 94–95; Burnet, p. 68; Diels, p. 231, cf. p. 236; Mieli, p. 46; Heath, p. 37. In differing degrees, Kirk, p. 136, Kahn, p. 62, and Guthrie, p. 95, fail to accept the usual reconstruction, in conformity with Kirk's objection to the usual reconstruction of the two figures for the sun wheel, see p. 432 n. 5 above.

^{page 427 note 1} Aet. 2. 15. 6 (A 18). Hippol. Ref. 1. 6. 5 (A 11). Hippolytus writes in the singular in section 4, and add. Diels> in section 5. Without intending to prejudge the solution to this difficulty, I have for convenience written of the star wheel in the singular throughout the present article.

^{page 427 note 2} Tannery, , Science kellène, p. 95; Diels, p. 231, cf. p. 236; Mieli, p. 46; again, Kirk, pp. 136–7, Kahn, p. 62, and Guthrie, pp. 95- 96, in one way or another do not accept the usual reconstruction. Burnet, p. 68, and Heath, p. 38, fail to mention the larger figure but they make no explicit objection to it.Google Scholar

^{page 427 note 3} There is a useful discussion of this subject by Vlastos, , ‘Equality and Justice in, Early Greek Cosmologies’, C.P. xlii(1947) 156–78.Google Scholar

^{page 427 note 4} This fact may be the foundation for the report that Anaximander's were equidistant, Aet. 2. 1. 8 (A 17); for the opposite view, attributed to Epicurus and Democritus, see also Hippol. Ref. 1. 13. 3 (68 A 40). Cornford, p. 12, rightly infers the equidistance of Anaximander's celestial wheels, apparently from Diels' diagram, p. 236, and suggests the comparison with the testimony in Aetius; but Cornford's statement of Anaximander's measurements is inaccurate; see p. 425 above.

^{page 428 note 1} Aet. 2. 31. 1 (31 A 61).

^{page 428 note 2} Id. 2. 21. I (12 A 21). Cf. Diog. 2. 1 (12 A 1), Aet. 2. 21. 2 (32 A 56), referred to Empedocles by Diels, Dox. 351.

^{page 428 note 3} Aet. 2. 13. 11 (31 A 54). A similar theory is attributed to Anaximenes at 2. 14. 3 (13 A 14), but mention of suggests that the first part of the entry in fact belongs to Empedocles.

^{page 428 note 4} Aet. 2. 1.4 (31 A 50).

^{page 428 note 5} It is conceivable that the wandering stars, which are mentioned at Aet. 2. 13. 11 (31 A 54), were left to occupy the place of Anaximander's moon.

^{page 428 note 6} Proposition 7, p. 376 Heath. Aristarchus' conclusion is repeated in a looser form by Plutarch, , De facie, etc., 925 c.Google Scholar

^{page 429 note 1} Diels, Dox. 63. Karsten, , Empedoclis Agrigentini carminum reliquiae, etc. (Amstelodami, 1838), p. 433 n. 136.Google Scholar Diels is followed by Millerd, , On the Interpretation of Empedocles (Diss. Chicago, 1908), p. 65.Google Scholar

^{page 429 note 2} Graecarum affectionum curatio 4. 24 ═ Dox. 362.

^{page 430 note 1} Pliny, N.H. 2. 84; Censorinus, De die natali, 13. 3–5; Martianus Capella, De nuptiis Philologiae et Mercurii, 2. 169–99. Cf. Heath, p. 113.Google Scholar

^{page 430 note 2} N.H. 2. 83. A work by Sulpicius on eclipses is cited again by Pliny, N.H. 2. 53. Hultsch reckons that Pliny's source is the sixth book of Varro'sDisciplinae, ‘Posei- donios über die Groβe und Entfernung der Sonne’, Abh. Kgl. Gesellschaft der Wissen-schaften zu Göttingen, Philog.-histor. Klasse, N. F. Band 1, No. 5, p. 11 n. 1.

^{page 430 note 3} For Eratosthenes, see Strabo, 2. 5. 7; for other references and discussions see Heath, p. 339. For Hipparchus, see Strabo, 2. 5. 34, cf. Heath, pp. 343–4. The same measurement is attributed to ‘Pythagoras’ by Censorinus, loc. cit.

^{page 431 note 1} pp.114–15.

^{page 431 note 2} Astronomie ancienne, pp. 332–3.Google Scholar

^{page 431 note 3} There is a similar ambiguity over Plato's figures in the Timaeus, 35 b, see Taylor's commentary, pp. 162–4. The inter pretation of Plato recorded by Porphyry, ap. Macrobius, In Somnium Scipionis, 2, 3. 13–16, is in fact the equivalent of the interpretation we are arguing for here in the passage of Pliny, namely that ‘triple’ means triple the number last mentioned, and not the number first mentioned.

^{page 432 note 1} A much freer Pythagorean extension of Anaximander's idea is recorded by Plutarch, , De anim. procr. in Tim., 1028 B-c. The <radius of the> central fire is 1, and the dis tances from the centre to the counter-earth, earth, moon, Mercury, and so on, follow the sequence 3, 3², 3³, etc.+central+fire+is+1,+and+the+dis+tances+from+the+centre+to+the+counter-earth,+earth,+moon,+Mercury,+and+so+on,+follow+the+sequence+3,+32,+33,+etc.>Google Scholar

^{page 432 note 2} It may be noted that no calculation can be founded on the supposed equality of Empedocles' elements. (The phrase , fr. 17. 27, has been inter preted in this sense by a number of scholars.) For if Empedocles had consciously and de liberately composed his world of elements equal in volume, then the distance from the earth's surface to the firmament would have been only of the earth's diameter, which is in itself ridiculously small, and would in particular make it impossible for the sun to be equal in size to the earth, as we have noted Empedocles said it was. The question of equal volumes for Empedocles' elements I have discussed in more detail elsewhere.

^{page 432 note 3} De facie, etc., 925 B-C.

^{page 432 note 4} Fr. 46. Cf. Diels, Poet. Phil. Fragm., ad loc.

^{page 432 note 5} I may perhaps add that the part of this tradition which I have not attempted to deal with is that represented by Plato's Timaeus. Cornford rightly observes that Plato's system is not founded exclusively on a musical scale, but in part on non-musical numerical proportions, Plato's Cosmology p. 6–72.