¹ CQ ix (1959) 294–309.

² Guthrie, W. K. C., A History of Greek Philosophy— Vol. i, C.U.P. 1962.Google Scholar

³ CQ ix (1959) 304.

⁴ Guthrie, op. cit. 47–9.

⁵ E.g. Heath (Aristarchus of Samos), Burnet, Kirk & Raven, Guthrie—cf. 299 f. of my article.

⁶ In this connexion, Kirk, and Raven, 's sensible remark deserves to be quoted (The Presocratic Philosophers, p. 7)Google Scholar, ‘Thus it is legitimate to feel complete confidence in our understanding of a Presocratic thinker only when the Aristotelean or Theophrastean interpretation, even if it can be accurately reconstructed, is confirmed by relevant and well-authenticated extracts from the philosopher himself’—a counsel of perfection which one can hardly expect to be exemplified in their own book.

⁷ Fotheringham, J. K. in JHS xxxix (1919) 164–84CrossRefGoogle Scholar; Burkert, W., Weisheit und Wissenschaft, 1962, 312.Google Scholar

⁸ Nat. Hist. ii 31 (DK 12A5), ‘obliquitatem eius [sc. zodiaci] intellexisse, hoc est rerum foris aperuisse, Anaximander Milesius traditur primus olympiade quinquagesima octava, signa deinde in eo Cleostratus, et prima arietis ac sagittarii, sphaeram ipsam ante multo Atlas.’ In view of the ready acceptance by most modern scholars of the truth of Pliny's statements here, it seems strange that the last five words of this quotation have been so sadly neg lected … do they not provide ‘incontrovertible evidence’ for the existence of a fully-developed, prehistoric, astronomical system—in Atlantis, of course? For juster estimates of Pliny's competence in scientific matters, see Bunbury, , History of Ancient Geography, ii 373 ff.Google Scholar and Kirk and Raven, op. cit. 103 n. 1.

The curious ambivalence exhibited by modern scholars in their treatment of the doxographical evidence, to which I have already drawn attention (CQ (1959) 305 n. 3), is well illustrated in Burkert's book (which is nonetheless useful for its comprehensive documentation). For example, he accepts Pliny's evidence without question, despite the mention of Atlas, but rejects (rightly—see below) Aëtius' attribution of knowledge of the planets to Anaximander (Aët. ii 15.6 = DK 12A18) which ‘beweist nichts, da Metrodor und Krates von Mallos in das Lemma mit eingeschlossen sind’ (p. 289 n. 68).

⁹ Wasserstein, A. in JHS lxxv (1955) 114–16.CrossRefGoogle Scholar

¹⁰ CQ ix (1959) 306.

¹¹ Neugebauer, O., The Exact Sciences in Antiquity, 2nd ed. 1957, 102 Google ScholarPubMed; cf. 25 and 140. Kahn, (Anaximander and the Origins of Greek Cosmology, 1960, 91–2)Google Scholar, as part of his attempt to justify his thesis of the advanced, mathematical nature of Anaximander's cosmological thought—on the erroneousness of Kahn's views, see further below—cites the first passage from the first edition (1952) of Neugebauer's invaluable book, without apparently being aware of the significant lowering of the date for the introduction of the zodiac divided into 360° in the second edition, which makes nonsense of Kahn's claim that ‘most, if not all, of this science had reached Miletus by the middle of the sixth century’.

¹² Ed. by Manitius, Dresden, 1888—a copy of this doctoral dissertation is very difficult to come by.

¹³ See my Geographical Fragments of Hipparchus, 1960, 148–9.

¹⁴ See his Commentaria in Arati et Eudoxi Phainomena (ed. Manitius, , Teubner, 1894)Google Scholar passim, and the quotations from his other astronomical works (which I am in the process of editing) in Ptolemy's Almagest.

¹⁵ This holds good for all the extant works of e.g. Autolycus, Euclid, Aristarchus, and Archimedes. There is, however, one piece of evidence which might seem at first sight to suggest that the use of degrees was known in the third century B.C. in Alexandria; in Almag. vii 3 Ptolemy lists the declinations of a number of stars as observed by himself, by Hipparchus, and by Timocharis and Aristyllus, two Alexandrian astronomers who were active between 295 and 280 B.C., and in each case Ptolemy gives the data in degrees north or south of the celestial equator. This appears to contradict our other evidence (cf. Pannekoek, A., A History of Astronomy, 1961, 124 Google Scholar ad fin.) which all points to the late introduction of the 360° division of the circle, not before the second century B.C. Yet, if degrees were in use at the time of Timocharis and Aristyllus, why did not Aristarchus and Archimedes use them instead of clumsy circumlocutions involving fractions of a certain segment? The latter at least had close connexions with Alexandrian scientists including Eratosthenes (cf. Heath, , The Works of Archimedes xvi Google Scholar), who likewise did not use degrees (see below). It is hardly conceivable that Aristarchus, for example, would have chosen to say that at quadrature the moon's distance from the sun is ‘less than a quadrant by one-thirtieth of a quadrant’ (ἔλασσον τεταρτημορίον τῷ τοῦ τεταρτημορίον τριακοστῷ) if he could have expressed exactly the same meaning by ‘87°’ (μοίρας πζ). Either we must assume that Timocharis and Aristyllus knew and used the circle graduated into 360° but that this was not taken up by scientists again until 100 years later—which in view of the obvious convenience of the usage seems incredible; or (and this is the most likely explanation) it was Ptolemy who tacitly converted the observations of Timocharis and Aristyllus (originally given in the customary fractions of a segment) into degree figures in order to make clearer the comparison with his own and Hipparchus' results. It is noteworthy that Ptolemy emphasises the inaccuracy of these earlier observations, which he characterises as (Almag. vii 1—ed. Heiberg, ii 3, 4) and πάνυ ὁλοσχερῶς εἰλημμέναι (id. vii 3—18, 3).

¹⁶ Ed. Heath, , Aristarchus of Samos 352.Google Scholar

¹⁷ §16, ed. Heiberg, ii 226.

¹⁸ Cf. Bouché-Leclercq, , L'astrologie grecque, 1899, 60 n. 2Google Scholar; of the other divisions he mentions, that into 144 parts (Sext. Emp., adv. astrol. §9 = adv. math. v §9) is simply a variant used by some of the Chaldaean astrologers, most of whom Sextus makes clear used the 360° division (i.e. 12 zodiacal signs of 30° each), for a particular astrological doctrine. A division into eight parts, cited by Bouché-Leclercq (279 n. 2) from Hyginus, astron. iv 2, is merely a method of avoiding fractions to express the ratio of the longest day to the shortest night at the summer solstice, i.e. 5:3 (equivalent to a latitude of 36°52′, where at the summer solstice five parts of the sun's diurnal circuit would be above the horizon and three parts below), instead of 7½:4½ on a division of the circle into twelve parts; it cannot be taken as evidence for a commonly-used division of the circle into eight. Bouché-Leclercq also cites (475 n. 2) a division of the zodiac into 365 parts from Censorinus, frg. 2 (not 3, as in the citation), 5 (p. 57, ed. Hultsch); but Censorinus' account (which, anyway, mentions the 360° division) is very garbled—he evidently confuses zodiacal signs, which are equal segments of 30° each, with zodiacal constellations, which are of unequal size, since he talks of ‘signa … quorum quaedam minora, quaedam amphora’, and then goes on to say ‘sed conpensatio in quinque partes creditur adplicari, ut sint omnes signiferi partes CCCLXV’, apparently a muddled reference to the fact that the sun takes 365 days and a little more to traverse the full circle. It should be noted that Bouché-Leclercq was writing before our understanding of the methods of Babylonian mathematics and astronomy and their historical interaction with Greek knowledge had reached its present (still imperfect) stage.

¹⁹ For a full discussion, see my Geographical Fragments of Hipparchus 167–8.

²⁰ See Cherniss, H., Aristotle's Criticism of Presocratic Philosophy, 1935 Google Scholar, some of the results of which he summarised in Journal of the History of Ideas xii (1951); for the inevitable reaction against the criticism of Aristotle's merits as an historian of thought, see Guthrie, W. K. C. in JHS lxxvii pt. 1 (1957)Google Scholar and his History of Greek Philosophy, vol. i 41–3.

²¹ CQ ix (1959) 301 ff.

²² On the whole subject of sundials and ancient time-measurement, see Bilfinger, G., Die Zeitmesser der antiken Völker, 1886 Google Scholar; Daremberg and Saglio, s.v. ‘Horologium’, iii 256–264—which contains a regrettable number of wrong references; RE, s.v. ‘Horologium’, viii 2416 f.; Diels, H., Antike Technik, 3rd ed. 1924, ch. 7Google Scholar; Basserman-Jordan, E. v., Die Geschichte der Zeitmessung und der Uhren, Bd. i Google Scholar, Lief. E by Drecker, J., Die Theorie der Sonnenuhren, 1925 Google Scholar; Kubitschek, W. K., Grundriss der antiken Zeitrechnung, 1928 Google Scholar: references to Anaximander's advanced astronomical knowledge should be discounted in all the above.

²³ In what follows, a geocentric universe is assumed and the observer is supposed to be situated north of the equator between the tropic of Cancer (23½°N. latitude) and the arctic circle (66½°N. latitude)—for a general description of Greek astronomical theory in its developed form, see my paper in BICS xi (1964) 43–53.

²⁴ Another method of recognising the two limits of the sun's movement would be to note that me shadow of a fixed object on the ground is shortest at the northern limit and longest at the southern at the same hour of the day in each case; but this already involves the assumption that the time of day is determinable on a theoretical division of it into equal parts, which is highly improbable for the early stages of Greek astronomy—cf. Neugebauer, O., ‘The Egyptian “Decans”’ in Vistas in Astronomy, i (1955, dedicated to Stratton, F. J. M.) 51 Google Scholar, ‘It is only within theoretical astronomy of the Hellenistic period that the Babylonian time-reckoning with its strictly sexagesimal division, combined with the Egyptian norm of 2 × 12 hours, led to the 24 “equinoctial hours” of 60 minutes each and of constant length.’

²⁵ As we are told was the opinion of Xenophanes and Heraclitus.

²⁶ Od. xv 404—see Stanford ad loc.

²⁷ Works and Days 564 and 663—even here there is a slight element of uncertainty, since both these lines occur immediately after passages bracketed in Rzach's text as having been proscribed by Plutarch.

²⁸ E.g. Hesiod tells us (WD 564 ff.) that when Arcturus rises in the evening, 60 days after the winter solstice, and is visible all night, the vines must be pruned.

²⁹ E.g. Thuc. vii 16; viii 39.

³⁰ For example, in Ptolemy's obliquity table in Almag. i 15, at the beginning, i.e. near the equinox, 1° on the ecliptic is equivalent to about o°24′ on the meridian, while at the end, i.e. near the solstice, 1° on the ecliptic is equivalent to less than o°1′ on the meridian.

³¹ See the list of shadow lengths at different lati tudes (undoubtedly taken from Hipparchus) given in Almag. ii 6.

³² Ptolemy mentions (Almag. v 10, ed. Heiberg, i 400, 13) that in lunar observations errors of ⅛th of an hour could be expected, and this was at the highest point of Greek astronomical development. For the inaccuracies of water-clocks, see Fotheringham, J. K. in CR xxix (1915)Google Scholar and cf. Rome, A., Annales de la Société Scientifique de Bruxelles lviii (1938) 11–12.Google Scholar

³³ As Nilsson, remarks (Die Entstehung und religiöse Bedeutung des griechischen Kalenders, (2nd rev. ed. 1962) 27–8 n. 3)Google Scholar, ‘Die Sonnenwenden sind nach den Wendepunkten der Sonne an einem gewissen Ort leicht zu beobachten, die Tag- und Nacht-gleichen können, da die Sonnenbahn kontinuierlich ist, erst durch Berechnung festgestellt werden’.

³⁴ This is clear from the methods used by Hipparchus and Ptolemy to determine the equinoxes (Almag. i 12, with Theon's commentary ad loc.). Two of the instruments employed, the meridional armillary and the plinth, have to be accurately aligned in the plane of the meridian perpendicular to the plane of the horizon; readings were then taken of the height of the sun at midday at each of the solstices, and the point exactly half-way between these two readings represented the zenithal distance of the equator, which could therefore be marked on the instrument. The actual time of the equinox could then be determined roughly by noting when the midday shadow of the pointer coincided as nearly as possible with the marked equator; for greater accuracy (since the moment of intersection of ecliptic and equator need not be at midday) several readings were taken on days near the equinox and interpolation carried out by means of the obliquity table—but this was a refinement which was not possible before Hipparchus. A third instrument, the equinoctial or equatorial armillary, consisting simply of a large bronze ring of uniform cross-section, had to be placed exactly in the plane of the equator (previously determined by one of the other two methods), and would then mark the time of the equinox directly by the moment when the shadow of the upper part of the ring exactly covered the lower part; Ptolemy specifically draws attention to the difficulty of ensuring that the ring was accurately set in the plane of the equator, a slight shift in position necessarily causing a large error in the time of the equinox (Almag. iii 1, ed. Heiberg 197, 11 ff.). For a detailed description of these and other ancient astronomical instruments, see my paper in Journal of the British Astronomical Association lxiv (1954) 77–85. The important thing to realise is the relatively advanced nature of the theoretical knowledge that must underlie a problem such as the determination of the equinoxes; without the fundamental concepts of equator, tropics, and ecliptic on the celestial sphere, the equinoxes are meaningless.

³⁵ A minor, but instructive, example of the manner in which the alleged scientific achievements of the Presocratics are gratuitously augmented by the doxo-graphers is provided by the three citations at the beginning of this article. Diogenes Laertius contents himself with saying that Anaximander was the first to discover and set up a gnomon (the word in this context means simply a vertical marker casting a shadow) ‘which marks solstices and equinoxes’, σημαίνοντα (note the present participle) giving a generic description of this instrument, thus avoiding stating in so many words that Anaximander himself actually observed solstices and equinoxes. By Eusebius, Anaximander is credited with the ‘construction’ of more than one gnomon (γνώμονας κατεσκεύασε—probably a rationalisation of the otiose addition καὶ ὡροσκοπεῖα κατεσκεύααε in Diogenes, which reads like a gloss) for the express purpose of distinguishing (πρὸς διάγνωοιν) the dates and hours of solstices and (presumably—but why ἰσημερίας in the singular? Another gloss?) equinoxes. In the Suda, finally, not only is knowledge of all the above attributed to Anaximander, but we are assured that he treated the whole subject on geometrical lines! It remains merely for Kahn to put the finishing touches to this imaginary edifice by assuring us (op. cit. 93) that ‘…in the cosmos of Anaximander the orbits of the sun and moon are represented by definite geometric (and probably mechanical) structures’—whatever this may mean—and by citing with approval (95) Diels' unfortunate remark (Archiv für Geschichte der Philosophie (1897) 237) ‘Anaximander steht dem Kosmos Kepplers näher als Hipparchos und Ptolemaios’—but see below for some more sensible remarks by Diels.

³⁶ E.g. Meteor. ii 6.364 b 1; ii 2.371 b 30; iii 5.377 a 12 and 14.

³⁷ 370c—variously attributed to the fourth or first century B.C. according to Leisegang, H. in RE s.v. ‘Platon’ col. 2366.Google Scholar

³⁸ §11 ( Corpus Medicorum Graecorum i, ed. Heiberg, , 67, 1927)Google Scholar—the author tells us that the following days are the most dangerous: The words underlined are ignored in Littré's translation (torn, ii (1840) 52) and in Adams', The Genuine Works of Hippocrates, (1939) 31 Google Scholar, and rendered ‘sogennanten’ by Kapferer, R., Die Werke des Hippocrates (Teil 6 (1934) 40)Google Scholar and ‘so reckoned’ by Jones (Loeb Hippocrates i 105). There seems to be no parallel for νομίζεσθαι used in this last sense, and ‘sogennanten’ hardly helps the meaning; one is tempted to read λογιζόμεναι, ‘calculated’, which gives the right sense and might easily have been misread by a scribe. At any rate, it is clear that there is a contrast between the solstices, which can be mentioned without any qualification as well-known phenomena, and the equinoxes, which as a less familiar concept require an explanatory description.

³⁹ The locus classicus for Greek astronomical calendars is Geminus, Isagoge, ch. 8; this is discussed at length by Ginzel, , Handbuch der mathematischen und technischen Chronologie, ii (1911) 366 ff.Google Scholar and Heath, , Aristarchus of Samos (1913) ch. 19, 284–96.Google Scholar Both these scholars appear to accept a very early date for Homer, and consequently tend to assign knowledge of the basic parameters to an earlier period than is warranted by the evidence as we can now interpret it. I have stated that the Metonic cycle was ‘the first scientifically formulated intercalation system’. Geminus describes what purports to be an earlier cycle, the octaëteris, consisting of eight years containing 2,922 days and ninety-nine lunar months including three intercalary ones; but there are several difficulties in accepting his account at its face value (in particular, it assumes a figure, 365¼ days, for the length of the year, which was not discovered until Callippus—cf. Heath, op. cit. 288–92), and according to Censorinus (de die natali, 18, 5) the octaëteris was usually ascribed to Eudoxus, although other names (including Cleostratus) were also connected with it.

⁴⁰ Cf. van der Waerden, B. L., ‘Greek Astronomical Calendars’, JHS lxxx (1960) 170 Google Scholar, ‘This date is given by three independent witnesses and accepted by all chronologers’.

⁴¹ Ptolemy, , Almag. iii (ed. Heiberg, i 207, 12 ff.).Google Scholar

⁴² De die natali, 18, 9.

⁴³ This was in fact the ‘festival year’ of the Athenian calendar—cf. Meritt, B. D., The Athenian Year (1961) 3 f.Google Scholar

⁴⁴ E.g. in the calendar that appears as ch. 17 of Geminus' Isagoge (which Manitius includes in his Teubner edition of 1898, but proves—pp. 280–2—that it belongs to a period 100 years earlier) p. 216 §3, [sc. ] and p. 228 §10, for the vernal equinox. On the parapegmata, see especially Rehm, A., ‘Parapegmastudien’, Abh. d. Bayerischen Akad. d. Wiss., Phil.-hist. Abt., Neue Folge, Heft xix (1941)Google Scholar, and his articles ‘Episemasiai’ and ‘Parapegma’ in RE, Bd. vii (1940) cols. 175–98 and Bd. xviii, 4 (1949) cols. 1295–366; cf. also my Geographical Fragments of Hipparchus 111–12.

⁴⁵ See especially Pritchett, W. K., ‘Thucydides v 20’, Historia, Bd. xiii, Heft 1 (Jan. 1964) 21–36 Google Scholar, with references to the more recent work done on the Athenian calendar.

⁴⁶ Ed. F. Blass, 1887, p. 25—the papyrus (the text of which shows many errors) was written between 193 and 165 B.C. and is, of course, not by Eudoxus himself; it may be a student's exercise with later information added.

⁴⁷ Cf. Heath, , Arist. 200 and 215–16Google Scholar; Pannekoek, op. cit. 111.

⁴⁸ Almag. iii 1 (ed. Heiberg, , 194–5).Google Scholar

⁴⁹ Ptolemy several times emphasises the approximate nature of Meton's and Euctemon's observations—e.g. Almag. iii 1 (Heib. p. 203, 13), [i.e. Meton, Euctemon and Aristarchus] παραδεδομένας (sc. θερινὰς) and again (Heib. p. 205, 15),

⁵⁰ Cf. his discussion of ‘The Doxography’, 28–71, passim, and particularly 59 ff.

⁵¹ Cf. p. 88, ‘Since the circles of the sun and moon are said to “lie aslant” (λοξὸν κεῑσθαι), Anaximander must have been familiar with the inclination of the ecliptic relative to the diurnal path of the stars. Pliny also attributes this knowledge to him, and other sources speak of his interest in solstices, equinoxes, and the measurement of the “diurnal hours”.’ Needless to say, there is not the slightest indication that Kahn has considered any of the implications of Anaximander's possession of such knowledge.

⁵² Typically, Kahn informs us (p. 103) that ‘here the link between meteorology and astronomy is dramatically established’!

⁵³ Probably to be accepted for Anaximander and undoubtedly a bold conception for his time, but hardly to be regarded as incontrovertible evidence for his mathematical insight.

⁵⁴ Pour l'histoire de la science hellène, 90 ff.

⁵⁵ As Diels remarks (op. cit. 232), ‘In Wirklichkeit ist diese ganze Zahlenspeculation nur eine dichterische Veranschaulichung’, and ‘Die Abmessung besagt also nicht viel mehr, als wenn die Inder drei Vischnuschritte von der Erde zum Himmel rechnen’. Curiously, Kahn cites (p. 95) the last statement as if it were an original judgment by Heath (Arist. 38), whereas it is clear from the context that Heath is summarising Diels' views.

⁵⁶ Cf. my remarks in CQ ix (1959) 304 ff.

⁵⁷ This was the unit which later astronomers (e.g. Aristarchus, Hipparchus, and Ptolemy) used in their attempts to estimate the sizes and distances of the sun and moon—see Heath's discussion (Arist. 337–50)—and it is undoubtedly recollection of this fact that has led both modern scholars and ancient commentators alike to assume the same for Anaximander.

⁵⁸ To the references I give in CQ ix (1959) 295–6, now add Neugebauer, , Proc.Amer.Philos.Soc. cvii (1963) 533–4Google Scholar, where he is even more emphatic than previously: ‘even the methods of the Seleucid period would not explain the alleged approximate prediction by Thales of a solar eclipse for Ionia’; ‘That Thales had even the faintest idea of the problems involved is out of the question’.

⁵⁹ Cf. Nilsson, op. cit. 31 and 45.

⁶⁰ In this connexion, Kahn's statement (p. 75), ‘In general, the Theophrastean doxography (where it can be reconstructed) is fully reliable for the detailed theories of heaven and earth’ (my italics), is open to considerable doubt. It seems to me that it is precisely in the details that one might expect the maximum distortion, since it is here that consciousness of later knowledge would cause the doxographers to interpret the evidence as nearly as possible in accordance with the notions of their own time—cf. CQ ix (1959) 302 ff.

⁶¹ Kirk, notes the ‘superficial glance which was all that many Pre-socratics seem to have considered necessary’ (Mind lxix (1960) 329 Google Scholar); cf. Popper, K. R., ‘Back to the Pre-Socratics’, Papers of the Aristotelian Society, Oct. 1958, p. 3 Google Scholar, ‘…but most of them [the ideas of the Presocratics], and the best of them, have nothing to do with observation’. However, when he goes on to say (p. 6), ‘thus it was a speculative and critical argument … which almost led him [Anaximander] to the true theory of the shape of the earth; and it was observational experience which led him astray’, Popper is greatly overstating his case; it was incomplete observation, not sufficiently thought about, that was the hindrance—observation could and eventually did show that the simplest explanation of all the phenomena was to assume a spherical earth.

⁶² As, indeed, it did in the atomist theory of the universe, where the astronomical ideas of Leucippus and Democritus closely follow the naïvetées of Anaximander, Anaximenes, and Anaxagoras—see Heath, , Arist. 121–9.Google Scholar

⁶³ Here I am in full agreement with B. L. van der Waerden, Die Astronomie der Pythagoreer (1951) as also on the strong Pythagorean influence on Plato's astronomical ideas; but on a number of important points—e.g. attribution of knowledge of the obliquity of the ecliptic to Anaximander and Cleostratus (p. 14), and belief in the Pythagorean origin of the concept of epicycles and eccentrics to represent the movements of the planets (pp. 37–49; the argumentation here is particularly unconvincing), and in the axial rotation of the earth in Platonic astronomy—van der Waerden goes far beyond the evidence and his views cease to be tenable. Burkert, on the other hand, goes too far in the opposite direction in denying Pythagorean influence on Plato's astronomy except for the doctrine of the harmony of the spheres and the spatial ordering of the planets (op. cit. p. 315).

⁶⁴ I am assuming that a view of the universe which attempts to comprehend all astronomical phenomena within a single, unified mathematical system represents a more advanced stage of astronomy than one where computational accuracy alone makes possible the prediction of the characteristic phenomena of, e.g., the moon and the planets without any underlying cinematical model at all. The latter stage is represented by Babylonian astronomy of the Seleucid period, which (as far as we can judge from the available cuneiform texts) operated without any knowledge of the fundamental concepts of the spherical earth set in the middle of the celestial sphere, of the obliquity of the ecliptic, and of geographical latitude and longitude; these are all Greek discoveries and in comparison with their fertility, the arithmetical methods of Babylonian astronomy proved sterile, useful as they were in providing some of the essential parameters in the initial stages of Greek mathematical astronomy. On the whole question, see the works (cited above) of Neugebauer, who remains the soundest guide despite a tendency to underestimate the importance of Hipparchus, which I hope to demonstrate elsewhere.

⁶⁵ This was the real impetus towards the study of the heavens, and the difficulties encountered in the attempt to measure time accurately by the motions of sun and moon (difficulties which it is all too easy to underestimate) provided the chief problem for Greek astronomy throughout most of its history. It was not until a solution to this problem had been found that other considerations, such as those implicit in the well-known phrase σῴζειν τὰ φαινόμενα and the working out of mathematical theories to account for the movements of the planets, became of greater moment. The point is clearly brought out in the Timaeus, where Plato explains that the Demiurge created the sun, moon, and planets expressly to enable men to grasp the general concept of time (38c); but, as is specifically stated later, very little was known about the periods of the planets ( 39C).

⁶⁶ Whose influence on the development of Greek astronomy has perhaps been underrated, and whose astronomical ideas deserve further investigation— Cornford, (Plato's Cosmology, 1937)Google Scholar has by no means said the last word on it, as witness recent attempts (to me unconvincing) to deny the sphericity of the earth for Plato; cf. Rosenmeyer, T. G., ‘Phaedo 111 C 4 ff.’ CQ vi (1956) 193–7CrossRefGoogle Scholar; Calder, W. M. III, ‘The spherical earth in Plato's Phaedo’, Phronesis iii (1958) 121–5CrossRefGoogle Scholar; Rosenmeyer, , ‘The shape of the earth in the Phaedo: a rejoinder’, Phronesis iv (1959) 71–2CrossRefGoogle Scholar; Morrison, J. S., ‘The shape of the earth in Plato's Phaedo ’, Phronesis iv (1959) 101–19.CrossRefGoogle Scholar

⁶⁷ See the quotations from Eudoxus in Hipparchus' commentary (ed. Manitius. Teubner, 1894) on the astronomical poem (the Phaenomena) of Aratus, itself a versification of Eudoxus' work.

⁶⁸ De sphaera quae movetur and De ortibus et occasibus, ed. Mogenet, J. (Louvain, 1950).Google Scholar

⁶⁹ Phaenomena, ed. Heiberg, (Teubner) viii 1916.Google Scholar

⁷⁰ Whose astronomical work as a whole has not yet received individual treatment— Gisinger, F.'s Die Erdbeschreibung des Eudoxus von Knidos, 1921 CrossRefGoogle Scholar (Στοιχεῑα, Heft vi) is concerned only with Eudoxus' geographical work; cf. Huxley, G. L. in Greek, Roman and Byzantine Studies iv (1963) 83–96.Google Scholar

⁷¹ Cf. Neugebauer, , Proc.Amer.Philos.Soc. cvii (1963) 534.Google Scholar

⁷² For a beguiling example, see West, M. L., ‘Three Presocratic Cosmologies’, CQ xiii (1963) 154–76CrossRefGoogle Scholar, who says confidently about Thales (p. 173), ‘his lost cosmology can be recovered by simple inference’!!