The Pythagoreans and later pre-Socratics

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ASPECTS OF GREEK AND ROMAN LIFE General Editor: Professor H. H. Scullard EARLY GREEK ASIRONOMY to Aristotle D. R. Dicks THAMESAND HUDSON

THE PYTHAGOREANS CHAPTER IV THE PYTHAGOREANS AND LATER PRE-SOCRATICS AS WE HAVE ALREADY SEEN, the concepts of periodicity, sphericity, and circular motion as applied to the universe as a whole are already present in the work of Heraclitus, Parmenides, Empedocles, and Anaxagoras; but astronomical thought is still in the prescientific stage, and the idea of the celestial sphere is still far from being worked out in detail. The nearest approach in the PreSocratic period to an astronomical scheme which might possibly have taken the place of the concept of the celestial sphere is in the system attributed to the later Pythagoreans of the last half of the fifth century. Now it has been said (Guthrie, vol. i, p. 146) that ‘The history of Pythagoreanism is perhaps the most controversial subject in all Greek philosophy’, and “No one can claim even to have plumbed what a modern scholar has despondently called “the bottomless pit” of research on the Pythagoreans’. Here we are concerned only with the role of the Pythagoreans in the history of astronomy; but even to elucidate this some attention must be paid to the difficulties peculiar to any discussion of Pythagorean beliefs. Put very briefly, the main problem is to try to distinguish the teachings and discoveries of Pythagoras himself from those of his successors in the school which he founded, and which continued as a recognized body of doctrines some two hundred years after his death — and to differentiate between these successors. The problem is complicated by several factors: (a) Pythagoras himself, who founded the Pythagorean brotherhood in the latter part of the sixth century Bc at Croton in south Italy, left no writings; (b) it was a religious and mystical association or sect, as well as a philosophical school, which had strict rules of secrecy concerning its teachings; (c) there was a strong tendency for later writers to 62 AND LATER PRE-SOCRATICS 63 attribute as many discoveries as possible to the Master, who rapidly became an almost superhuman figure — unhistorical legends about him were already circulating in Aristotle’s time; (d) the original brotherhood, which had by this time set up branches in many towns of Magna Graecia, was forcibly disbanded in the middle of the fifth century, and its members dispersed throughout Greece carrying their teachings with them; and finally (e) the sources which purport to tell us most about the movement, namely the so-called Lives of Pythagoras by Porphyry and Iamblichus (Neo-Platonists of the third and fourth centuries AD), at best go back to fourth-century Bc accounts which were already uncritical in character (as just mentioned), and at worst are patent amalgams of Pythagorean, Orphic, and Neo-Platonic doctrines. In fact, as in the case of Thales, the tertiary sources are utterly unreliable for Pythagoras himself. Of the secondary sources, Herodotus mentions the Pythagoreans once (ii, 81) and Pythagoras once (iv, 95), both times in connection with the doctrine of transmigration and the immortality of thesoul. Plato, who was undoubtedly greatly influenced by Pythagorean teaching, and not least in his astronomical ideas (as we shall see later), yet names Pythagoras only once (Rep. x, 600b, where he contrasts him favourably with Homer for setting a good example for his followers to emulate), and the Pythagoreans once (Rep. vii, 530d, where Socrates draws attention to the importance attached by the Pythagoreans to the sister sciences of astronomy and harmonics-see pp. 108f.). Aristotle, in the extant works, makes only two incidental references to Pythagoras, one of which occurs in a passage where the text is disputed (Met. A 5, 986430), and neither of which gives any information about him. (The other passage is Rhet. 1398b14, where the name occurs in a sentence illustrative of inductive reasoning.) On the other hand, Aristotle frequently mentions the Pythagoreans, whom he sometimes designates as of xaAovpevor Iudayéperor, ‘those called Pythagoreans’, and he is, in fact, our most reliable authority for their scientific teachings. He wrote a work Ilepi r&v Ivdxyopetwy which has, unfortunately, not come down to us. From the state of the evidence, then, it would appear to be a

apportion various ce of time to try toeve hopeless task at thisduadisl tan Aristotle was hagoreans, when n opi doctrines to indivi do so.PytHe knew that different nions were not in a position to but he was apparently unableh current among these philosophrersnam, es, and has to be contentothwiters particula to connect them with Pyt . . . while hagoreans think this saying ‘some of the h the other Pre-Socranketicrss reas in dealing witnes think that. . .” - wheibut dual thi es specific doctri to todiffinderenivitiat he nearly always attr e between by name. Attempts by modern scholars and self of Pythagoras him to be the views rest what they supposilse can s and basi m ore on any fir those of his pup nted. Innotpartheticref stat as on the e of should be discou wledge in Pytulahagr,oraHeas’th’tims eide(six th century BC) astronomical kno p. SI), are far too sanguine. He says (Arist., of Pythagoras refore, that the theory oth It appears probable, unithever earth, and the ertheheacenventrely, himself was that thein shape,se,thathet the th is at rest in bodies are spherical fixed stars hasear ly rotation from east that the sphere, of the passing througah dai centre of the earth,ir to west about an axiss have an independethe ement of the and that the planetosite to that of the daintlymov rotation, i.e. from own in a sense opp h advanced d evidence for suc n, there is no goo As we have seethis picture is period, and historicmyallyartithis knowledge in earstilyc (on cles on Thales this see further to follow completely anachroni tle’s best that we can doknoiswledge whiArichstothe and Anaximander).minThee the re ronomical example, and exad evidence ast era that the Pythagoretanbeschrefoolerrinedgento thel is reasonably goog in mind tha possessed, bearin fifth centurytBC.most of it mus latter part of the ek ans introduced inte oonGrethe y that the Pythagore The great noveltugh le was their insistdexench that the philosophical tho bert. asNuambwho for them the stuff (6am) importance of numers sought. Nuermbwas ers were the basberics, in some Ionian philosoph verse developed - num and which he out of which the wholewasuninev er able to fathom, way which Aristotle west to east. THE PYTHAGOREANS AND LATER PRE-SOCRATICS 65 evidently and with good justification regards as extremel perverse (cf. Met. A 8, 989b29f. and N 6, 1092b26f. = DK # B22 and B27), conceived of as actual physical entities occu = spatial extension, not intellectual abstractions; and sum ica relationships constituted the governing principles of the nn an Er not the place to go into the details or speculate ni : Fe o this remarkable doctrine. Perhaps the discoveries (tra tionally ascribed to Pythagoras himself) of the chief musical heal the octave, fourth, and fifth, expressed as the numerical = ci i E , n2, of the fact that the first four integers add up adi n a a the Ip and regarded as ; at the diagonal o is 1 surable with its side (the famous een ofPytha rag”),“al elements of the universe — but this belongs properly to th ee contributed to their belief that numbers formed the Éndam a 1 of mathematics. en a astronomy the Pythagoreans also introduced a startling ovation. This was to displace the earth from the central position in the cosmos which it seems to have occupied i hy astronomical ideas of most of the Pre-Socratics, and to r rad N as another celestial body moving in a circle e che nen pr and stars, round a central fire which provided the moro! Pes for the whole universe and was variously called the alia tower or the throne of Zeus, or the hearth of the sa m Aristotle tells us (De Caelo ii, 13, 293423 = DK 58 3837; f Diia Simplicius ad loc.) that, as well as the earth, the Li mil scheme postulated a counter-earth («vrty0wv) VETTA is = al round the central fire, closer to it than the earth, but ice invisible to us because we live on the hemisphere facin wi from the counter-earth.?5 Aristotle’s account does not n the planets by name; we are merely told that the Pythagor E regarded the earth as ‘one of the stars’ (Ev tév Korean), but some is a general word (as indeed is &oryp) which can bea lied indifferently to the fixed stars, the planets, the sun, and x a + A tertiary source (Aétius, DK 44 A16 and 17) fills in some detail and specifically attributes the scheme to Philolaus, a Pytl = of the latter half of the fifth century BC.

(B1-B19) as Under Philolaus (DK 44) DK lists nineteen passages tunately, the definite fragments of a work Ilepi déoeuwc.76 Unfor will have none of genuineness of these is disputed (KR, p. 311,ince they are false), conv them; Guthrie, vol. i, p. 331, is far less rentlydconn ected with but anyway only one fragment (87) is appa is that in the middle this astronomical scheme, and all that says(év 1% péow ri odal pas of the sphere is what is named the hearth and 17), in the toria voreiraı). According to Aëtius (DK 44 AI6 rth, then the er-ea middle was the central fire, next came the count the five planets, and earth, then the moon, then the sun,rsethenwhic h carried the fixed finally the outer sphere of the unive the indiv idual planets is stars. It is noteworthy that the order of the Greek fact, in d; not specified, nor are they actually name Zeus, Cron of names for Saturn, Jupiter, and Mars, i.e. the starsomis (987cus, of ) and Ares respectively, appear only in the Epinin the Timaeusthe (as extant texts before Aristotle,?? although Plato ury, Merc and us) (Ven we shall see) mentions the Morning Star er (38c-d). If we and knows that the planets are five in numb generally accepted assume that the order of the planets was that order of their sidereal in later Greek astronomy (which is thesun), then the complete periods and of their distances from the from the outside, 76 Philolaic scheme will have been (starting ury, sun, nepiéyov) fixed stars, Saturn, Jupiter, Mars, Venus, Merc bodies in all ng ten moon, earth, counter-earth, central fire - maki ng in circles round the (counting the fixed star sphere as one) movi The postulate of the counter-earth is a puzzling feature of the fiery centre. DK 58 54) Aristotle system. In one place (Met. A 5, 9864to3f.= suggests that the only reason for it is bring the total number of d number of the celestial orbits up to ten, which was the sacre nine, i.e. fixed stars, Pythagoreans, the visible orbits being onlyher passage (De Caelo five planets, sun, moon, and earth. In anot ii, 13, 293b21f.) he mentions the view held by ‘some’ that there us, also encircling the middle were other bodies, invisible toh were supposed to explain why (depsodaı rept TO ugcov), whic — an idea, as we have lunar eclipses are more frequent than solar seen, already attributed to Anaxagoras. It has been suggested that THE PYTHAGOREANS AND LATER PRE-SOCRATICS 67 the counter-earth might have performed the same function in the Philolaic scheme. This, however, is impossible, since the orbit of the moon is outside the earth’s, while that of the counter-earth is inside it (i.e. nearest the central fire). The other bodies mentioned by Aristotle were presumably envisaged as having their orbits between those of the moon and the earth if they were to produce more frequent lunar eclipses, but the counter-earth itself could not have had this effect.78 Simplicius, in his commentary on the above passage of the De Caelo, says that the Pythagoreans called the moon dvrtyBwv and also a ‘heavenly earth’ («ifeptav y%v). There is nothing intrinsically improbable here (pace Guthrie wal i p- 291) ; both moon and counter-earth encircle the central fire one on either side of the earth, so that either could be described in some sense as dvti, ‘over against’, ‘counter to’ the earth.?9 In the same passage Simplicius informs us that “those who are familiar with the more genuine doctrine call fire in the centre the creative force which from the centre gives life to the whole earth and warms again that part of it which has grown cold’.80 The onl difference between this and Aristotle’s version is that the in speaks of the central fire without mentioning its ‘creative force’ and its effect on the earth — presumably, knowledge of this constitutes the ‘more genuine’ doctrine. Perhaps a more cogent reason for the postulate of the counter-earth was to ehfor the fact that we never see the central fire, and to exclude the possibility that some daring explorer might go round to the other side of the earth and wonder why he still could not see the fier centre, which, as consisting of divine fire that provided the ue tive force for the whole cosmos, might be expected i be a spectacular sight. Assume the existence of a body like the counterearth which moves with our earth at the same speed in an orbit between us and the central fire,81 and at least you have a speci reason for our never seeing it. ied | Aristotle says specifically that according to the Pythagoreans the earth being one of the stars and carried in a circle round the centre makes (roreiv) night and day’ (De Caelo 293a22-3), and this is duly confirmed by Simplicius who adds that night nd ala depend on the position of the earth relative to the sun. Exactly

mption that the earth was how is not explained, but the assu the centre, the moon 29% days, supposed to take 24 hours to circle acco very roughly for some and the sun a year would suffice to ens asuntseen m the earth. Day of the main phenomena of the heav bited partfro was facing the sun would be produced when the inha and night whe n it had moved on the same side of the central fire,centre. This is pres ly what round 180° to the other side of theon to say (p. $12, 16-1umab t that 7) Simplicius means when he goes into the cone of its shadow: nigh e sinc results from the earth’s coming r othe the t is produced when we live only on one hemisphere, nighand its shadow over our hemisphere faces towards the sun be casts oxim ld appr ately accounted side. The phases of the moon wou moon and (b) and for: in Fig. 9, position (a) would bethenearlattenew tions (when the (c) near fall moon, but in betweensun, earth,r posi ter-earth, and moon was on the line joining a terrestriacoun l observer it must central fire) it would seem that for Again ever th there disappear briefly and then reappear. days and nighytsmon ld have wou and would have to be a solar eclipse, over the world. to be of equal length always all as glassy (dadosıdhg), the Aétius says that Philolaus regardedin thesuncosm filtering ‘receiving the reflection of the fire us, so that inos,a and sense ain cert both light and warmth through to the heaven (év rá odpavé) and there are twin suns, the fiery one init’ (DK 44 AI9). Unfortunately, the fiery one by reflection frontm here, for Philolaus seems to have it is not clear which fire is mea rmost surrounding fiery envisaged two sources of fire, the oute was, according to the sphere (this originally Heraclitanral idea Pre-Socratics) and the doxographers, common to seveay, later a is central fire (DK 44 AI6); anyw it difficult to see how reflected sun really helps matters. h makes much, Arist., Another minor difficulty (of which Heat and the tertiary sources, pp. 1o1f.) is that, according to Aristotleten bodies moving in ten in the Pythagorean scheme there weredaily rota ofthe heavens orbits round the central fire; but if themoving rountion d the central fire, is to be accounted for by the earth’smotion of the fixe d star sphere, there is no need to postulate any only nine circular motions, so that there would have been THE PYTHAGOREANS AND LATER PRE-SOCRATICS 69 CE = counter-earth CF = central fire Fig. 9. Schematic representation of the Philolaic system contrary to what all our sources affirm. To resolve this discrepanc it has been suggested that the sphere of the fixed stars was ee endowed with a very slow revolution, and that this must have been intended to represent the phenomenon of the precession of the equinoxes (see pp. 15f.). However, to suppose that astronomical theory or observational technique had reached such a level in Philolaus’ time that the effects of precession (about 50” of arc a year for stars on the ecliptic) would be noticed, is quite out of the

THE PYTHAGOREANS second question, and it is now certain that it was Hipparchusofinthetheea century Bc who made this discovery. The inventors earth and the central fire (neither of which has any observationa basis) could well have assumed a very slow Be ofandthew.vi sphere, which could anyway not be disproved, and woicA would bring the total number of revolutions up to ten O fit in well with their preconceived notions on the construction the universe. umpThe whole scheme is a good example of the type ofpresi al nomic tive theorizing that characterizes much of the astroct of the study ing of the Pre-Socratics; it is very much a produ n (e.g. it and bears little relation to the facts of actual observatio tions of varia al tudin longi takes no account of the latitudinal and e, schem the that the planetary bodies). Van der Waerden s belief noastro which he describes as “eine so raffiniert ausgedachten ir al mische System’, must belong to a stage in astronomic e ke ly whol is BC, 360 c. after the Timaeus, i.e. not before a ami was Plato h Rather is it just the sort of scheme with whic A h whic from his knowledge of Pythagorean doctrines, and o unsuccessfully tried to reconcile with the slightly later ra the celestial sphere and the a earth at the centre (see below, | a far described in the Er Na: fatal nenti = it (as so orbits the of the earth and a er V, especially p. 149). that it apparently envisages the heavenly bodies round the central fire as being in the same p the a, whereas, of course, to correspond with observed phenomen ned incli be d plane of the orbits of sun, moon, and planets shoulinclined orbit to that of the earth. There is only one mention of e he states,s in our sources and that is by Aétius (DK 44 A21) wher ‘Some say that the earth is at rest; but Philolaus the e a slanting circle says that it is carried in a circle round the fire onmepupé peatian rep} in a similar fashion to the sun and moon’ (kiKre n)- En it xd Tp Kate KbKAov AoËdV önororpönag Maw aut oekhvPhilo a to buted attri be stands, and if the whole sentence is to bo three all this can hardly mean anything other than that Yet this woI earth, sun, and moon, move in an inclined orbit. not produce the required results. It is possible that the last four AND LATER PRE-SOCRATICS 7I words are not Philolaus’, but added by Aétius or his source, and this apparently is how Heath takes it when he says, “The earth revolves round the central fire in the same sense as the sun and moon (that is from west to east), but its orbit is obliquely inclined; that is to say, the earth moves in the plane of the equator, the sun and the moon in the plane of the zodiac circle. It would no doubt be in this way that Philolaus would explain the seasons.’84 Clearly, this entails reading a great deal more into the evidence than is in fact there. ‘O A0%d¢ xbKAog was in later Greek astronomy a normal expression for the ecliptic; it seems more than probable that Aétius (or his source), knowing this, added it to the astronomical knowledge attributed to Philolaus simply to make the latter’s views sound more plausible.85 It is noteworthy that in the longer passage of Aëtius that describes the complete scheme (DK 44 A16), and in Aristotle’s and Simplicius’ account, there is no mention at all of inclined orbits, and it would seem very questionable to accept the unsupported statement of a tertiary source such as Aétius in a case like this. Very little astronomical sense is apparent in another feature of the Pythagorean scheme, the famous ‘harmony of the spheres’. According to Aristotle (De Caelo ii, 9, 290b12f. = DK 58 835), an absurd and extravagant opinion (his own words) was held by the Pythagoreans, to the effect that, with so many huge celestial bodies whirling at such great speeds round the centre, it was impossible that no noise should be generated by their motions, but each body must produce a different tone according to its distance from the centre, so that the whole system created a ‘harmony’. An ingenious explanation was given of the awkward fact that no one ever hears this harmony, namely that everyone, from the moment of birth, has this sound as a constant background and therefore does not consciously hear it, since there is no absolute silence to contrast with it. This poetic fancy (presumably suggested by the discovery of the ratios governing the chief musical intervals — see above) was taken up by Plato in the myth of Er in Republic x (see p. 111), and further elaborated by later writers who invented all sorts of musical schemes supposed to represent the proportionate distances of the heavenly bodies - Heath (Arist., pp. 105f.) treats of these at

no significance for mathematical some length. Nevertheless it hasgrip ped the imagination of later astronomy, however much it once more how prone the ages, except in so far as to demonstratefacts of natural phenomena Pythagoreans were to subordinate the | to their philosophical and mystical predilections. it me, sche ean agor Despite the many drawbacks of the Pyth influenced Greek permanently also displays several features which ed the circular motions of the astronomical thought. It emphasiz al point; the concept was heavenly bodies round a common centr but the Philolaic system already prominent in Empedocles’ ideas, ing ulat an imaginary centre went a step further by actually post concept in the later of rotation, and this was destined to be a keytheor ies. It differentidevelopment of the epicyclic and eccentric tial objec ts, and there ated between the planets and the other celes but imally, ition (trad is no good evidence that this distinction was of the any by probably, credited to Pythagoras himself)Abovemade all, it accustomed earlier Pre-Socratics except Anaxagoras.as what one might call the men to thinking in terms of the sphere for the universe as a whole typical astronomical shape, not onlysince Parmenides), but more (this had been generally accepted r the fifth century particularly as the shape of the earth itself.hAfte the exception of the Bc no Greek writer of any repute (wit held somewhat who atomists, Leucippus and Democritus,below) conc d of the reactionary views on astronomy — see Socrates youteive shape earth as anything other than a globe. Iner (cf. p. 94), buth the the great of the earth was still a debatable matt in a spherical earth (see authority of Plato, who certainly believed agorean astronomical p. 98) and who did much to maketoPyth put the matter beyond notions respectable, was sufficient beyo any question (De doubt. Aristotle accepts the sphericitythe propndonen ts of a flat or Caelo ii, 14, 29748ff.) and dismisses | . drum-shaped earth in a few sentences (ibid. 2944) is re sphe a earth as That the Pythagoreans did regard the o where Aristotle is Cael certain. In a curious chapter of the De which is ‘left and er” discussing which is ‘upper’ and “low theand us) unnatural view ‘right’ in the universe (ii, 2), he takes (to that the invisible (i.e. south) pole is the upper one, and those THE PYTHAGOREANS AND LATER PRE-SOCRATICS 73 living there are in the upper hemisphere and on the right, while we (i.e. the inhabitants of the northern hemisphere) are in the lower hemisphere and on the left, ‘contrary to what the Pythagoreans say; for they make us the upper ones in the right-hand part, and those at the south pole the lower ones in the left-hand part’ (285b25-7). However odd the argumentation appears to us,86 it is at least clear that the Pythagoreans considered the earth as spherical. This is confirmed by one of the reasons that Aristotle reports for the Pythagorean view that the earth and the counterearth move round the centre: he says (293b25-30) that they considered that it made no difference to the observed phenomena, since, even on the assumption that the earth (not the central fire) was at the centre of the universe, we ourselves anyway lived half a diameter of the earth away from its centre. Thus the sphericity is again assumed, although the truth of the Pythagorean argument entails ignoring completely the different effects of parallax in the two cases, a procedure which Heath justifiably describes as ‘a somewhat extreme case of making the phenomena fit a preconceived hypothesis’ (Arist., p. 100). Another very influential tenet of Pythagorean thought was their insistence on the divine nature of the celestial bodies. This also received the sanction of Plato and Aristotle, became orthodox doctrine which was accepted even by the mathematical astronomers (see the introduction to Ptolemy’s Almagest, ed. Heiberg, pp. 6, 23; 7, 20ff.), and provided the fundamental basis for astrology. There is little doubt that the idea of the divinity of the planets, at any rate, came originally from Babylonia, where an astral religion is attested as early as the second millennium sc.” According to the tertiary sources, two individual Pythagoreans from Syracuse, Hicetas and Ecphantus (DK 50 and 51), introduced a modification of the Philolaic system by postulating a central earth rotating on its own axis from west to east, thus accounting for the daily movement of the heavens. Cicero (Acad. Prior. ii, 39, 123), ostensibly quoting Theophrastus, would have us believe that Hicetas regarded the earth as the only moving body in a universe where the sun, moon, and stars were all stationary. This, if true, would demonstrate an unbelievably imperfect knowledge

THE PYTHAGOREANS AND LATER PRE-SOCRATICS of astronomy on Hicetas’ part, since it would argue that he completely ignored the proper motions of the planetary bodies in the zodiac. However the tertiary evidence is very meagre, and even the actual existence of these two Pythagoreans has been doubted knowledge of this double motion can be attributed to such an early figure as Alcmaeon is extremely doubtful. Aétius also mentions (DK 58 837c) three Pythagorean theories about the Milky Way: some thought that it was the track of a burnt-out star which had fallen from its proper place; others that it was the original course of the sun (presumably made visible by a sort of residual after-glow !); and others that it was the reflection of the rays of the sun in the heaven, just as the rainbow is its reflection in the clouds. Finally, we are told that they called the Pleiades the ‘lyre of the Muses’ and the planets the ‘hounds of Persephone’ 74 (cf. Guthrie, vol. i, p. 323). As to other astronomical knowledge attributed to the Pythagoreans, Aétius reports that Philolaus regarded the moon as like the earth, but with animals and plants fifteen times the size of terrestrial ones and a day fifteen times as long (DK 44 A20); this is obviously an inference from the length of a month. Diogenes Laertius says that they knew that the moon was illuminated by the sun (DK 58 814), which is probable enough as it was certainly known by Anaxagoras; on the other hand, according to Aétius (DK 58 836), some of the later Pythagoreans still thought of the moon’s waxing and waning as caused by its own flame — which indicates little awareness of the true nature of lunar phenomena. From the concept of the spherical universe and the spherical earth, it would seem but a small step to the acceptance of the idea that all the celestial bodies are spherical; but there is no good (DK 58 c2). evidence that the Pythagoreans actually took this step. Heath (Arist., p. 115) cites Aétius for the statement that the Pythagoreans regarded the sun as spherical (of Iudaysperor abatpoetdy roy AAov, Aët. ii, 22, 5 = Dox. Gr., p. 352); but this comes from Stobaeus’ Eclogae (compiled about AD 500), is unsupported by any other source,88 and cannot be regarded as reliable testimony for Pythagorean beliefs. In fact, immediately above this passage, Aétius says that Alcmacon (a Pythagorean of the early-fifth century BC) believed that the sun was flat (rAdruv elvan rèv HAtov, DK 24 a4). The same Alcmaeon, in agreement with ‘certain of the mathematicians’ is also credited by Aétius (loc. cit.) with knowing that the planets have a movement from west to east. This is the movement along the zodiac in the opposite direction to the daily rotation of the heavens, and could be roughly accounted for on the Philolaic system by assuming different speeds of rotation for each planet round the central fire (that is if the considerable deviations in latitude of the planets is ignored, as also their retrograde movements and stationary points); but whether 75 e Despite their insistence on the importance of number, we have practically no information about how the Pythagoreans applied numbers in their astronomical thinking. The sources tell us nothing, for example, about the periods allotted to the revolutions of the celestial bodies in the Philolaic scheme; it is true that later commentators indulge in much speculation about the different intervals and notes that they suppose to have comprised the harmony of the spheres, but they are not forthcoming about any actual parameters. Presumably the very fact that the scheme envisaged the revolutions of the different bodies as occurring in a particular order shows that some attention must have been paid to observed phenomena, and some quantitative information about solar, lunar, and planetary movements must have been utilized. The only concrete evidence we have in this connection is a statement by Censorinus, a Roman grammarian of the third century AD who wrote a work, De Die Natali, containing a certain amount of calendaric information (not always accurate), that Philolaus the Pythagorean made a ‘Great Year’ consist of 59 years, including 21 intercalary months, and an ordinary year of 3644 days (op. cit. 18, 8). A ‘Great Year’ was a period after which sun, moon, and planets were supposed to occupy exactly the same positions again as at the beginning 89 but it came to be regarded as a common multiple of solar and lunar periods only for calendaric purposes (see below), and this is the sense in which Censorinus uses the expression — he gives several figures for this period as put forward by various authorities (op. cit. 18, 5{f.). On the basis of

this attribution to Philolaus, the Italian scholar Schiaparelli® sets out a list of planetary periods (duly reproduced by Heath, Arist., p. 102, note 2) which he compares with the modern figures, claiming that they show an extraordinarily close correspondence. It is important to realize that there is no evidence whatsoever that these figures were known to Philolaus; they are obtained merely by dividing the 21,505 days of his Great Year by the nearest whole number of revolutions which each planet makes during that period according to modern knowledge, but counting Venus, Mercury, and the sun all together as completing one revolution in 3643 days. This foisting on an ancient scientist of knowledge based on modern data is a common feature of many present-day treatments of ancient astronomy, and one that it is continually necessary to guard against. | Another Pythagorean, Archytas, a contemporary and friend of Plato, and a mathematician of note who used a three-dimensional construction to solve the famous problem of doubling the cube,°1 provides some evidence of a general kind that mathematical techniques were to some extent applied to natural phenomena; he says (DK 47 81), ‘the mathematicians transmitted to us clear means of discerning (Giéyvwow) about the speed of the stars and risings and settings, and about geometry and numbers and sphaeric [i.e. the geometry of the sphere with particular reference to astronomical problems] and not least about music.’ This is the Archytas whom Horace apostrophizes as ‘measurer of earth and sea and sand without number’ and as one who has ‘scaled the airy dwellings and traversed the round heavens with a mind that was after all to die’ .92 The concept of the spherical earth must soon have provoked attempts to estimate its size, and it is possible that a figure of 400,000 stades for the circumference, which Aristotle (De Caelo ii, 14, 298415-17) attributes to ‘some of the mathematicians’, may have derived from Archytas (although it might equally well have come from Eudoxus - see below); and Horace's last two lines might refer to astronomical investigations by Archytas. He is also said (by Eudemus, DK 47 A24) to have asked the percipient question whether, ifhe stood on the outermost edge of the universe, i.e. the sphere of the fixed stars, he would be able PYTHAGOREANS AND LATER PRE-SOCRATICS 77 to extend his arm and stick outwards; the natural affirmative answer would entail acceptance of a boundless universe. Archelaus, a pupil of Anaxagoras, seems to have held much the same astronomical opinions as his master, but to have introduced a few variations. According to the tertiary sources, both regarded the stars as fiery masses, with the earth lying motionless at the centre of the cosmos, and the heavens tilted towards the south; but Archelaus apparently considered the earth not as a flat disc, but as a disc with a raised edge and a hollow middle part. This, he thought, explained why the sun does not rise and set at the same time in all regions, as it ought to do if the earth were level (ôuarñ — DK 60 a4 = Hippol., Ref. i, 9, 4). Presumably the idea was that the sun would appear to rise and set at different times behind the raised outer rim according to the position of the inhabitants on the slopes of the hollow part; again this is a recognizable attempt to accommodate theory to the facts of observation (cf. p. 59). We are also told (DK 60 AI and 44) that he regarded the sun as the largest of the celestial bodies, the moon as the next largest, while the others (not specified) were of various sizes. Another philosopher who followed Anaxagorean notions was Diogenes of Apollonia (flor. c. 430 Bc). For him, the &pyñ was air, which he considered to be divine, eternal, immortal, and the guiding principle of the whole universe. From air, by the different combinations of its characteristics, i.e. temperature, moistness or dryness, rarefaction and condensation, and motion, were produced all the phenomena of the visible world. Warm air is the mark of intelligence, the amount of it contained in a particular organism determining its character. Pure divine air was fiery, and there were innumerable gradations of warmth down to inanimate objects which contain no warm air (fragments 5, 7, and 8 and the tertiary evidence DK 64 As, 6 and 7). Much of this (amusingly satirized in Aristophanes’ Clouds 225f.; 264; 828f.) recalls what the tertiary sources assert of Anaximenes. He also regarded air as the px, and it is presumably recollection of this that caused part of the doxographical tradition to make the absurd assertion that Diogenes was actually a pupil of Anaximenes (DK 64 AI).

The scanty fragments of his work remaining give us no details about his astronomical ideas, for which we have to trust the tertiary sources. According to these he regarded the earth as ‘round’ (orpoyyökn), supported by air in the centre of the cosmos (ibid). Unfortunately, orpoyyükos (like its English equivalent) is ambiguous in meaning;% it may mean ‘round’ like a ball (synonymous with ohupoaBñce, ‘spherical’), or ‘round’ like a dish, or simply ‘curved’ (see LS s.v.). Here, since Simplicius tells us (DK 64 As) that Diogenes followed Anaxagoras ‚views in many respects, the word can hardly mean ‘spherical’, but refers to a disc-shaped earth (cf. Guthrie, vol. ii, p. 372 note 1); he is also coupled with Anaxagoras in thinking that the cosmos was tilted towards the south (Aétius, DK 59 A67). The stars, the sun, and the moon he regarded as consisting of red-hot pumice-stone (uonpoe:d7), through the pores of which came rays from the aether. This sounds very odd, particularly for the moon, which Anaxagoras knew shone by reflected sunlight, and it is likely that the source, Aétius (DK 64 A12-14), has his facts muddled i he even says that Diogenes considered that the sun was extinguished by cold acting in opposition to the heat! Another obvious borrowing from Anaxagoras is the notion that, as well as the visible stars, invisible stones are also carried round the earth like the one that fell at Aegospotami (412). This refers to the fall of a large meteorite in 467 BC, which caused a considerable sensation and which was supposed to have been predicted by Anaxagoras (cf. DK 59 art and 12). To him we must also trace the idea that the drawing up of moisture by the sun’s heat from the regions round the earth produces winds and the turnings of sun and moon; the remaining moisture forms the sea which will gradually become dried up (a17). The same process was used to explain the annual flooding of the Nile in summer, the sun drawing water from the sea and releasing it into the river (A18). From what we know of the opinions of Empedocles, Anaxagoras, Archelaus, and Diogenes (and it must be remembered that weare largely dependent on the tertiary sources for them), it would seem that there was a common store of astronomical ideas in the second half of the fifth century sc which was drawn on by all the THE PYTHAGOREANS AND LATER PRE-SOCRATICS 79 thinkers of the period.94 Certainly, the atomists, Leucippus and Democritus, whom we come to next, drew on it. This is not the place to give a detailed account of the atomic theory developed by them, modified later by Epicurus, and expounded with missionary zeal by Lucretius in his De Rerum Natura. Suffice it to say that, according to this theory, matter consists of the conglomeration of many, small, invisible (and indivisible), homogeneous particles, which originally were scattered in infinite numbers throughout the void, differing from each other only in size and shape (some being round, some hooked, some triangular, and so on). By the action of the primeval vortex (in), vaguely described as having been set in motion by necessity (’ävé&yinv), the atoms came together, like shapes being attracted to like, to form first a sort of spherical membrane or caul (sbomua odarpoerdés . . . olov duéva). As this whirled round, the finer atoms (e.g. of fire) went out towards the surrounding void and formed the celestial objects, while the coarser ones collected towards the centre and formed the earth and all its contents. This process goes on continuously throughout the limitless void, local conglomerations of atoms coming together to form countless worlds which grow, flourish, and then dissolve into their constituent atoms again (Diog. Laert. ix, 30ff. = DK 67 AI; Aétius, A24). Of the two proponents of atomism, Leucippus was the older, and his work, the “Great World-System’ (uéyas Siékoouoc), is generally dated to between 440 and 430 Bc; Democritus was about ten years younger than Socrates (born in 469) and long outlived him. In the sources they are generally mentioned together when the basic principles of the system are being described, but their astronomical views are reported as showing considerable differences, and so here they are treated separately. According to Diogenes Laertius (ix, 33), Leucippus said that the circle of the sun was the outermost, that of the moon the nearest to the earth, and those of the other celestial bodies (not specified) were in between. The earth is described as ‘riding (or being carried) in a whirl round the centre’ (thy yñv dyeioban mepl rd uécov duwouuévnv — ix, 30), a description which at first sight seems to show strong affinities with the Pythagorean moving earth.

However this is so foreign to what we know of the rest of atomist astronomy that it seems certain that Diogenes’ account is confused here: he knew that the whole cosmos was supposed to have been formed by the action of the ötvn and carelessly uses the verb 3wéw in connection with the earth as though the process was still going on. Other ideas attributed to Leucippus by Diogenes are that the earth is ‘drum-shaped’ (tupravadys — cf. Aétius, DK 67 A26), i.e. shaped like a tambourine, that the stars are made red-hot by the speed of their revolution, as is also the sun which is made more fiery by the stars, and that the moon receives only a small portion of fire. Then follows a passage where solar and lunar eclipses are apparently explained by the tilting of the earth towards the south, the northern part being always snowy, very cold, and frozen (ix, 33). The bizarreness, not to say incomprehensibility, of this ‘explanation’ has led most scholars to assume a lacuna in the text, because although the tilting might be adapted to explain differences in the seasons and the lengths of day and night (as had already been suggested by Anaxagoras, who makes the cosmos, not the earth, tilt - see above, p. 59), it is difficult to see how it can be made to account for eclipses. On the other hand, it is obvious that Leucippus’ astronomical ideas were remarkably primitive for his time, and it may well be that he failed to understand the reasoning behind the theory of tilting. Diogenes ends his account by saying that, according to Leucippus, the sun is seldom eclipsed, while this is constantly (svvex&s) happening to the moon because their circles are unequal. Aëtius adds very little; he says that both Leucippus and Democritus considered the cosmos as spherical (DK 67 A22), and gives as a further reason for the tilting of the earth the porousness or rarity (&pauérne) of its southern regions (427) — presumably the picture was of a topheavy earth weighed down by snow and ice in the north and out THE PYTHAGOREANS AND LATER PRE-SOCRATICS 81 rejected or ignored the theoretical advances made by the Pythagoreans and taken up by Plato, e.g. the concept of the spherical earth. It was, perhaps, Plato’s consciousness of the defects of Democritus’ astronomical views that gave rise to the story, reported by Diogenes Laertius on the authority of Aristoxenus that Plato wanted to burn all Democritus’ books he could cet hold of, but was dissuaded from this by two Pythagoreans (Diog. Laert. ix, 40). Once again we have to rely on secondary and tertiary sources for the details of Democritus’ astronomical beliefs, since of the nearly three hundred passages listed by DK as B fragments only half a dozen have any relevance at all to astronomy. Thus Bsb, BIIr, and B13, which can hardly count as actual fragments of Democritus’ writings and might well have been included among the A references, are quotations of titles only, namely Ilept tév ravhrov (On the Planets), Meyas &vinvrögY “Aotpovopin (the Great Year or the Astronomy) — also referred to as "Aorporoyi« and Tlept dorpovoutac) — and Haparınypa (Calendar). Fragment B14 is a collection of data from the last-named, mostly taken from the calendar attached to Geminus’ Isagoge and Ptolemy’s Phaseis (on these sce pp. 84f.). Fragment BI 5 is concerned with the shape of the inhabited world and is a very dubious fragment anyway (see below). Fragment 525 informs us that Democritus regarded ambrosia as the vapours by which the sun is nourished.95 To judge by the list of over sixty titles attributed to him by Diogenes Laertius on the authority of Thrasyllus (an Alexandrian amologer of the late-first century Bc), Democritus’ intellectual interests extended over a wide range, and it is a great pity that not a single one of his writings has come down to us complete. In astronomy, he corrected Leucippus’ erroneous view of the of balance with the dry, warm, and light south. order of the celestial bodies and stated that the moon was closest to the earth (which he regarded as having been formed before the stars). Then came the sun, and then the planets (unspecified) than his predecessor’s and show a greater willingness to which have not all the same height (i.e. distance from the earth) - d Democritus’ astronomical views are much more sophisticate pay attention to the facts of observation, but on the theoretical side he made no advances and his ideas are an amalgam of those of Anaxagoras and his pupils. In particular, he seems to have this is according to Hippolytus (DK 68 A4o). Aétius says that he put the fixed stars first (reckoning inwards from the surrounding void), then the planets (again unspecified), then the sun, then

Dochépos (i.e. Venus), and then the moon. The fixed stars he regarded as stones (presumably fiery) and the sun as a red-hot stone (A8s-7). On the other hand, Seneca (Nat. Quaest. vii, 3, 2 asserts that Democritus suspected that there were several stars which were not fixed, but he did not enumerate them by name because the courses of the five planets were not yet understood.96 If this were true, and it may very well be, granted Democritus’ apparent rejection or ignorance of Pythagorean astronomical ideas (despite a misguided attempt by part of the doxographical tradition to connect him with both Pythagoras himself and Philolaus - cf. Diog. Laert. ix, 38), then it is difficult to see what he could have put into a work entitled On the Planets. Sun and moon he regarded as composed of smooth and round bes atoms, Acto Kal mepubepdiv Syke (ix, 44); nepıdepng descrithe and fire spherical atoms which are the constituents alike of soul substance and voüc ‘mind’, which he equated with the divine (Aétius, A74, voùy rdv Osby ¿v rupi odatpoedet: AI35 = Theophrastus, De Sensu 68, rod Beppod TO cyNua chaposudéc). Aristotle, who wrote a book,on Democritus (cf. Simplicius, A37), tells us that he regarded the sphere as the most mobile shape (AIOI = De Anima i, 2, 405411). Originally, sun and moon were not fiery, being made of the same type of atoms as constituted the earth, but later, in the process that led to the enlarging of the sun’s circle, fire was cut off in it (A39). This view did not prevent Democritus from realizing that the moon shines by light from the sun (Plutarch, A894). Despite his avowed dislike of Anaxagoras, whom he accused of plagiarizing old ideas about the sun and moon (85), many of Democritus’ own astronomical ideas, as reported in our sources, are identical with those of Anaxagoras. Thus both believed that the moon was like the earth in having mountains and glens and plains (DK 59 477 and 68 Ago), and both gave the same explanation of the Milky Way (68 AgI) and of comets (68 492); both regarded the earth as flat, but Democritus followed Archelaus in supposing that it was disc-shaped and hollow in the middle (494). Water collected in the hollow parts, and local excess accumulations of water caused the land mass to shift and so produced THE PYTHAGOREANS AND LATER PRE-SOCRATICS 83 earthquakes (497). This passage comes from Aristotle, who, as we have seen (p. 46), connects Democritus with Anaximenes and Anaxagoras in believing the earth to cover the air beneath it like a lid. The earth was tilted towards the south not, as Leucippus had thought, because its northern parts were heavier, but because the southern part through an over-abundance of natural produce and growth outweighs the virgin north (tà Bépeux &kpata); either Aétius’ account is faulty (496) or Democritus had very confused ideas of the Anaxagorean notion of tilting, since the passage actually talks about the “greater weakness of the southern part of the surrounding (air)’, 3. td dodevéotepov eivar tò ueonuBpivèv rod neptéyovroc, which makes very little sense here. In the beginning the earth moved about (nAdLeodar) because of its smallness and lightness, but as it grew denser and heavier it remained. stationary (A9s). According to Agathemerus (B15), compiler of a small and very bad geographical treatise of uncertain date but undoubtedly post-second century ap, Democritus thought that the inhabited part of the earth (% oixovyévy) was not round (orpoyyüXog again), as the ancients believed, with Greece in the centre and Delphi in the middle of Greece. This was the traditional picture, descended from the Homeric concept of the all-encircling Ocean stream, and already criticized by Herodotus (iv, 36). Democritus, on the other hand, maintained that it was oblong (xpos), its length (i.e. west to east) being half as long again as its breadth (north to south). The same source informs us that Democritus wrote a I'¢ replodos, ‘Circuit of the Earth’, and a Ieptmdoug, literally a ‘sailing round’, that is a navigational account; but neither of these titles occurs in the list given by Diogenes Laertius (A33). Agathemerus is a poor authority, and it is surprising that Diels should classify the passage as a B fragment. Finally, Lucretius tells us (De Rerum Natura v, 621f. = A88) that Democritus believed that the sphere of the fixed stars revolved with the greatest velocity, while the sun and moon, being nearer the earth, were less affected by the ‘revolution of the heavens’ (caeli turbo) and therefore moved more slowly, the moon being the slowest of all; hence the sun was overtaken by the zodiacal signs in a year and the moon in a month, but to our eyes it seemed as

THE PYTHAGOREANS AND LATER PRE-SOCRATICS though the latter moved faster. This is an idea that is implicitly criticized by Plato in the Laws (see below, p. 139; cf. Aristotle, De Caelo ii, 10). It is evidently an attempt to account for the different speeds of revolution of sun and moon relative to the most of our information about them.101 Both these calendars were compiled at a time when mathematical astronomy had already reached a high level of proficiency, and so they cannot be regarded as typical of the earliest examples; in fact, they contain meteorological and astronomical data!02 deriving from many different observers in different localities. Thus the calendar attached to Geminus’ work uses as sources Democritus (the earliest authority cited, which confirms the title, Iaparnyua, attributed to him - see p. 81), Euctemon, Meton, Eudoxus, and Callippus. Ptolemy (about three hundred years later) adds 84 fixed stars from west to east, but it manifestly confuses the diurnal revolution of the whole heaven in the plane of the equator with the movements of the sun and moon in the plane of the ecliptic. If it were merely a question of relative speeds, all the revolutions would be in the same plane. Alexander of Aphrodisias, a thirdcentury AD commentator on Aristotle, attributes to the Pythagoreans the idea that the celestial bodies which are furthest away move with greater speed than those closer to the earth (in Met. A 5); but this cannot be true of the Philolaic system, in which (as we have seen) the earth itself was a moving body and the sphere of the fixed stars was either motionless or was endowed with a very slow movement. | In the last decades of the fifth century sc, the Hesiodic type of observational material mentioned above (p. 60) began to be correlated with current astronomical ideas, and one of the first results was the emergence of the ‘parapegmata’ or astronomical calendars. These were a kind of almanac engraved originally on stone or wooden tablets, giving astronomical and meteorological phenomena for all the days of the month. Each day was originally represented by a hole at the side of that part of the engraved text which gave the prognostication for that particular day, and into the hole a movable peg was inserted; next day the peg was inserted into the next hole and so on (hence the name, from naparhywuur, ‘fix beside’). Fragments of four stone parapegmata from Miletus and elsewhere, the earliest of which dates from the second century Bc (thus comparatively late in the development of Greek astronomy), have actually been found.9? The information it given was of the type: ‘Day 6: the Pleiades set in the morning; in rises Orion is winter and rainy’ or “Day 26: summer solstice; the morning; a south wind blows’; and apparently from the first such data were also written up as separate texts.°8 It is from two extant examples of these, the calendar attached to Geminus’ Isagoge®® and Ptolemy's Phaseis, that we derive 85 émonuactat from the Egyptians (who observed rap’nuiv, i.e. in Alexandria - exactly who these were is not clear), Hipparchus, Julius Caesar, Dositheus, Metrodorus, Philippus, and Conon. Ptolemy, of course, was aware that the data connected with the various days of the year depended on the latitude of the observer (cf. pp. 14f.), and he gives (Phas., p. 67 ed. Heib.) the places where the observers made their observations. This fact was apparently not appreciated by the general public who presumably used the parapegmata as calendaric guides for the business of everyday life. Thus we find a body of material that soon became traditional in character and was copied and recopied indiscriminately by compilers and popularizers who never made any observations themselves and ignored the discrepancies arising from the different regions to which the data were applicable. One result of this can be seen in the rustic calendar set out in ch. 25-31 of Book xviii of Pliny’s Naturalis Historia (first century AD), where he complains of the different dates he finds given for the same phenomena in various authorities, and demonstrates his own scientific incompetence in dealing with the material. Obviously, to be any use at all such data must be attached to a fixed calendaric scheme based on the solar year, and here a wellknown difficulty obtrudes itself. The most natural means of dividing the year into convenient periods longer than single days and nights is by the lunar (synodic) month - the time that elapses between one phase of the moon and the next recurrence of that phase. The Babylonian calendar, for example, like the early

THE PYTHAGOREANS AND LATER PRE-SOCRATICS Jewish calendar and the official Mahommedan calendar to this day, was at all times a lunar calendar; a new month began with the first visible appearance of the crescent of the new moon (hence the importance attached to being able to predict this and the elaborate computational schemes for this purpose).103 Moreover, the moon plays a very important role in the religious practices of most peoples, in that the occurrence of religious festivals is largely regulated by its phases (the date of Easter, for example). Nilsson has shown that most Greek festivals took place at or near full moon (Primitive Time-Reckoning, p. 343), and that all the Greek names common multiple of the lunar and solar cycles, and to intercalate months as necessary during any one period. According to Geminus (loc. cit.), the earliest such intercalation cycle was one of 8 years, the “octaéteris”, since 8 solar years of 365 days are roughly equal to 99 lunar months of 294 days. However his description of how this evolved is unsatisfactory (see below, pp. 188-89) and there is considerable doubt concerning the origin of this cycle. Censorinus (De Die Nat. 18, 5) tells us that it was usually ascribed to Eudoxus, but that other names were also connected with it, including that of Cleostratus of Tenedos. This latter is a shadowy figure of the second half of the sixth century BC, mentioned less than a dozen times in the tertiary sources (see DK 6) and supposed to have written on astronomy. The scholiast on Euripides, Rhesus 528 quotes two of his hexameters (Diels 86 for months (which vary from city to city, each having its own particular calendar) are connected with religious festivals.104 Unfortunately, the lunar month is incommensurable with the solar year: no convenient whole number of months makes up exactly one year. The lunar month is a little more than 29} days; 12 of these amount to 354 days and 13 to 384 days, whereas the sun takes very nearly 365} days to complete one full cycle. Thus a purely lunar-based calendar is very soon going to become greatly out of step with the sun. A festival supposed to be held at full moon in mid-summer would in the course of years be taking place in the autumn, winter, or spring. In fact, the Mahommedan year of 12 lunar months is about 11 days out by the sun each year, and every date in this calendar goes the complete round of the seasons every 33 years. Now this is all very well for the followers of Mahommet, but it would not do for the Greeks. One of the characteristics of both Greek and Roman religion is the insistence on exact ritual; the gods were displeased if the rites were not carried out in exactly the fashion laid down, and this, of course, included having them on the same day or days each year. Geminus, Isagoge ch. 8, the locus classicus for Greek calendaric cycles, is very clear on this point. There is also the obvious absurdity in holding, say, a harvest thanksgiving festival at a time when the corn had not even been planted. So the Greeks expended considerable thought in establishing a luni-solar year, inwhich the months and days are measured by the phases of the moon but which still keeps in step with the sun. The problem then is to find an extended period which is a 87 supplies a third, DK 6 81), and it is possible that he wrote a poem in the Hesiodic manner giving some information about the constellations then known; but it is wholly impossible that he introduced the zodiacal signs and understood the concept of the ecliptic, as Pliny tries to make out, since this does not appear until the end of the fifth century Bc;105 and attempts to build up Cleostratus as a key figure in early Greek astronomy106 are certainly misconceived. The first well-attested intercalation cycle is connected with the names of two Athenian astronomers, Meton and Euctemon, who flourished about 430 Bc and, according to Ptolemy (Phas., p. 67, 2), made observations at Athens, in the Cyclades, in Macedonia, and in Thrace. In the Almagest (iii, 1) they are cited for observations of the summer solstice, including one on 27 June 432 BC, which, despite their inaccuracy by the standards of later astronomy (emphasized by both Hipparchus and Ptolemy - modern calculations show that the solstice actually occurred about 14 days later), were nevertheless used as confirmation of the figure that Hipparchus decided on for the length of the year and that Ptolemy also accepts (viz. 365} days less 360 of a day). Meton suggested a period of 19 years, called after him the Metonic cycle, to bring the lunar month into correlation with the solar | year. This cycle contained 235 lunar months (7 of which were

THE PYTHAGOREANS AND LATER PRE-SOCRATICS intercalary) and 6,940 days, and, according to Geminus,10? 110 of the months were ‘hollow’, i.e. of 29 days each, and 125 ‘full’, i.e. of 30 days each. This would give amean lunar month less than two minutes too long and a solar year of 36575 days, about 59 years (DK 41, 9). It is possible, as Tannery suggests,110 that, starting with the figures of 29% days for the lunar month and 365 days for the solar year, Oinopides realized that the smallest whole number of years to contain a whole number of lunar 30 minutes too long.108 months would be 59 (2 x 293), containing 730 (2 x 365) months 88 Meton and Euctemon are frequently cited in the parapegmata, and are the earliest names connected with the observations of equinoxes as well as solstices. Moreover, according to a secondcentury BC papyrus fragment known as the Ars Eudoxi,199 Euctemon gave the lengths of the astronomical seasons starting from the summer solstice as 90, 90, 92, and 93 days respectively (the modern figures to the nearest whole day are 92, 89, 90, and 94), which shows that he was aware of the non-uniformity of the sun’s course round the earth. Now, recognition of the equinoxes and of the inequality of the seasons implies a comparatively sophisticated stage in astronomical thought, and presupposes at least some knowledge of the concept of the celestial sphere and a spherical earth - see my article inJHS 86, 1966. Thus the Pythagorean ideas were now beginning to bear fruit when applied to the observational material that was available, and it would seem that a much clearer picture was being obtained of at least the sun’s course, with the solstices and equinoxes marking the four seasons of the solar year. An essential part of this picture is the concept of the sun’s circuit of the heavens marked by its passage through the zodiacal constellations in a plane inclined to that of the equator. As we have seen, this was not part of the Philolaic scheme. The invention of the ecliptic as the sun’s oblique path is attributed by Eudemus to Oinopides of Chios (DK 41, 7), who we are told was a little younger than Anaxagoras (ibid. 1), and who is mentioned in the pseudo-Platonic dialogue Amatores (132a-b) in connection with drawings of inclined circles; he, too, seems to have been a Pythagorean. No actual figure for the obliquity of the ecliptic is ascribed to Oinopides, but he may have known the rough estimate of 24° (see below, pp. 157-58). According to Censorinus (De Die Nat. 19, 2) Oinopides made the length of the year 36553 days, while Aelian and Aétius ascribe to him a Great Year of 89 which would be equivalent to 21,557 days, and this divided by 59 would give 36535 days. Equinoxes and solstices and other parapegma data are also mentioned in the medical treatises of the Hippocratic corpus, especially the works entitled On Airs, Waters, Places and On Diet.H1 These treatises are notoriously difficult to date,112 but certainly none of them can be earlier than 425 BC. Hence all the evidence points to the conclusion that the last decades of the fifth century Bc saw the real beginning of mathematical astronomy in Greece, although the celestial sphere as a fully developed concept does not appear until the fourth century. It seems certain that calendaric problems provided the initial impetus for this development. There is ample evidence that in the fifth century the Athenian civil calendar was in a state of confusion. Aristophanes in the Clouds (610ff.) makes the moon complain that the Athenians were not arranging the days properly in accordance with its phases (cf. Peace 406). Thucydides (v, 20) explains that time-reckoning by the tenure of office of state magistrates (this was the normal official method, e.g. an event would be dated in such-and-such a year of so-and-so’s archonship) was bound to be inaccurate (it would anyway only be readily intelligible to a reader in one city, since each city had its own magistrate list and calendar), and the only safe method was by counting summers and winters. This would be with the help of a parapegma. He also uses the astronomical phenomena listed in the parapegmata, such as the solstices (vii, 16; viii, 39) and the rising of Arcturus (ii, 78) for dating specific events. It must be realized that astronomically based cycles, such as the Metonic cycle, were only used in scientific texts, while in the ordinary civil calendar of each state no systematic scheme of intercalation was apparently in use, but intercalation depended on the vagaries ofofficialdom.118 The new astronomical ideas naturally did not immediately

win full acceptance, and many of the old, crude notions of the early Pre-Socratics lingered on into the fourth century and even later, to judge from the sources. Antiphon (the sophist of the second half of the fifth century, not the orator), who was no mean mathematician,114 is said to have believed that the moon shone by its own light, but that the concealed part round it was dimmed by the proximity of the sun, since the stronger fire dims the lesser one, which happens also with the other stars (DK 87 827). He also thought (826) that the sun’s fire fed on the damp air round the earth and that its risings and settings were caused by the recurrent failure of its burning owing to the opposing effect of moisture; and he is coupled with Alcmaeon and Heraclitus in supposing that the moon was bowl-shaped (cxadoedy¢), and that eclipses were caused by the turnings and inclinations of its bowl (828) — all three of these ‘8’ fragments (in Diels’ classification) come from Aétius. Metrodorus of Chios, one of Democritus’ disciples, apparently still believed that night and day were caused by the alternate extinguishing and rekindling of fiery vapour in the sun, that this also produced eclipses, and that the sun created the stars out of ‘radiant water’ (Axuxpoÿ úsaros, DK 70 As). Aétius connects him with Anaximander and Crates (flor. second century BC) in putting the sun as the highest of the celestial bodies, then the moon, and below these the fixed stars (which were illuminated by the sun) and the planets (DK 12 a18; cf. 70 A9). The same source tells us that according to both Thales and Metrodorus the moon was illuminated by the sun (70 A12 — the coupling together of these names is patently absurd), and that Metrodorus explained the Milky Way as the sun’s circle. Hecataeus of Teos or its colony Abdera is joined with Heraclitus by Aétius in allegedly stating that the sun is an ‘intelligent, ignited mass from the sea’ (&vaupa vospòv 7 èx OaAckernc, DK 73 89); Hecataeus is dated to the end of the fourth century Bc. The sophists in general did not profess a specialist knowledge of astronomy - their forte was to teach people how to ‘get on in life’ by inculcating the arts of rhetoric and argumentation and the handling of affairs. However Hippias, a sophist who was specially disliked by Plato, is portrayed as claiming a profound knowledge THE PYTHAGOREANS AND LATER PRE-SOCRATICS OI of the stars and celestial matters (Hipp. Maj. 285b), and certainly seems to have been an accomplished mathematician.115 Unfortunately, there is no evidence as to what his astronomical ideas were. According to the pseudo-Plutarchian Lives of Ten Orators, the funeral monument of Isocrates, who died in 338 Bc, depicted Gorgias, one of the older sophists (c. 485-375 BC), as looking at an astronomical sphere (eis chaipav &otponoyikhv Bhérovra — DK 82 A17); but this is probably no more than artistic convention, since a globe was a recognized decorative feature.116 There is no evidence in the extant fragments of Gorgias or in the tertiary sources? that he paid any particular attention to astronomy.

EARLY GREEK ASTRONOMY TO NOTES ARISTOTLE DK H. Diels, Die Fragmente der Vorsokratiker, 6th ed., Dox. Gr. H. Diels, Doxographi Graeci, 1879 EGP J. Burnet, Early Greek Philosophy, 4th ed., 1930 GFH D. R. Dicks, Geographical Fragments of Hipparchus, Guthrie, Hist. of Greek W. K. C. Guthrie, History of Greek Philosophy, 1962- 221 1 Part of the material in this chapter has been adapted from my article in Bull. Inst. of Class. Stud. No. 11, London, 1964, pp. 43ff. revised by W. Kranz, 1951-52 2 Hencea 1960 description of the type ofinstrument used in later Greek astronomy, e.g. by Hipparchus and Ptolemy, has been postponed to the second volume—meanwhile, see Journ. Brit. Astron. Assoc. 64, 1954, pp. 72-85 3 Much of this may be found in the elementary handbooks of astronomy written by Geminus in the first century Bc (Isagoge in Phainomena, ed. Manitius, Teubner, 1898) and by Cleomedes in the first century AD Philos. Harv. Theol. Rev. Harvard Theological Review Heath, Arist. T. L. Heath, Aristarchus of Samos, 1913 T. L. Heath, Greek Astronomy, 1932 Heath, Greek Astron. (Cyclica Theoria, ed. Ziegler, Teubner, 1891) 4 E.g. by Autolycus of Pitane in his On Risings and Settings, ed. Hultsch, Teubner, 1885, the earliest extant Greek astronomical treatise, dating from Heath, Hist. of Greek Maths. T. L. Heath, History of Greek Mathematics, 2 vols., J. Hist, Id. Journal of the History of Ideas the last decades of the fourth century Bc 5 Adapted from O. Schmidt’s paper on Autolycus in Den 11. skandinaviske matematikerkongress, Trondheim, 1949, pp. 204-05 Journal of Hellenic Studies 6 Ptol., Geogr. i, 7, 4 Amer. Orient. Journal of the American Oriental Society 7 Cf. Fig. 13, (p. 222) a diagrammatic representation of the terrestrial sphere Brit. Astron. Journal of the British Astronomical Association JHS Journ, 1921 with a parallel of latitude 00 at which the plane of the observer’s horizon is HH. Note that the latitude is given by the angle which by elementary Soc. Journ. geometry is the same as the height of the north celestial pole above the Assoc. horizon, but not directly by the angle «, which is the angle that the JNES Journal of Cuneiform Studies Journal of Near Eastern Studies JRS Journal of Roman Studies 90° — > KR G. S. Kirk and J. E. Raven, The Pre-Socratic Philo- Journ. Cuneif. Stud. equatorial plane makes with the horizon and is, in fact, the ‘co-latitude’ = 8 This is the ratio accepted by Hipparchus for Athens (Comm. in Arat. i, 3, 6), and gives a latitude about 1° too low - see p. 154 9 A ratio given by Eudoxus - see p. 154 sophers, 1960 L’Antiq. Class. L’Antiquité Classique LSJ H. G. Liddell and G. S. Scott, A Greek-English Lexicon, 9th ed., revised by H. S. Jones 10 On ancient trigonometry, see especially Heath, Hist. of Greek Maths., vol. MNRAS Monthly Notices of the Royal Astronomical Society 11 See GFH, pp. 159; 162-63 Neugebauer, ACT O. Neugebauer, Astronomical Cuneiform Texts, 3 vols., 12 See a news story in The Times of 14 April 1965, headed ‘Error Found in Neugebauer, Ex. Sci. O. Neugebauer, The Exact Sciences in Antiquity, 2nd 1955 Philol. Untersuch. Philos. Moon’s Orbit’ 13 Cf. O. Neugebauer, The Exact Sciences in Antiquity, 2nd ed., 1957, P. 99, “Mythological concepts which involve the heavens, deification of Sun, ed., 1957 OCT li, pp. 257-60, 265-73, 276-86 Moon, or Venus cannot be called astronomy if one is not willing to Oxford Classical Texts Philologische Untersuchungen count as hydrodynamics the existence of belief in a storm deity or the personification of a river. Also the denomination of conspicuous stars or Phron. Philosophy Phronesis Proc. Amer. Philos. Soc. Proceedings of the American Philosophical Society constellations does not constitute an astronomical science” 14 See A. Pannekoek, Hist. ofAstron., English trans., 1961, ch. 7; Neugebauer, RE Rhein. Mus. Pauly-Wissowa, Real-Encyclopädie Altertumswissenschaft Rheinisches Museum für Philologie op. cit., ch. 4 15 Cf. GFH, p. 14. The idea that astrology is an early, bastard form of astronomy is based on no good evidence at all—f. Neugebauer, op. cit., der classischen Ross, Arist. Met. W.D. Ross, Aristotle’s Metaphysics, 2 vols., 1924 Ross, Arist. Phys. W. D. Ross. Aristotle’s Physics, 1936 Van der Waerden, Anf. B. L. van der Waerden, Die Anfänge der Astronomie, 1956 p: 168 16 Plato’s recommendation in the Laws of the public worship of sun, moon, and stars (821 c-d) was never put into practice 17 See Hermes 91, 1963, pp. 6off.

EARLY GREEK ASTRONOMY TO NOTES ARISTOTLE 18 19 North celestial pole H 3. e. a Ce] > A parallel of 0 10) latitude / equator € ® A Fig. 13. Diagram illustrating the angles formed by the intersection of the terrestrial equator and north-south axis with the horizon at north latitude & 223 T. B. L. Webster, From Mycenae to Homer, 1958, pp. 44-5 To suppose that it was regarded as a thick disc is mere anticipation of later Pre-Socratic views (see p. 58); in reality, no clear idea of the shape and position of the earth in relation to the heaven and the underworld can be gained from the poems. At Il. viii, 13-16, Zeus threatens to hurl any disobedient god ‘into murky Tartarus, far, far away, where the deepest chasm is under the earth, and where there are iron gates and a brazen threshold, as far beneath Hades as the heaven is from earth’. Now obviously this is the language of poetic imagination, not that of cosmological speculation; but it is also the language of ‘mythopoeic’ thought, which does not operate with the same concepts of space, time, cause, effect, subjectivity and objectivity as were later to be made familiar by the Greek philosophers and hence absorbed into modern European thought (see H. and H. A. Frankfort, Before Philosophy, Pelican, 1961, ch. 1 and 8). It is therefore vain to expect the Homeric world picture to exhibit even that imaginative consistency in detail which Dante displays in his description of earth, heaven, and hell in the Divina Commedia — consistency, a sine qua non in scientific thinking, played a very minor role in pre-scientific (i.e. pre-fifthcentury Bc Greek) thought 20 Cf. Kirk and Raven, The Pre-Socratic Philosophers, 1960, pp. 12-13 21 Which I regret having followed myself in e.g. JHS 86, 1966, p. 31 22 The whole passage (x, 82-6) is odd: “Where herdsman calls to herdsman, the one driving in his flocks, while the other answers as he drives his out. There a sleepless man could earn two wages, one tending cattle, and the other pasturing silvery sheep; for the paths of day and night are close together.’ A sleepless man can always earn two wages anywhere, especially as it is made clear that the jobs are different (concerned with cattle and sheep respectively). One is tempted to suggest the excision of lines 84-5, i.e. There. . . sheep’; then the last line follows closely on the allusion to a night so short that no sooner has one man driven in his flocks, than another drives his out. The coalescence of two separate men into one sleepless man, and the differentiation of cattle and sheep, may have been an unhappy elaboration introduced by someone who did not understand the reference to short summer nights in the original lines 23 Eclipses are not mentioned as such, although there is one reference to the sun’s vanishing from the heavens (Od. xx, 356-57). This, however, occurs in the description of the supernatural terror and portents with which Athene afflicted the minds of the suitors before their impending doom (ibid. pp. 345ff.), and in the context can hardly refer to an actual event, although some of the ancient commentators took it as such (see Stanford ad loc.); the idea is occasionally revived by modern interpreters, according to whom a solar eclipse occurred in 1,178 sc with the line of totality passing through the island of Leucas (assumed to be Homeric Ithaca) - cf. T. L. MacDonald, Journ. Brit. Astron. Assoc. 77 (5), 1967, pp. 324ff. How

NOTES much this is pure coincidence or whether it represents a vestigial memory of an eclipse enshrined in the epic tradition, it is impossible to say. One would, perhaps, have thought that such a rare and impressive phenomenon as a total solar eclipse, if it had actually been experienced, would have merited more than such a brief allusion. According to Plutarch (De Fac. in Orb. Lun. 931e) solar eclipses were mentioned by Mimnermus and Archilochus (both of the seventh century BC), Stesichorus (seventh - sixth century) and Pindar (sixth - fifth century) as well as by Cydias (early-fifth century). Of these only the two mentioned by Archilochus (fr. 74 Anth. Lyr. Gr., ed. Diehl) and Pindar (Paean ix, 1-5 fr. 44, Bowra) can be identified with any certainty, the former = the eclipse of 6 April -647 (Jacoby’s doubts about this in CQ 35, 1041, pp. 97-8 are unnecessary), and the latter that of 30 April -462, being the largest visible at Thebes in Pindar’s time (cf. J. K. Fotheringham, ‘A Solution of Ancient Eclipses of the Sun’, MNRAS 81, 1921, pp. ro4ff; 107; 109) 24 As Finley points out (World of Odysseus, 1956, pp. 151-52), all that Helios can do when Odysseus’ men kill his cattle (Od. xii) is to rush off and complain to Zeus 25 Cf. Il. viii, 41, where a particular day is described as ‘bringing evil’ for the Greeks, and Od. i, 283, where rumour ‘brings news’ for men 26 Normally in the literary sources, unless the context clearly indicates otherwise, as it does at 567, ‘rising’ (ëruroX, distinguished from the daily rising which is évatodh — cf. Geminus, Isag. 13) and ‘setting’ (36015) refer to the heliacal rising and cosmical setting, both phenomena occurring before sunrise - cf. p. 13 27 The standard works in this field are P. V. Neugebauer, Tafeln zur astronomische Chronologie, 1912-25, and Astron. Chron., 1929; the astronomical data in F. K. Ginzel, Handbuch der math. und techn. Chron., 3 Bd., Leipzig. 1906-14 (photo-lith. repr. 1958) are based on Neugebauer’s tables bue Ginzel also gives additional tables listing useful data not tabulated by Neugebauer; U. Bachr, Tafeln zur Behandlung chron. Probleme, 1955 (Veröffentlichungen des Astron. Rechen-Instit. zu Heidelberg, Nr. 3) repeats some of Neugebauer’s tables using more recently worked values for the different constants 28 E.g. in the ‘parapegma’ texts, see pp. 84f. 29 Cf. M. P. Nilsson, Primitive Time-Reckoning, 1920, pp. 40-1; 49; 56; 64; 89; 115f.; 129f.; Aratus, Phain. 264f. and schol. ad loc. Men 30 Cf. 586-88, ‘Women are most wanton and men most feeble when Sirius parches the head and knees, and the skin is dry because of the heat’; similarly at Scut. Her. 397. As in II. xxii, 30-1, it is highly improbable that the figurative language used here implies a belief that the stars actually affected conditions on earth - cf. above, p. 95 31 W. Kubitschek, Grundriss der antiken Zeitrechnung (in Müller’s Hdbk. d. 225 Altert.), 1928, p. 109, fixes it at 28 Dec. for latitude 38°N. about 800 Bc 32 Well explained by A. W. Mair in an addendum, entitled ‘The Farmer’s Year in Hesiod’ (especially pp. 1305 142), to his translation of Hesiod’s poems (Oxford, 1908) 33 As is stated by the scholiast on Aratus, Phain. 254 — cf. 172 — and alleged extracts from which are given in Pseudo-Eratosthenes, Catast. fr. ı and 32 (ed. Robert, Berlin, 1878; cf. Maass, Philol. Untersuch., Heft 6, 1883, pp. 3-55); cf. Diod. Sic. iv, 85; Plato, Epin. 990a; Callim. Ep. 27 34 Cf. my article ‘Solstices, Equinoxes, and the Pre-Socratics’, JHS 86, 1966 35 W. K. C. Guthrie, History of Greek Philosophy, vol. ii, 1965, p. 345 36 First ed. 1903; sth ed. 1934-37 revised and re-edited by W. Kranz in three vols. and reprinted several times since 37 E.g. in Metaphysics A - although there is little doubt that his historical notices of earlier doctrines are sometimes coloured by his own preconceptions; cf. H. Cherniss, Aristotle’s Criticism of Pre-Socratic Philosophy, 1935 38 Cf. CQ 9, 1959, pp. 294-309, especially 298 39 Anthologies of the collected ‘opinions’ (68a — also dp£okovre, Latinized as placita) of earlier thinkers were best-sellers in late antiquity 40 Cf. also Heath, Arist., pp. 2f. 41 Cf. JHS 86, 1966, pp. 29f. J. E. Raven, The Pre-Socratic Philosophers, 1960, p. 7 - here42 G. S, Kirk and after referred to as KR 43 Cf. Aristophanes, Clouds 180; Birds 1009; Plato, Theaet. 1744 44 Both these theorems are attributed to Thales on the authority of Eudemus (Proclus, Comm. in Eucl. i, ed. Friedlein, pp. 299, 1; 352, 14). For Thales bringing geometry into Greece from Egypt, see the “Eudemian summary’ in Proclus (op. cit., p. 65, 7; Wehrli, Die Schule des Arist., Heft 8 - Eudemos von Rhodos, fr. 133) 45 Which would require, as well as an accurate knowledge of solar and lunar cycles and the moon’s deviations in latitude from the ecliptic, an understanding of the concept of geographical latitude in order to be able to predict the totality of the eclipse in a given region. Such an advanced level of knowledge was not even reached by Babylonian astronomy of the Seleucid period (the last three centuries Bc), much less that of the sixth century BC 46 Cf. the creation myths of the ancient Egyptians and Babylonians and of Genesis (KR, ch. 1, especially pp. 33f.). Recent speculation has attributed a similar type of cosmogony, with the personified figures of Ilépoc and Téxpop (apparently “Contrivance” and ‘Differentiation’) to the seventhcentury BC Spartan poet, Alcman - see M. L. West, CQ 13, 1963, pp. 154-56, and CQ 17, 1967, pp. I-15 47 The same word is used by Socrates (Phaedo 10942) of the heavens (odpavós) in a similar context - see p. 95

48 Cf. the waters of the firmament in Genesis 1 49 See especially C. H. Kahn, Anaximander and the Origins of Greek Cosmology, Columbia Univ. Press, 1960, passim so Compare the accounts of Anaximander’s supposed ‘system’ given by Heath, Arist., 1913, ch. 4; J. S. Morrison, JHS 75, 1955, pp. 62-3; KR, pp. 134-37; Kahn, op. cit., pp. 87ff.; Guthrie, vol. i, pp. 93-9; O’Brien, CQ 61, 1967, pp. 423ffs1 It is very improbable that the planets were yet differentiated (cf. JHS 86, 1966, p. 30), and, if they were not, occultations of stars by them would presumably not be noticed, so that Anaximander’s alleged order of the celestial bodies might not seem so crass; but occultations of stars by the moon are relatively frequent and more easily observable 52 Strangely, no modern booster of the Pre-Socratics as ‘super-scientists’ has, to my knowledge, seized on this as “convincing evidence’ for their understanding of the principle of the hovercraft . . . No doubt this will come in time — we have already had it suggested that Wegener’s theory of continental drift was anticipated by Thales’ earth floating on water! (K. R. Popper, ‘Back to the Pre-Socratics’, Proceedings of the Aristotelian Society, Oct. 1958, p. 3). For a sensible rebuttal of such fancies see G. S. Kirk, ‘Popper on Science and the Pre-Socratics’, Mind 69, 1960, p. 328 53 The dates of the Pre-Socratics are largely guesswork, although some guesses are more informed than others 54 This type of contradiction is frequent in the tertiary sources, and serves to demonstrate why they are so untrustworthy as independent evidence 55 Heath (Arist., p. 42-3) also compares another passage in Aétius (ii, 23, 1 = DK 13 ats), which speaks of ‘the stars making their turnings by being thrust off course’ by wind (3EwPobpeva tà Kotex rag rpondg moretoOan). This is another notion that we shall meet again in connection with later Pre-Socratics 56 DK 21 A32; A33; A37-41; A45 57 Hisis the famous dictum mévra pel (cf. Plato, Theaet. 1814), and the remark that you cannot step into the same river twice (DK 22 831) 58 His is the first extant use of the actual word wéouos in its philosophical sense of ‘world-order’, i.e. practically equivalent to “universe” — cf. J. Kerschensteiner, Kosmos, Munich, 1962 (Zetemata, Heft 30) 59 J. H. Morrison in JHS 75, 1955, accepting every scrap of evidence from whatever source, has attempted a reconstruction which is based on attributions to both Anaximander and Parmenides of astronomical knowledge (e.g. of the ecliptic) which it is highly improbable that they possessed (see my article inJHS 86, 1966) 60 This from Strabo via Posidonius, A44a — it is, of course, completely wrong, as the theory of zones is a gross anachronism for Parmenides’ time: cf. my GFH, pp. 23-6 61 &dAStELOV dá, properly ‘a light belonging to someone or something NOTES 237 else’ - the phrase is evidently a pun on the Homeric &XM6rptog doc, ‘a foreign man’, Il. v, 214; Od. xviii, 219 62 Cf. fr. 115, 11, aidépos . . . Sévauc and the alBEprog Sivos of Aristophanes, Clouds 380 63 &lofetc — not necessarily “globulated”, as some translators have it 64 Unfortunately, the text of Plutarch, De Fac. in Orb. Lun. 929c (which provides the fragment) is uncertain; for the Ms dneoxebace dé of adyós, Bore alav xußörepdev, Diels conjectured dneotéyacey . . . lor av in xaObrepev, followed by KR who translate (p. 334), But she kept off the sun’s rays, so long as it was passing over above her, and cast a shadow over as much of the earth as was the breadth of the pale-faced moon’ (cf. Guthrie, vol. ii, p. 197). Yet the verb &rooteydto, here translated ‘kept off’, is used again in fr. 100, 14 where KR translate it ‘uncover’ (the meaning given by LSJ, s.v.), which is also how Diels translates his own conjecture (DK, vol. i, p. 330, “Der Mond deckte ihr (der Sonne) die Strahlen ab”). Cherniss (Moralia, vol. xii, Loeb, ad loc.) retains the Ms reading, but prints dneoxéSucev for dneoxebace, and translates, ‘His beams she put to flight . . . From heaven above as far as to the earth, Whereof such breadth as had the bright-eyed moon She cast in shade’ 65 Compare the famous clepsydra simile in Broo (also from Aristotle - De Resp. 7, 47359), designed to illustrate the corporeality of air by the behaviour of water in a double-ended vessel when one end is blocked up. This is not, as sometimes claimed (e.g. by Burnet, Early Greek Philosophy, p. 27), an instance of the use of the experimental method in ancient science — see KR, p. 342; Guthrie, vol. ii, pp. 225-26 66 Unless Aristotle misunderstood the point of Empedocles’ analogy. For a discussion of various views on this passage, see Guthrie, vol. ii, p. 198-99 67 J. Longrigg in CQ 15, 1965, has an ingenious notion that this idea might well have been ‘derived from his observation of the formation of salt under the action of the sun’s heat’! (p. 251) 68 Aristotle obviously had a similar feeling when he contrasts the sobriety of Anaxagoras’ views with the random opinions of his predecessors (Met. A 984b17) 69 Cf. Xenophon (Mem. iv, 7), who makes Socrates assert that Anaxagoras must have been out of his mind (mupedpdvycev) to have said such things, and makes him refute them by some painfully naive arguments 70 The scientific ideas that Aristophanes pokes fun at and attributes to Socrates and his ‘thinking-shop’ in the Clouds, are mainly those of Anaxagoras 71 His word for the primal movement is repixdpnote, ‘rotation’, instead of Stvn 72 Diog. Laert. ii, 12 (cf. Diod. Sic. xii, 39). Plutarch (Per. 32) connects Anaxagoras’ impeachment with a decree proposed by one Diopeithes, c. 431 BC, and aimed at ‘those who do not believe in the gods or who teach doctrines about celestial matters’. This, together with Plutarch’s

EARLY GREEK ASTRONOMY TO ARISTOTLE exaggerated description of the hostility of the Athenian public to new NOTES 80 astronomical ideas (Nic. 23 - see my forthcoming review in CR of T. W. Africa’s Science and the State in Greece and Rome, 1968) has led some astronomy was officially forbidden at Athens during the latter part of the fifth-century Bc. Nothing could be further from the truth. As we shall see, this was the time when Greek mathematical astronomy had its beginnings, with the collation and codification of astronomical and meteorological phenomena in the ‘parapegmata’, the diffusion of Pythagorean ideas on the sphericity of the earth and the circular orbits of celestial bodies, the discovery of the obliquity of the ecliptic by Oinopides, and the activities of Meton and Euctemon in measuring solstices and equinoxes and improving the calendar. The circumstances of Anaxagoras’ impeachment are by no means clear — see the discussions by Taylor (CQ 11, 1917, pp. 81-7), Davison (CQ ns. 3, 1953, pp. 42-5), and Guthrie (vol. ii, pp. 322-23); but it seems most likely that it was really Pericles who was being attacked through his old master, Anaxagoras. As a former Persian subject, Anaxagoras also came under suspicion of ‘medism’. The fact that he advocated unorthodox opinions about the celestial bodies may have helped the prosecution, but with Stoic ideas here 81 condemn him - just as a similar charge did not suffice in the case of Socrates, who was condemned mainly because of his anti-democratic connections and sentiments 73 Cf. K. R. Popper, “Back to the Pre-Socratics’, Proceedings of the Aristotelian Society, Oct. 1958, p. 3, ‘. . . but most of them [the ideas of the PreSocratics], and the best of them, have nothing to do with observation’. Kirk notes the ‘superficial glance which was all that many Pre-Socratics seem to have considered necessary’ (Mind 69, 1960, p. 329) 74 The mathematical relationship expressed by which is now known to have been familiar to the Babylonian mathematicians at least a thousand years before Pythagoras 75 This, as Heath points out (Arist., p. 99), entails one complete rotation of the earth on its axis as it completes one circuit of the central fire 76 This, however, is a stock title which the doxographers attribute to practically every single Pre-Socratic - cf. KR, p. 101 77 On the nomenclature of the planets see F. Cumont, ‘Les noms des planètes et l’astrolatrie chez les Grecs’, L’Antiq. Class. 4, 1935, pp. 5-43 78 Unless, indeed, the moon was supposed to reflect the light of the central fire and not that of the sun. Apparently, some Pythagoreans realized that the moon shone by reflected sunlight (Diog. Laert. viii, 27), but others still spoke of its own fire being kindled, spreading to the state of full moon, and then being gradually extinguished (Aétius, DK 58 836) 79 Cf. the use of the word évratpew in a geographical sense - GFH, p. 125 The Greek is of DE yvyotdtepov adróv neraoyövres Tp pèv dv TH pto Aéyovor Thy Önmiovpyuchv Sbvanıv thy Ex wéoov rca thy viv Cwoyovoÿcav Kal td drebuyyévoy abris dva0aArotoay. Surprisingly, this has been interpreted as referring to another brand of Pythagoreanism which believed in a fiery core at the centre of the earth, itself situated in the middle of the universe — as though the words év 7 uéow and &x péoov referred to the earth’s centre and not the centre of the cosmos (H. Richardson, CQ 20, 1926, pp. 118-21; Guthrie, vol. i, pp. 290f.). Not only does the context show this interpretation to be impossible, but there is no good evidence for the idea of a fiery core to the earth in Pythagorean thought. Guthrie can only point to a similar idea in Empedocles and assume that this might have formed part of early Pythagoreanism, and the single piece of evidence for a geocentric universe in this school (which entirely contradicts what we are told by Aristotle who, after all, did write a book on the Pythagoreans) is the muddled account of Diogenes Laertius (viii, 25 ad fin.), * ostensibly reporting Alexander Polyhistor, which does not mention the Philolaic scheme at all, but attributes a ‘spherical cosmos possessing soul and intellect and surrounding the central earth that is also spherical and inhabited all round’ to ‘Pythagorean writings’. There is obvious confusion scholars (e.g. J. B. Bury, CAH, vol. v, p. 383) to suppose that the study of it is highly improbable that this alone would have been sufficient to 229 This is implicit in Simplicius’ words, (pp. 511-12 ed. Heiberg, à dt dvttyOwv rkivovpévm mepè td uéoov kal Exopévyn TH YH TadTy odg épärar dp hubv Frà td Enınpooheiv Auty del Td Tic yij¢ cópa) 82 As Dreyer sensibly remarks (Hist. of Astron., Dover reprint, 1953, p. 48), it would require an observer at the centre of motion itself to differentiate between a motionless outer heaven and an earth revolving in exactly twenty-four hours, and a slowly rotating outer heaven with an earth revolving in a slightly shorter period 83 B. L. Van der Waerden, Die Astronomie der Pythagoreer, Amsterdam, 1951, p. 54. The book gives a totally misleading idea of its subject matter, and is based largely on what the author thinks Pythagorean astronomy ought to have been; thus, to explain the Philolaic system Van der Waerden makes up his own “einzige Lösung? (p. 60) according to which the order of the orbits from the centre is sun, Mercury, Venus, earth (with moon encircling it), Mars, Jupiter, and Saturn — an order for which, needless to say, there is not a shred of evidence and which contradicts the little we are told about the scheme 84 Arist., p. 100 — but his translation of the passage ‘. . . that it revolves round the fire in an oblique circle in the same way as the sun and moon’ (p. 97) does not square with such an interpretation (which Dreyer also seems to accept - op. cit., p. 45). As far back as 1810, A. Boeckh evidently took the same view (Gesammelte Kleine Schriften, Bd. 3, Leipzig, 1866, pp. 266; 85 This is obviously the motivation of Boeckh, Heath, Dreyer, and Van der

NOTES 231 Waerden as well; but it is surely not justifiable in the face of the bulk of 105 Pliny, Nat. Hist. ii, 31 — on this see JHS 86, 1966, pp. 26-7; 30 the evidence 106 E.g. J. K. Fotheringham, in JHS 39, 1919, pp. 164-84; refuted in detail by E. J. Webb in JHS 41, 1921, pp. 70-85; Fotheringham’s reply in JHS 45, 1925, pp. 78f., based on incorrect ideas of early Babylonian astronomy (including the so-called Babylonian ‘saros’ - on which see Neugebauer, 86 Cf. Guthrie, Aristotle On the Heavens, Loeb, 1960, pp. 136-37 87 Cf. Van der Waerden, Anfange der Astronomie, 1966, pp. 49-50. On the influence of Babylonian astronomy on Greek, see above, pp. 163ff. 88 Hence Diels omits it from DK 58 - cf. Dox. Gr., Prolegomena, p. 69 89 Cf. Timaeus 39d 90 I precursori di Copernico nell’ antichita, Milan, 1873, p. 8 91 Heath, Hist. of Greek Maths., vol. i, pp. 246-49 92 Odes i, 28, 1-6 93 Hence the unnecessary doubts that have been raised as to whether Plato regarded the earth as spherical; but Socrates in the Phaedo opposes orpoyybAog to mitos, ‘flat’ (97d - see above, p. 94), which is the word specifically connected with the Anaxagorean disc-shaped earth (see p. 58), and so in this case there is nothing to prevent otpoyytAog meaning ‘spherical’ - and the rest of Plato’s astronomical passages undoubtedly imply a spherical earth (see p. 98) 94 Or, perhaps more accurately, there was a common stock of astronomical notions ascribed to earlier thinkers from which all tertiary sources draw 95 The notion that the celestial bodies are nourished by exhalations from the earth (probably on the analogy of burnt offerings to the gods) is attributed by Aétius to both Heraclitus and Philolaus (DK 22 AIT; 44 A18) 96 sed nec numerum illarum posuit nec nomina, nondum comprehensis quinque siderum cursibus 97 See A. Rehm’s article in RE, Bd. 18 (4), 1949, col. 1299f. H. Diels (Antike Technik, 3rd edition, 1924, Tafel 1, pp. 6-7) gives an illustration of one fragment 98 See the detailed study by Rehm, ‘Parapegmastudien’, Abhandl. d. Bayerischen Akad. d. Wiss., phil.-hist. Abt., neue Folge, Heft 19, 1941, pp. sff. 99 Ed. Manitius, Teubner, 1898, pp. 210-33; Manitius shows that the calendar actually belongs to a period about one hundred years earlier than the main text which is dated to c.70 BC 100 Ed. Heiberg, vol. ii, 1907, Claudii Ptolemaei Opera Astronomica Minora, Teubner, pp. 1-67 101 Other Greek calendars are published in Sitz.-Berichte Akad. Heidelb., phil.-hist. Kl. I (1910), If (1911), IMA (1913) — this contains a conjectural restoration by Rehm of Euctemon’s parapegma (on whom see below) — IV (1914), and V (1920) 102 émonuactat, ‘signs or indications of weather” — émonuatveww is used of marking a change in the weather; cf. Rehm’s article ‘Episemasiai’ in RE, Suppl. Bd. 7, 1940, cols. 175-98 103 O. Neugebauer, The Exact Sciences in Antiquity, and ed., 1957, ch. 5 104 M. P. Nilsson, Primitive Time-Reckoning, p. 343; Die Entstehung . . . griech. Kal., 1962, pp. 31f.; 56 Ex. Sci., pp. 141-42), is not convincing 107 Isag. ch. 8 - Geminus connects Euctemon but not Meton with this cycle (§ 50), but Meton’s share in the discovery is amply attested by other sources (cf. Heath, Arist., p. 293) and it is possible that his name may have dropped out of the text - see Manitius ad loc. 108 This figure is expressly mentioned by Hipparchus as the estimate of Meton and Euctemon — Almag. iii, 1, p. 207, 9 ed. Heiberg 109 Ed. F. Blass, 1887 — it is not, of course, by Eudoxus himself, but may be a student’s exercise based partly on Eudoxan data, but containing many errors and with later material added 110 Quoted by Heath, Arist., p. 132 111 See the calendar compiled by W. H. S. Jones (Loeb Hippocrates, vol. i, pp. 67-8) 112 Cf. R. Joly, Hippocrate: Du Régime, Budé, 1967, pp. xiv-xvi 113 On the whole subject see B. L. van der Waerden in JHS 80, 1960, pp. 168-80; W. K. Pritchett in Historia, Bd. 13, Heft 1, 1964, pp. 21-36 114 He suggested a method of squaring the circle by successively inscribing regular polygons with double the number of sides of the previous one - see Heath, Hist. of Greek Maths., vol. i, p. 222 115 Heath, Hist. of Greek Maths., vol. i, pp. 23; 225 116 Cf. A. Schlachter, Der Globus, ed. F. Gisinger, 1927 (Stoicheia, Heft 8), pp. 174f. The author’s attribution of knowledge of the celestial sphere and advanced astronomical ideas to Anaximander and Parmenides should be disregarded 117 With the single exception that a fifth-century AD writer on rhetoric, Sopater, attributes to him the opinion that the sun is a molten lump (DK 82 B31) 118 E.g. A. E. Taylor (A Commentary on Plato’s Timaeus, Oxford, 1928) was firmly convinced that the whole world-system expounded in that dialogue was not Platonic at all, but fifth-century Pythagorean - a “Taylorian heresy’ that has been sufficiently refuted by F. M. Cornford in Plato’s Cosmology, 1937, pp. ixf. On the other hand, the extent to which what are generally regarded as typically ‘Platonic’ doctrines (e.g. the theory of Ideas, the immortality of the soul, and the recollection of knowledge) are the creations of Socrates or of Plato himself remains a question which is as insoluble as ever (cf. C. J. de Vogel, Phronesis 1, 1955, pp. 26-35) 119 Thus the description of the spindle of Necessity with its eight whorls (Rep. x, 616b-617b) forms part of the myth of Er which is avowedly only a tale (cf. the beginning, 614), 85 note. . . and the end, 621}, cat obtac, è

Trobxov, 15006 60. . .), and the whole of Timaeus’ account of the genesis of the universe (including, therefore, the astronomical section, Tim. 36b-40d) is no more than a ‘likely tale’ with which mere mortals must be satisfied (id. 29d) 120 One is irresistibly reminded of Fitzgerald’s Omar Khayam, Myself when young did eagerly frequent Doctor and Saint, and heard great argument About it and about: but evermore Came out by the same door where in I went (Stanza 27) Because both Simmias and Cebes had consorted with the Pythagorean Philolaus (6146-7), Simmias’ assent has been used as evidence (somewhat illogically) for a non-Philolaic, presumedly early, version of Pythagorean cosmology, in which the spherical earth and not the central fire (note 80) was placed at the centre of the universe (cf. Burnet, EGP, p. 297 note 3). This is at complete variance with what Aristotle tells us about Pythagorean doctrines, as is also the only other evidence for this belief, namely, the garbled account of Diogenes Laertius (Diels, Vorsokr. p. 58 B1a6); when it comes to choosing between the latter and Aristotle, there is little doubt as to which to follow. Moreover, Simmias’ assent need only refer to the statement that the earth needs no support, which is equally apposite for the planetary earth in the Philolaic system itself; the conditional form in which Socrates states the central position and circularity of the earth (despite the fact that there can be little doubt that this is Plato’s own view - see below) may have been purposely chosen so as to command Simmias’ assent to the proposition that the earth needs nothing to support it. Socrates might have thought, ‘I know that you, as a Pythagorean, do not agree that the earth is at the centre of the universe, but grant me for the sake of argument that it is, then you will certainly agree that it needs no support, won't you?’, and Simmias, of course, does 122 This is probably a reference to the dodecahedron, which can be constructed from twelve regular pentagons; its volume approaches closely that of the circumscribed sphere, and if the pieces are made of flexible material stitched together (as here) and filled out, a sphere would result - see Burnet ad loc. In the Timaeus (s5d-56b) four of the five regular solids are appropriated to the four elements (earth = cube, fire = pyramid or tetrahedron, air = octahedron, and water = icosahedron), but the fifth, the dodecahedron, which cannot be constructed from Plato’s basic right-angled triangles, is merely stated somewhat vaguely to be used by the god ‘for the whole’ (rt rd máv, 550) - very possibly with this passage of the Phaedo in mind. It is highly improbable that any allusion to the twelve signs of the zodiac is intended, which is an entirely different concept, and still less likely that an astronomical system of mapping the sky into twelve zones 121 NOTES EARLY GREEK ASTRONOMY TO ARISTOTLE 233 is referred to, for which there is no evidence at all (see Cornford, Plato’s Cosmology, 1937, p. 219) 123 J. A. Stewart, The Myths of Plato, ed. G. R. Levy, 1960, p. 119 124 The situation is similar in modern science fiction; it is the writers who operate on a plausible basis of moder scientific concepts (of course, imaginatively employed and extended) who succeed best in this genre 125 Aristotle, characteristically, fails to realize this, and subjects Plato’s fanciful picture of the earth’s subterranean waters (11 1d-112e) to a solemn, scientific criticism (Meteor. ii, 2, 355b32ff-); cf. also Friedlander, Plato, vol. i (English trans. 1958), p. 267 126 No ancient commentator ever had any doubts as to this, but some modern scholars have exercised their ingenuity in manufacturing them; e.g. T. G. Rosemeyer, CQ 6, 1956, pp. 193-97, and Phronesis 4, 1959, pp. 71-2; J. S. Morrison, Phron. 4, 1959, pp. 101-19 127 Presumably, this implies indirect observation of the sun’s image on a liquid surface, not direct observation through, e.g., a liquid-filled flask, since the words bévraoux and eixdv would hardly be appropriate for the latter method. Since Socrates is still talking about the time when he was a young man, unless Plato is here committing an anachronism (which is by no means improbable), this would seem to indicate that the observation of eclipses was a well-known proceedure in the middle of the fifthcentury BC 128 J. Adam, The Republic of Plato, and ed., vol. ii, p. 67 129 For which see the monumental bibliography compiled by H. Cherniss in Lustrum 4-5, 1959-60 130 Some of the more percipient treatments of this and other topics in Platonic philosophy are to be found in the collection of articles entitled Studies in Plato’s Metaphysics, ed. R. E. Allen, 1965 131 Met. A 6, especially 987b14ff.; for the other passages imputing this doctrine to Plato, see W. D. Ross, Aristotle’s Metaphysics, vol. i, 1924, p. 166 ad loc. 132 Cf. A. Wedberg, Plato’s Philosophy of Mathematics, 1955, who upholds Aristotle’s interpretation; for weighty arguments against it, see H. Cherniss, Aristotle’s Criticism of Plato and the Academy, vol. i, 1944, pp. 226f.; 244; 289f. and notes 133 Cf. Wedberg, op. cit., p. 32, ‘Between extreme nominalism, which denies the existence of any abstract entities, and an extreme realism, which accepts more or less wholesale all significant expressions as designating entities (abstract if not concrete), there is an entire spectrum of possible positions . . . Plato did never clearly define where along this spectrum he took his stand’ 134 Socrates is somewhat unfair here; there is no reason why Glaucon’s remark should be taken absolutely literally - he might himself have been thinking of astronomy in a metaphysical way - particularly in view of Socrates’ own phrases earlier where he speaks of ‘leading the soul upwards’

EARLY GREEK ASTRONOMY TO NOTES ARISTOTLE matics becomes, what Plato in his theory of education requires it to be, (ävo moe &yer thy Yoxhy, 525d) and ‘making it see the Idea of Good’ the stimulus to philosophy”); cf. F. M. Cornford, Mind 41, 1932, pp. 37-52 TÒ rrotely KariSely thy od dyabod idéav, 526e) and 173-190 (“The distinction of objects [in the Line] is a matter of 135 There is an obvious allusion to the comic caricature of ‘Socratic science’ in expediency in teaching”) Aristophanes Clouds 188ff.; cf. Plato Apol. 19c 136 E.g. H. S. Williams, Hist. of Sci., 5 vols., 1904-10, vol. i, pp. 180ff. (Plato’s it is not the observable phenomena of the heavens that Plato regards as unchanging and eternal, but ‘unwandelbar sind nur die Gesetze, die dem Wunderbau des Himmels zugrundeliegen’ (“Platons 141 As E. Dént well remarks, point of view ‘essentially non-scientific’); W. C. D. Dampier-Whetham, Hist. of Sci., 1929, p. 28 (Plato's science ‘fantastic . . . he roundly con- Spätphilosophie und die Akademie’, Österreichische Akademie der Wissendemned experiment’); F. K. Richtmyer, Introd. to Mod. Phys., 2nd ed., schaften, Sitzungsberichte, phil.-hist. Klasse, Bd. 251, Abh. 3, Wien, 1967, 1934, p.9; C. Singer, Short Hist. ofSci., repr., 1943, pp. 34f. (but Singer does see some redeeming features in Plato, especially for mathematics and astronomy); B. Russell, Hist of West. Philos., 1945, p. 165 (the Timaeus is “silly”); J. Jeans, The Growth of Physical Sci., 1947, pp. 47ff. (Plato, a ‘major disaster’ for physics); J. O. Thomson, Hist. of Anc. Geogr., 1948, p. 101; B. Farrington, Greek Sci., Pelican, 1953, p. 120 137 E.g. J. Adam, The Republic of Plato, 2nd ed., 1965, Appendices I and II to Book vii 138 The translation is my own but obviously owes much to other versions, of which P. Shorey’s (in the Loeb Plato) probably comes closest to it. The Greek text (about which there are no serious ms doubts) is as follows (529c-d): tadta iv tà dv tH obpavé moridpara, ¿mebmep dv death memotKirtar, «dMuota pev HyetoOar Kal dkpiBiorara TV ToLlodtayv Eye, tiv Sì dAnOwdyv ord Evdelv, dc TO dv Téyoc Kal $ do Bpadurhs ev TO ¿Adivó dpiduò Kat nar rola KAndEcı oyhuaor bopéc te mpdc nda héperat cod tà Evévra déper. The infinitive hyeto0a depends on Seîv understood from Glaucon’s question; tév &Andıvöv I take to mean the true realities compared and contrasted with tv torodtav which are the things of the visible world; ds . . . dopéc is adverbial accusative serving to define both rond évdeiv and déperar, and tà évévræ must, in my view, mean the actual celestial bodies which are carried round in the 235 Gf de similarly hyperbolical statement that the man out of the Cave will . 6 142 be able to look on the actual sun itself’ (516b - quoted above) p. 152): “His advice 143 Well represented by Neugebauer (Ex. Sci., 2nd ed., to the astronomers to replace observations by speculation would have destroyed one of the most important contributions of the Greeks to the exact sciences” 144 His standpoint in this respect is consonant with his hostility to the views of Democritus, who composed a ‘parapegma’ or at least made observations for one (see above) 145 There is no evidence anywhere in the extant works of Plato that he ever conceived of anything other than the earth as lying at the centre of the universe; nor does Aristotle attribute any such notion to him. The wellknown story found in two passages of Plutarch (Quaest. Plat. viii, 1 and Numa 11 — the former by hearsay, gaot, but the latter allegedly on the authority of Theophrastus) that, towards the end of his life, Plato repented of having given the earth this central position, which should be occupied by something better, may safely be dismissed as a speculative piece of gossip or a misunderstanding of the sources. 146 This, of course, is not the first time this has been pointed out - ef. A. N. orbits that Plato hypostatizes as ‘real speed’ and ‘real slowness’. For other Whitehead, The Concept of Nature, 1920, p. 18 (‘Plato’s guesses read much interpretations of this passage, see Adam, App. X to Book vii 139 TpoPAnuacw Kea, Av Sey, ypouevor donep yewpetolav obta Kal &otpovouiav uerıuev, tà Sev TÁ obpav@ Édoouev — note the last word; they are more valuable. The main outline of his ideas is comparable with Plato does not use here the phrase yatpewv ¿dv, ‘to renounce’ or ‘dismiss altogether’ (frequent elsewhere in Plato, e.g. Phaedo 63e; Prot. 348a; Phileb. 59b), as he might well have done had he meant to imply that observation could be dispensed with entirely, but the simple verb meaning ‘to let be’ or ‘leave on one side’, evidently for the time being while the astronomer concentrates on the mathematical side of his subject 140 Many interpreters of the Line have been led astray by a failure to appreciate the twofold purpose of the simile, and, by trying to force Plato’s thought into a rigidly consistent scheme, have rendered it a good deal more obscure. For an eminently sensible treatment of the Line, see J. L. Stocks, CQ 5, 1911, 73-88 (p. 76, ‘The Line is not a progression’; p. 78, “Thus mathemore fantastically than Aristotle’s systematic analysis; but in some ways that of modern science’); Sci. and the Modern World, 1926, pp. 42-3; P. Shorey, ‘Platonism and the History of Science’, Proc. Amer. Philos. Soc. 66, 1927, pp. 159-82; A. Rey, La sci. dans Pantig., 6 vols., 1930-48, vol. iii, 282ff.; G. C. Field, ‘Plato and Natural Sci.’ Philos. 8, 1933, pp. 131-413 A. Momigliano (reviewing Farrington’s Sci. and Polit. in the Anc. World, 1939) in JRS 31, 1941, pp. 149ff-;J. E. Boodin, ‘The discovery of form’, J. Hist. Id. 4, 1943, p. 191 (‘. . . Platonic intuition of form and measurement everywhere’); W. Heisenberg, Philos. Probs. of Nucl. Sci., trans. F. C. Hayes, 1952, pp. 33f. (Plato’s stress on mathematical laws of nature underlying natural phenomena); p. 57; and on the whole subject, G. E. R. Lloyd, ‘Plato as a Natural Scientist’, JHS 88, 1968, pp. 78-92 147 Plato seems here to have taken over the semi-mystical Pythagorean

conception of numbers as the basic ‘stuff’ out of which the universe is composed (see pp. 64f.). There is obviously less justification in the case of harmonics for a purely theoretical treatment than in astronomy, and it would seem that Plato in this instance allowed himself to be unduly influenced by Pythagorean notions, in the interests of emphasizing his cherished conviction that mathematical harmony underlies the whole phenomenal world - cf. the number mysticism of Rep. viii, 546b-c, the notorious ‘Platonic number’, which has nothing to do with astronomy 148 Taking &vadev with xadopäv (cf. 616d, xbxAove &vadev tà zelin datvovrac and Phaedo 110b, ei ic &vadev Berto) — others take it with rerauévov ‘stretched from above’ (cf. Adam, ad loc.) 149 Adams translates mepibopás as ‘revolving spheres’, which is misleading as there is no mention of spheres in the description at all; repıbop& means the particular form of movement appropriate to a circle, i.e. revolution or rotation (cf. Arist., De Anima. i, 3, 13, vod uèv yap Kivnoic vónote, KbKov SÈ reprpopd) 150 Cornford’s picture of a ‘nest of hemispherical bowls’ (Plato’s Cosmology, p- 75; The Republic of Plato, p. NOTES 237 Morrison) unconvincingly takes Sk here in the sense of ‘over’, despite the clear parallel in Tim. 40b tov Sid navrdg médov terapévo (cf. Adam, vol. 11, App. VI, p. 471) 153 olov tà Úrolóparta tv rprhpwv — again there is doubt as to the meaning; the reference might be to ropes passed horizontally round a ship from stem to stern, or to ropes going under the keel and up the sides in a vertical plane, both types serving to strengthen the hull (see Adam ad loc.) 154 Cf. Adam ad loc.; Cornford, Tim., p. 88 and Rep., p. 354; Heath, Greek Astron., p. 48;. Shorey in the Loeb Rep. translates ‘with returns upon itself’, which is hardly illuminating 155 If Zeus is the sphere of the fixed stars, are we to imagine the other gods as standing and being carried round on his back? 156 R. Hackforth, Plato’s Phaedrus, 1952, pp. 72-3; but the reason he gives (p. 74, * . . . it seems an insuperable objection that the planets of Greek astronomy did not have hosts of satellites’) is irrelevant — there is no question of planetary satellites, but of a multiplicity of gods and daemons which is well attested for Plato (cf. Polit. 272e; Tim. 40d; 41a; Rep. 617e; 620d; 350) is an unwarranted inference from the actual Greek text which mentions neither spheres nor hemispheres. We 157 Cf. J. Bidez, Eos ou Platon et l'Orient, 1945, ch. 8 are told simply that the whorls fit inside each other xaß&rep of xádor of 158 Both Sophocles and Euripides equate Hestia with the earth - Soph. fr. 615 elo dAdhAovg &puörrovres. Now the x&ödog in shape is generally taken to (Pearson, vol. ii); Eur. fr. 938 (Nauck); of Tim. Locr. 97d; Plut., De Primo resemble the amphora, having two handles and a neck narrower than its belly (cf. Amyx in Hesperia 27, 1958, pp. 186-90); this, of course, makes it impossible for such xé3dot to fit into one another. It seems likely that here Plato is using x&8og in its other sense of a measure of volume (see LSJ s.v.); two such standard measures, in the form of bronze cylinders, one fitting inside the other, have actually been found and are dated to c.400 Bc (The Athenian Agora, vol. x, 1964, Pl. 14, DM 42 and 43). The notion of hemispherical bowls is in any case excluded by the description of the outer whorl as being ‘hollow and scooped out all through’ (Kolko Kat 2£eyAupuévo Siaurepéc) and the spindle’s shaft as being ‘driven right through’ (Staurepès &AnAdodcı); rather, we should think of thick, cylindrical discs, fitting closely inside each other, but each able to rotate round the shaft. It is possible that Plato conceived of the discs as tapering slightly, so that the whole shape would be that of a truncated cone; Strabo uses the word oróvivios to describe that segment of the terrestrial globe lying between the equator and the Arctic Circle (Str. ii, 5, 6, C 113) 151 Both interpretations go back to the ancient commentators: the former to Proclus (in Remp. ii, p. 130, 4 ed. Kroll), upheld by A. Boeckh, Kleine Schriften, 1866, vol. iii, pp. 298ff., and recently revived by J. S. Morrison in JHS 75, 1955, pp. 66-7 (who does not mention Boeckh); and the latter to Theon of Smyrna (Ad Leg. Plat. Util., p. 143 ed. Hiller), preferred by Adam (vol. ii, pp. 446-47) 152 die mavtd¢ tod obpavoü Kal yñc rerapévov — Boeckh (duly followed by Laws 899b; Epin. 948d) Frigido 954f. 159 The extant work (itself a paraphrase of Plato’s Timaeus) that goes under his name is a first-century aD forgery 160 Cf. the two articles by G. Vlastos in Studies in Plato’s Metaphysics, ed. R. E. Allen, 1965, ch. 18, where most of the pertinent literature is cited 161 For which see Cornford’s admirable commentary, pp. 59-72 162 In this famous phrase, it is a mistake to stress u50ov at the expense of elxéta — the notion of ‘likeliness’ or ‘plausibility’ is emphasized in 29c (cf. Cornford, pp. 30ff.). It must be remembered that in Platonic doctrine it is axiomatic that there can be no true knowledge of sensible phenomena; anyone can make up an implausible account of the genesis of the universe (cf. Hesiod’s Theogony and the creation myths of the Egyptians and the Babylonians), but it is the business of the philosopher to give the most likely account consistent with his insight into the nature of real knowledge (cf. Tim. 53d) 163 He even goes so far as to assert (p. 74), ‘Plato probably had it before him as he wrote’! 164 Properly speaking, an armillary sphere is a representation, by means of circular rings mounted on a stand, of the main circles of the celestial sphere (equator, tropics, zodiac, horizon, solstitial and equinoctial colures) with the earth globe at the centre; it does not show the planetary orbits or the fixed stars, except in so far as the constellations of the zodiac may be marked on the band that represents it. An astrolabe is essentially a

NOTES sighting instrument used to determine the position of the sun or moon and the risings and settings of the more prominent fixed stars relative to a particular horizon (cf. my GFH, pp. 195-99). An orrery is a more complicated device that imitates the actual movements of the heavenly bodies round the earth by mechanical means (cf. R. T. Gunther, Early Science in Oxford, vol. ii, 1923, pp. 267f.) 165 Gunther, op cit., pp. 264ff. with illustrations 166 For ancient astronomical instruments in general, see my paper in Journ. Brit. Astron. Assoc., 64, 1954, pp. 77-85 167 Cf. Heath, Arist., pp. 162-63 168 Cf. Cornford (p. 103) quoting Aristotle, Phys. iv, 223b; for some criticisms of Cornford’s remarks, see Vlastos in Studies in Plato’s Metaphysics, pp. 400f. 169 Burnet’s text reads eig [rdv] thyer tv lo6öponov Milo kôkdov iévrac, why Sévavetav elanydtag adtH Sóvapev. vóv is the unanimous reading of all the best mss as well as Proclus and Stobaeus (and is retained by Hermann in the Teubner text and Rivaud in the Budé text), but its retention involves the attribution to Plato of the notion that the sun, Mercury, and Venus all move on one and the same circle, which is undoubtedly wrong in the present context and for Platonic astronomy in general; hence Burnet brackets it. Cornford (p. 105 note 2) suggests that róv may have been read on the mistaken supposition that Plato believed that Mercury and Venus revolved round the sun (the theory attributed to Heracleides of Pontus — see p. 219), in which case all three bodies would have one main orbit. There is, however, another reading, tob¢, which is given in the ‘vulgate’ and by a later hand in Y, and printed by Stallbaum and Bury (the latter in the Loeb Timaeus), and which gives the same sense as the omission of róv — Taylor, (Tim., p. 196), though rejecting tovc, rightly construes “sig (xbxAovc) lövras loddpopov HAlp KbKAov, KUKAov being an accusative of the internal object after î6vrac 170 Cf. Heath, Arist., pp. 166ff.; Heath himself leaves the matter open 171 But see my explanation of this phrase, p. 112 172 Contrast this with the statement on pp. 86-7, ‘We can now see why the changes in the relative positions of the planets are not ascribed merely to differences of speed, though that would be a possible way of representing the facts’ (my italics) 173 Cornford rightly emphasizes (pp. 92-3; 109) that Plato is not writing a treatise on astronomy, but a myth of creation 174 This was generally accepted by the Greek astronomers; Ptolemy takes it for granted, and makes the mean, daily longitudinal movement of Venus and Mercury exactly the same as that of the mean sun (Almag. ix, 3 and 4). In Eudoxus’ system also the same assumption is made, and Plato may well have derived his knowledge of the phenomenon from this source 175 Both Cicero (Tim. 25) and Chalcidius (Tim. 36d, p. 28 ed. Waszink) translate thus 239 176 And could readily be paralleled by similar instances in the comments of ancient and modern scholars unversed in scientific language - e.g. (si parva licet . . .) Guthrie (vol. i, p. 94), in discussing Anaximander’s alleged astronomical system, actually speaks of a ‘spherical plane’! ! 177 This is the explanation favoured by Proclus (in Tim. 221e-f) after rejecting various others 178 Taken with laborious seriousness by Adam (vol. ii, App. I, pp. 264-312); but cf. Shorey’s remarks (Loeb Rep., vol. ii, Introd., p. xliv) 179 It is difficult to imagine what is meant by all eight orbits - i.e. including apparently the revolution of the Same, in terms of which all the others are measured, 3946 — completing their courses together 180 In Tim. 276d ad fin. - followed by Heath (Arist., p. 174) and Cornford (p. 119) 181 ynv dt Tpopdv pev Huetépav, elAkouévnv Sè mepl tov Sid mavrès n6Aov Tetapévov, dbixka Kal Snurovpyóv voKTES TE Kal huépas EunXavhouto, meaty Kal mpeoBurárnyv Oey aor évtdg odpavod yeydvacty. This seems to be the soundest text. Burnet (OCT) reads . . . iAAouévnv Sè thy wept tov... and notes in his apparatus criticus ‘b8 iAAouévnv FPr. Aristoteles Plut.: eihouévnv A: eilouévnv P cr thy AP: om. FYPlut.’ K. Burdach, however, in an article that deserves to be better known (‘Die Lehre des Platonischen Timaios (40b) von der kosmischen Stellung der Erde’, Neue Jahrb. f. d. klass. Altertum 49, 1922, pp. 254-78), after a careful and exhaustive survey of the various instances, shows that the form with eı is to be preferred here, and that the two word-familiesin eit- and ix- which originally had separate meanings (the former indicating ‘press, crowd together’ and the latter ‘roll, wind, turn’) became confused in Hellenistic times not only in spelling (both er for t and its converse being common in Alexandrine recensions), but also in meaning, so that in this case little weight can be attached to readings transmitted through literary sources; in particular, he shows that the notion that {io is an older and more genuine form of etAdw is entirely wrong. The retention of rhvin Burnet’s text is indefensible, as Cornford points out (p. 120 note); it is not mentioned by any of the ancient commentators who quote the passage and is found in two ss only 182 In both passages, the words translated ‘coils and moves’ are the same, Disodar kat xivetoda: (which is the consensus of all modern editors), but the mss also transmit the forms eldeiodar, sldetodar, e{ArcoBa. Burnet’s choice of iAkouévnv at Tim. 40b-c is evidently influenced by these two passages in the De Caelo 183 Cf. H. Cherniss, Aristotle’s Criticism of Plato and the Academy, 1944, Appendix VIII, pp. 557-58 - the whole of this Appendix is a valuable discussion of Aristotle’s criticism with special reference to astronomical ideas 184 This is apparently Heath’s final conclusion, op. cit., p. 178

Cornford confuses his own argument by asserting, “The effect is that in relation to absolute space she [the earth] stands still, while in relation to the other makers of day and night, the fixed stars, she rotates once every twenty-four hours in the reverse sense’ (p. 131) - cf. p. 121, where he remarks more logically that ‘the Earth must stand still, relatively to the diurnal revolution of the stars’ 186 Cornford’s citation (p. 130 note 3) of Epinomis 983b-c as evidence for a moving earth is misconceived because, as Cherniss points out (op cit., pp. 556-57) yfiv te Kai obpavév here ‘is merely a solemn expression for “the whole material universe”, the specific subject being the stars (including sun and moon) which carry out their revolutions in years, months, and 185 days’ The weakness of which is demonstrated by the unconvincing nature of the scanty evidence adduced in support of it - e.g. when Timaeus Locrus describes the earth as év n£ow iSpuuéva (97d), Cornford is constrained to remark ‘a word which does not exclude motion’ (p. 121 note 2) — Proclus knew better (in Tim. 281e). It is also difficult to reconcile a rotating earth with Cornford’s own simile of the moving staircase (see above), which would seem to require the assumption of an absolutely stationary earth; it is noteworthy that he makes no attempt to explain this 188 Or, apparently, to Cornford - but Duhem (Systeme du monde, vol. ii, 1913, p. 88) read the sentence in this way 187 189 Cf. T. H. Martin (Etudes sur le Timée, vol. ii, pp. 88f) who as long ago as 1841 gave what is essentially the correct interpretation Cf. Proclus, in Tim. 281b ad fin., té odpave Sbvapw Exovod mag &vrieporov, and, for night and day, 282c; Plut., Quaest. Plat. viii, 3, 1006e-f 191 In Tim. 281e ad fin.: ‘Let Heraclides of Pontus. . . hold this opinion [viz. that the earth rotates], since he moves the earth in a circle; but Plato keeps NOTES The word is éravaxurAfoetc. If my interpretation (above, p. 112) is correct, this means literally ‘additional circlings’, backwards in this case, i.e, retrograde movements of the planets in contrast to npoywphoetc, ‘progressions’, forward motion along the zodiac; this is in accord with Proclus, who read dvaxvkrhoerg and rpocxwphoers (284a-c), but paraphrased by SronoStopouc, ‘retrogradations’, and rpono8touoic, ‘advances’ (of. Hypotyp. vii, 4). Cornford (p. 135), who notes that Heath’s ‘returnings of their orbits upon themselves’ is unsatisfactory and himself translates ‘counter-revolutions’, nonetheless agrees that retrograde motion is meant (cf. above, pp. 132f.) 196 Apparently, even at this date, the identity of the Morning and Evening Stars with the single planet Venus was not generally recognized among non-scientists, despite the fact that, according to the doxographers, Parmenides had already pointed this out (see p. 51). The mention of the sun as also ‘wandering’ may perhaps refer to Eudoxus’ (erroneous) belief that it exhibited deviations from the ecliptic in latitude (on this, see below); but, as so often in Plato, the text here is doubtful (cf. England’s note ad loc.) and the meaning may be ‘the sun and the moon do what we all know they 195 do’ Cf. Heath’s critical discussion of such views (Arist. pp. 182f.) As Taylor holds (Plato: The Laws, trans. A. E. Taylor, 1960, p. 210 note) 199 As suggested by Taylor (Plato: The Man and his Work, p. 486 note) 200 This is not to say that Plato knew the complete Eudoxan system, for which there is no evidence in Platonic astronomy; ‘hints’ of such knowledge 197 198 found by Ross (Aristotle’s Physics, 1936, p. 95) and Guthrie (Loeb De Caelo, pp. xix-xx, footnote) are chimerical — cf. Lasserre, Die Fragmente des 190 Eudoxos von Knidos, 1966, pp. 181-82 201 it unmoved’ 192 In De Caelo, p. 519, 9-11; cf. 444, 34ff.; 541, 28ff. 193 40d — whether we read &vev Sidews Tobrav 90 TÓV ulunudtov. . . with most of the mss, or &vev dr’ dbews . . . with Burnet (OCT) and Rivaud (Budé text), the sense is clearly that mere description of the phenomena without ‘imitations’ of the movements is insufficient for a proper understanding of them. However, as we have seen (pp. 120-21), such ‘imitations’ are not to be thought of as complicated models like the planetaria or orreries envisaged by Cornford, or the astrolabe mentioned by Proclus (in Tim. 248b); rather what is meant is a simple celestial globe that by its rotation can demonstrate risings and settings, or diagrams of the planetary movements such as Eudoxus must have used in constructing his system — yuuhuoro can include drawing (cf. Epin. 9754) 194 406, yopelac. . . Kal napaßoiks ¿AA Ac — Proclus (in Tim. 248c) correctly explains napaBorks as “comings together’ in longitude, i.e. as applied to stars which rise or set simultaneously 241 On this concept, see Guthrie, Hist. of Greek Philos., vol. ii, pp. 163-64; f. 41a. E.g. by Nicomachus (c. AD 100), Arith. i, 3, 5, ed. Hoche, Teubner, 1866 The single exception of any note (Diogenes Laertius’ remark (iii, 1, 37) that ‘some’ attribute the Epinomis to Philippus of Opus is hardly good evidence for denying its Platonic authorship) is Proclus, who complains that it is ‘full of spurious, mystical matter and betrays a foolish and senile mind’ (in Remp. ii, p. 134, Sf. ed. Kroll), and who, according to the Prolegomena in Platonis Philosophiam ascribed to Olympiodorus (Hermann, Platonis Dialogi, Teubner, vol. vi, p. 218), put forward two very unconvincing arguments (one of which hinges on an astronomical point — see below) purporting to show that Plato could not have written the dialogue on these arguments see E. des Places (Epinomis, Budé ed., 1956, p. 102) 204 For which see J. Harward, The Epinomis of Plato, 1928, pp. 26-58, and the edition of Des Places cited above, note 203, where most of the relevant literature is mentioned; cf. the latest editor F. Novotny, Platonis Epinomis, Prague, 1960. E. Dént (see above, p. 235 note 141 - cf. also

Wiener Studien 78, 1965, p. $4) accepts it unquestioningly as a work written by Philippus of Opus — a position that few modern scholars would defend 205 Gnomon 25, 1953, pp. 371-75 206 Reviewing Novotny’s ed. in AJPh 83, 1962, pp. 313-17 207 Plato: the Man and his Work, p. 498 note 1 208 Cf. Timaeus 47a-b for the same thought. At 4745 Burnet (OCT, followed by Cornford) reads after ¿vtauróv meptodor the words ai tonueptar Kai zporrat from one Ms (F) although they are omitted by the two other best mss (A and Y), and consequently by Hermann (and before him Stallbaum) in the Teubner text. Cicero (Tim., ed. F. Pini, 1965, § 52) translates the Greek by ‘annorumque conversiones’ and evidently did not have equinoxes and solstices in his text; Chalcidius (§ 47, p. 44 ed. Waszink) has ‘annorumque obitus et anfractus’, which also suggests that he read ¿viautóv meptodor alone, without the addition of F’s words (cf. his commentary, op. cit., p. 156). In fact, the words kat tonueptar Kai tpomat, which add nothing essential to the sense, would seem to be an otiose gloss incorporated into the text of F 209 The sentiments here are very similar to those expressed in Laws 966-67 (see p. 141) 210 We should very much like to know what these ‘proofs’ were. Guesses about the size of the sun go back as far as Heraclitus, who thought it was only a foot wide (see p. 48), whereas Anaxagoras stated it was bigger than the Peloponnese (p. 58), and Archelaus that it was the largest of the celestial bodies (p. 77); but these are evidently no more than guesses. Later astronomers, as we shall see, used measurements of the earth’s shadow at lunar eclipses to estimate the relative sizes and distances of sun, moon, and earth, and such methods may well have been known to Eudoxus who, according to Archimedes (Arenarius, p. 7 ed. Dijksterhuis) proved that the sun’s diameter is nine times that of the moon. In all probability, then, it is to Eudoxus’ ‘proofs’ that Plato refers 211 Much of this has already been said in Laws x - see above 212 The position of aether («i@he) here has been held to constitute an argument against the genuineness of the Epinomis (Cherniss in Gnomon 25, 1953, p372), on the ground that in this dialogue ‘the ether is situated between fire and air’, and ‘since the regular solid which the Epinomis assigns to ether could still be only the dodecahedron and since the faces of this figure cannot be constructed out of Plato’s two elementary triangles, the location of such a fifth body between fire and air would prevent the mutual interchange and transmutation of their corpuscles and so would disrupt the rationale of the “stereometric atomism” of the Timaeus’. The reference here is to Tim. $3c-57¢ where Plato gives his views as to how the basic elements combine to form different substances (see above, p. 232 note 122); according to Xenocrates (one of his pupils), Plato in the Epinomis intended NOTES 243 the dodecahedron to be the figure representing the fifth element, aether (Xenocrates fr. 53, Heinze). However, Cherniss’ argument is invalidated by the simple fact that the aether, as an element, is not situated between fire and air in the Epinomis. It is true that at 984b6 we find ai0épa uèv yde werk rù nôp Oñ ev, but this does not refer to the order of the elements, but to the order of the living beings whose main constituents are the elements; this is made absolutely clear by the preceding lines, viv div Sh rept Heöv éyzetpdSyev . . . tà Sho Karıöövres CHa dpatd Huiv, & dapev xd ey &Odvatov, To SE yhivov draw Ovytdv yevovévat, tà tela ta pica rdv révre tk peratd tobtav. . . meipaßfivar Aéyeuv. The divine beings whose main constituent is aether are the first of the three classes intervening between the star gods and terrestrial life, but there is no reason to suppose that Plato intended this to be the actual order of the elements in the sense that Cherniss intends, nor that Plato or any of his readers would have found this statement inconsistent with the doctrine of the Timaeus; rather, it would seem logical to assign to two invisible classes of being, intermediate between the visible types, the appropriate invisible elements, aether and air, the former of which has already been postulated as the purest type of air in the Phaedo (109b; 111b) and Timaeus (58d). In any case, perà at 984b6 may very well indicate not a spatial relationship, but a temporal one in the genesis of the universe, or an order of rank or importance; cf. 984c7, Seútepa Se Kal tplra Kal Tétapra Kal neunte dro dev tov davepdy &pEdueva yevécewc ele Aug odg dvOpemove drroteisorày, and 984d. It does not necessarily follow that, because Plato chose to make aether the primary constituent of the second class in his hierarchy of living beings, this must reflect his conception of the physical order of the elements. Still less is it safe to assume (nor does Cherniss assume) that there is any spatial significance in the verbal order in which they are mentioned in the later dialogues; in the Epinomis itself (981c) they appear in the order fire, water, air, earth, aether; in the Laws (889b and 891c) the order is fire, water, earth, air; in the Timaeus the apparent order (to judge from 53c and ssd) is fire, earth, water, air — but in 53e we have one clear reference to spatial order when we are told that earth and fire are the extremes with the others (not actually named here) in between. Moreover, Cherniss’ objection rests on the assumption that the dodecahedron is the regular solid to be assigned to the element aether; but there is nothing in the Epinomis to warrant this assumption, and Cherniss himself rightly remarks that this is probably Xenocrates’ own ‘attempt to read Aristotelian doctrine back into the Timaeus’ (loc. cit., note 4). The train of thought in the Epinomis is simply different from that in the Timaeus; in the former Plato is not concerned with the elements and their configuration out of ‘atomic’ triangles, nor with the interaction and transformation of elemental substances, but with a hierarchy of living organisms and their relationships to each other and to mankind - he is, in fact, operating on a different plane

EARLY GREEK ASTRONOMY TO NOTES ARISTOTLE of imagination, and to demand a rigid correspondence in every detail between two such planes is to try to force a mechanical consistency on an intellect which has as many facets as there are stars in the heavens. The addition of aether as a fifth element in the Epinomis is certainly a novel development in Plato’s thought (perhaps not entirely unheralded in the Timaeus — cf. Cornford, pp. 220-21, on 55c-d), but there is no justification 245 the horizon at intervals of 10 days), which were used as a crude type of astronomical calendar; and they were interested in the heliacal rising of the bright star Sirius because it happened to coincide for some centuries with the annual flooding of the Nile, the main event in the life of the country. Apart from these few observational data there are no traces of any real astronomical concepts or of any underlying mathematical theory 214 On the other hand, there is plenty of imaginative fantasy to be found in the in old Egyptian texts. The Egyptian calendar, however, consisting of 12 months of 30 days each plus 5 additional days at the end of the year, became the standard astronomical time-scale used by the Greek astronomers (and still by Copernicus in the sixteenth century), and the Egyptian division of day and of night into twelve parts each also became standard other Platonic dialogues, and in some ways (e.g. the importance of religious beliefs and of astronomy as an educational discipline) the Epinomis merely 223 This refers to the annual motion of the planets among the stars which for treating it as an argument against the genuineness of the dialogue 213 For a comparison of the demonology outlined here with that found in other Platonic dialogues (especially the Symposium and the Phaedrus) see the comments of Harward, Des Places, and Novotny ad loc. carries to a logical extreme tendencies and opinions already apparent in his earlier work. The senility of which Proclus complains (see above) may be more apparent than real, and although Plato was an old man when he wrote the dialogue, it would be presumptuous to decide that the new directions in which his thoughts were turning were unworthy of Platonic philosophy as a whole 215 A. Bouché-Leclercq, L’astrologie grecque, Paris, 1899, pp. 24, note 1 and De 28f.; 75f. 216 Cf. M. P. Nilsson in Harv. Theol. Rev. 33, 1940, pp. 1-8, who points out that there were no indigenous cults of the heavenly bodies in early Greek history (Helios and Selene being merely gods of mythology), and that Plato was the first to insist on the divinity of the visible stars and suggest that they should be worshipped with full rites 217 Cf. my GFH., pp. 12f. (where in footnote 4, for ‘Kramer’ read ‘Cramer’) practice - see below takes place from west to east (opposite to the direction of the daily rotation of the heavens), and is therefore towards the right if one contemplates a conventional drawing or model of the celestial sphere with the north pole at the top (of. Fig. 4, p. 18). Proclus (see above, note 203) tries to use this passage as an argument against the genuineness ofthe Epinomis by pointing to the apparent contradiction to the statement in the Timaeus that the revolution of the Same (i.e. the diurnal movement) is towards the right; but his argument is misconceived (in that he fails to appreciate the different viewpoints of the two passages — see pp. 121f.), and anyway this statement the Epinomis is consistent with Laws 760d where motion to the right is i stated to be eastwards (tò 8’ ¿mi Seba yıyvecdo mo TOG to) 224 Burnet (OCT), followed by Harward, actually inserts odx, for which there is no ms authority at all, before &ywv. Des Places, followed by Novotny, points out that this is unnecessary since the same sense can be 218 Cf. J. Bidez, Eos ou Platon et l'Orient, 1945. Bidez does not accept the Platonic authorship of the Epinomis obtained without the insertion of od« — he translates ‘pourrait avoir l'air d’entrainer les autres, du moins aux yeux des gens mal informés de ces 219 For the different types of astrology, see my article ‘Astrology and astronomy questions” in Horace’, Hermes 91, 1963, pp. 67f. 220 The best ss give (9866) pla Sè zav rAavytév dorecv which is impossible since the sense demands that the reference here must be to the fixed stars, the planets being designated as mévre St &repar — hence Burnet (OCT) brackets mAxvyntév and Hermann (Teubner) reads érhaväv, but it is difficult to see why this easy reading should have been changed to rhavnräv. Des Places (Budé) prints n&vrov which has some ms support, and Novotny (ad loc.) is inclined to accept this reading 221 On planetary names see especially F. Cumont, ‘Les noms des planétes et Pastrolatrie chez les Grecs’, L’Antig. Class. 4, 1935, pp. 5-43 222 Cf. Neugebauer, Ex. Sci., pp. 8off. It seems that the Egyptians could recognize some thirty-six constellations and stars (only two of which, Sirius and Orion, can be certainly identified with those familiar to us), later known as ‘decans’ (so called because they were supposed to rise above | 225 This explanation was first suggested by Heath (Arist., p. 18 5) and approved by Cornford (pp. 91-2). In his later (and slighter) book (Greek Astronomy, 1932, pp. xliii and 61-2) Heath seems to have accepted the other interpretation 226 The order given here is the order of the synodic periods, and also probably reflects the type of data found in Babylonian sources; the moon was the most important object of study for the Babylonian astronomers because their calendar was at all periods a strictly lunar one, the solstices were also tabulated, and tables are extant dealing with observations of Venus from the second millennium sc. If Plato had been speaking as a Greek professional astronomer, he would surely have placed the sun as the first of the seven orbits to be studied, in view of its fundamental importance as providing the basic time unit (the tropical year) and the basic line of reference (the ecliptic) in astronomical calculations

NOTES 227 A saying which Aristotle (De Anima 411a18) attributes to Thales - probably 239 It needed proof because apparently many authorities doubted it, 314 To Siorálecdar mapà rot MOAROIG, i, 2, I wrongly, cf. CQ 9, 1959, pp. 296-97 228 The geographical fragments have been edited by F. Gisinger, Die Erdbeschreibung des Eudoxos von Knidos (Stoicheia, Heft 6), 1921. The only collection of all the fragments is the recent edition (with commentary) by F. Lasserre, Die Fragmente des Eudoxos von Knidos, De Gruyter, Berlin 1966; Lasserre’s arrangement of the material leaves much to be desired pe regards clarity, and his commentary is unilluminating for astronomical detail, but at least we now have all the relevant sources for Eudoxus (and much that is dubiously relevant) between the covers of one book 229 Op. cit., pp. 5-6 230 G. de Santillana, ‘Eudoxus and Plato’, Isis 32, 1949, pp. 248-62; cf. Lasserre, pp. 137-42 dn 231 In 365 according to De Santillana, or 360 according to F. W. F. von Bissing in Forschungen und Fortschritte 25, 1949, p. 225f. 232 E.g. Diog. Laert. viii, 87; Plutarch, Marcell. xiv, 11 233 Which we have on the excellent authority of Aristotle himself, Nic. Eth. i, 12, 1101b27f. and x, 2, 1172b9. In the latter passage Aristotle remarks on the temperance of Eudoxus’ own character (Siadepdvtms yàp &86xeı cddewv elvat), which was not at all pleasure-loving, in spite of his philosophical opinions 234 E. Frank, ‘Die Begründung der math. Naturwissenschaft durch Eudoxos’ in Wissen, Wollen, Glauben, ed. L. Edelstein, 1955, pp. 134-57, especially 145-50 23 A Apparently based solely on the undisputed fact that Eudoxus did at some period visit Sicily - cf. Aelian, Var Hist. vii, 17; Ptolemy, Phaseis, p. 67 ed. Heiberg, where he is stated to have made ‘weather observations’ (erionuaoiaı - see above, p. 85) in Asia, Sicily, and Italy 236 He was responsible for the redrafting of the theory of proportion, as set out and used in Euclid Books v and vi, to make it applicable to all magnitudes whether commensurable or incommensurable, and also for propounding the so-called ‘method of exhaustion’ for determining the areas and volumes of various curvilinear figures by ‘exhausting’ or using them up (Sanavav) by inscribing polygons the areas of which were known - cf. Heath, History of Greek Maths. vol. i, pp. 322f.; O. Becker, ‘EudoxosStudien I-V’ in Quellen und Studien zur Geschichte der Math., Astron. und Physik, Abt. B, Bd. 2, 1933, pp. 311-33 and 369-87; Bd. 3, 1936, pp. 236-44; 370-88; 389-410. Becker’s attempt to construct a pre-Eudoxan general ag of proportion is criticized by Heath, Maths. in Aristotle, 1949, pp. 1-3 237 In Arati et Eudoxi Phainomena commentariorum libri tres, ed. Manitius, Teubner, 1894 — hereafter cited as Comm. in Arat. 238 This is more accurate than saying that the poem is simply a versification of Eudoxus, as I did on p. 1 of GFH 247 240 For the calculation of latitude from the longest day, see Chapter I, pp. 19ff. The obliquity of the ecliptic in Eudoxus’ time was 23°44’ (see my GFH, p. 168), and this is the value I have used in the present calculations 241 Lasserre argues confidently for this (pp. 181ff-), to the extent of assigning fragments to the two works even when Hipparchus does not specify them by title (e.g. fr. 52 and 53) - on the assumption that the Enoptron contained better observations and ‘stylistic improvements’ (p. 192, comment. ad loc.) 242 5:3 gives 15 hours and 12:7 gives 15 hours 9 minutes; differences in the lengths of the day at the summer solstice were the means of differentiating latitudes north of the equator commonly used by pre-Hipparchian geographers — cf. GFH, pp. 159; 163 243 Le. the great circles intersecting at the poles and passing through the solstitial and equinoctial points respectively of the ecliptic - called x6dovp01, i.e. ‘curtailed’, because their lower segments are cut off from view by the horizon (cf. Geminus, Isag. 5, 49) 244 Using such phrases as ovpddveg tots darvouevors or ovveyyiter Tú darvoptvo (17 danbela) 245 One might perhaps in these cases suspect textual corruption in the Mss of Eudoxus’ works that Hipparchus used 246 In fact, Eudoxus was more correct here than Hipparchus; according to Baehr’s tables, the declination of Canopus (a Carinae) in the former’s time was -52.8° and in the latter’s -52.7°, so that it would be near the limit of visibility at latitude 37° and invisible at the true latitude of Athens, 38°, but in both cases it would (just) be visible at Rhodes (cf. Geminus, Isag. 3, 15 and Manitius’ note ad loc.) 247 These are probably «à Draconis and 5 Urs. Min., the latter being a fourth magnitude star listed by Ptolemy among the &uöpbwro: of Ursa Minor, i.e. those not counted in the actual constellation figure (Synt. ii, 38, 12 ed. Heib.) 248 On the role these played in ancient astronomy, see Chapter I, p. 19 249 Cf. ii, 1, 1 and especially ii, 1, 26, Kai 6 EüdoËoc Sé, & kataxorovOynKey 6” Apuroc, tov œurèv tedmov drotibetat év Tac ovvavaroraig TAG Koya cov CoStov ent rc dvaroNig - this evidently refers to a separate work of Eudoxus entitled Simultaneous Risings (Evvavarorat) also apparently used by Aratus (cf. i, 4, 19 andi, 5, 15). Curiously, Lasserre ignores the evidence for such a work, although he is ready to attribute to Eudoxus another treatise with the improbable title On Solar Occultations (Iepì dbavrouv Adaxdy — LS] s.v. dhavıouss also give this attribution) on very slender evidence (pp. 212-13) 250 See JHS 86, 1966, pp. 27-8 for the development of this usage 251 Stars not assigned letters by Bayer are usually designated by their numbers in Flamsteed’s British Catalogue published in 1725

252 Cicero (De Rep. i, 22) quotes Gallus (a Roman astronomical writer of the NOTES 260 second century Bc) on Eudoxus’ globe, eandem illam sphaeram solidam astris quae caelo inhaererent esse descriptam, and expressly contrasts this early type of solid globe with the sphaera Archimedis, which imitated the movements of sun, moon, and planets, and therefore was much more than a simple attributes the making of the first globe to Thales. . . . 253 Lasserre’s contention (p. 191) that Eudoxus did not use a globe because the terms ‘right’ and ‘left’ are inappropriate for its surface is ill-conceived; one can perfectly well speak of ‘the right’ and ‘the left’ of figures on a globe (as the Greeks did), regardless of whether the directions are the same for the observer. Thus it makes no difference whether the figures are drawn as seen from the inside (as on celestial globes with the observer supposed to be at the centre), or as they actually appear in the sky relative to the right and left hand of the observer (as on many star maps); the left arm or the right foot or the head of the figure will in both cases denote the same stars. This was well understood by the Greek astronomers (cf. 261 JHS 86, 1966, p. 29 tempting to give precision to his descriptions of figures by using the terms 262 especially ch. 3-5 and cf. his remark on p. 63, ‘If we look at the stars as they appear in the sky [a thing that very few scholars do, as Webb rightly complains] . . . we shall perceive in many cases . . . obvious reasons for names which have been quite obscured by the artificial figures, constructed often long ages after the names themselves had become traditional’ 255 Cf. the information collected by M. P. Nilsson, Primitive Time-Reckoning, Lund, 1920 Theoretically, the vacant space should correspond to the ‘antarctic’ circle, i.e. the limit of the stars never visible at that time and place, its centre should mark the position of the south pole (because, owing to the effect of precession — see above, pp. 15f this pole has shifted its position among the stars), and its radius the latitude of the constellation-makers 257 E. W. Maunder, The Astronomy of the Bible, 2nd ed., 1908, pp. 157-59 258 makers so-called - see below Comm. in Arat. i, 4, 9-11, where Hipparchus commends Aratus for at- 254 E. J. Webb, The Names of the Stars, 1952 (published posthumously) - see 256 M. W. Ovenden, ‘The Origin of the Constellations’, Philosophical Journal 3(1), 1966, pp. 1-18. Ovenden seeks to demonstrate that the constellations were designed by the Minoans mainly as navigational aids round about 2,800 BC + 300 years at latitude 36°N. + 14° and longitude 264°E. - he has even found a suitable island in the Dodecanese for their observatory, the island of Stampalia (locally known as Astropalia ‘which has an obvious astronomical “ring” about it’)! Some of the arguments he uses are remarkably circular; in trying to prove (pp. 5-6) that certain constellations were arranged symmetrically with respect to the celestial north pole of that epoch, he uses a statistical method based on the hypothesis that they were so arranged as ‘a band of the sky equidistant from the celestial pole’ (and what? Ovenden does not say, but presumably means the equator). It is to be hoped that the ‘results’ of this fascinating paper will not be taken seriously; apart from the fallacious argumentation and fanciful speculation it contains, its whole thesis is vitiated by the totally unfounded assumption of the advanced astronomical knowledge possessed by the constellationglobe. Gallus is no great authority, it is true, since in the same passage he ‘left’ and ‘right’); it is only modern commentators who have introduced confusion here. Where there was any likelihood of ambiguity, stars were described as lying further west, east, south, or north as the case might be R. H. Allen, Star Names and their Meanings, 1899, pp. 14-15 259 Ptolemy says specifically that he himself has not always used the same shapes for the constellations as his predecessors, just as they did not always use the same as the astronomers before them, but made alterations in the 249 For the difficulties inherent in the concept of equinoxes, as opposed to solstices which are easily observable phenomena requiring no astronomical theory for their perception, see my article inJHS quoted above 263 Often made with the help of an instrument known as a ‘precession globe’, i.e. a celestial globe the poles of which are adjustable in circles round the ecliptic poles to take into account the shift in position (about 1° in 72 years) of the celestial poles owing to the effect of precession — see above. Even with this aid, such comparisons are of very doubtful validity, since we know neither the exact boundaries of the ancient constellations, nor the latitude of the original observations, nor the standard of accuracy involved; the latter especially, one suspects, is commonly overestimated by modern commentators 264 Robert Brown, Researches into the Origin of the Primitive Constellations of the Greeks, Phoenicians and Babylonians, 2 vols., 1899, 1900, p. 15 -a highly misleading work, packed with erroneous and outdated material. Only marginally less misleading is W. Hartner’s article, “The Earliest History of the Constellations in the Near East and the Motif of the Lion-Bull Combat’, JNES 24, 1965, pp. 1-16, which, based on totally inadmissible premisses, attributes sophisticated astronomical concepts to the Sumerians of the fourth millennium! Equally misguided are the attempts made to impute complicated astronomical motives to the builders of ancient monuments such as Stonehenge (e.g. by G. S. Hawkins in Vistas in tom Bayer onwards have made further changes, until in 1930 by inter- Astronomy, vol. x, 1968, pp. 45-88); such fantasies are reminiscent of the ‘pyramid literature’ (on which see Neugebauer, Ex. Sci., p. 96) - and equally valueless, despite the modern trappings of computer calculations national agreement the present constellation boundaries were standardized with which they are invested interests of a more convenient arrangement, and he gives an example from Hipparchus (Synt. vii, 3, ed. Heib. vol. ii, p. 37, 11ff.). Modern astronomers

EARLY GREEK ASTRONOMY TO R. Böker, ‘Die Entstehung der Sternsphare Arats’, Berichte über die Verhandlungen der sächsischen Akadamie der Wissenschaften zu Leipzig 99, 1952, pp. 3-68. Böker finds fault with Hipparchus’ criticism of EudoxusAratus because it is based on the supposition that the data were valid for Greece and that the colures were drawn through the beginning of the signs (p. 5); he completely ignores Hipparchus’ own discussion of the latitude appropriate to the observations (Comm. in Arat. i, 3, 5-12), and his emphasis on the different placing of the solstitial and equinoctial points by Eudoxus and Aratus (ii, 1, 15ff:; 20ff.; 2, 5-6), which shows that he was fully alive to the difficulties of assessing the older material fairly. Böker’s lack of historical sense is demonstrated by his reference to Aratus’ astronomical source as ‘Pseudo-Eudoxos’ (duly castigated by Ludwig in RE, s.v. Aratos, Suppl. Bd. 10, 1965), his belief that the Greek constellations go back no further than the sixth century sc (thus apparently ignoring those mentioned in Homer and Hesiod - see above), his supposition that Eudoxus used the 360° division of the circle (in flat contradiction to the available evidence — see above), and his reference (p. 105 of a ‘Nachtrag’ to a German translation of Aratus by A. Schott - Das Worte der Antike VI, Munchen, 1958 — where Böker repeats much of the nonsense in his earlier paper) to Anaximander’s famous sixth-century Bc workshop in Miletus where he busied himself with all possible astronomical and meteorological instruments (!!). Moreover, Béker’s supposedly scientific treatment of the Aratean data is basically unsound since he does not take into consideration the conditions and limitations of the original observational material (cf. Ludwig, loc. cit.), and anyway a close examination shows that out of the twelve Aratean passages he discusses in pp. 19-29, only three agree fully with the results obtained by his methods. Unfortunately, the erroneous conclusions he arrives at (that the Aratean sphere is valid only for the epoch — 1,000 + 30-40 years at a latitude between 32°30’ and 33°40’, with the colures marked at the end of 15° of the relevant signs, and with the position of the zero point of the zodiac at about 26° of the ecliptic of AD 1900 ~ p. 8) have been accepted by Van der Waerden in his latest work, Die Anfänge der Astronomie ( = Erwachende Wissenschaft II), Noordhoff, Groningen, 1966 - on which see further below 266 In the period between Hipparchus and Eudoxus the north celestial pole would have shifted westwards some 3°, thus altering the positions of the stars relative to the circles of the celestial sphere 267 On a very rough count, there are twenty-three such instances in Book i of the Commentary — admittedly, the disagreements are more than twice as numerous, but then its main purpose is to criticize and correct 268 This passage alone is enough to refute a large part of Ovenden’s thesis, since he makes much play with alleged differences in the respective ‘zones of avoidance’ of the Eudoxan-Aratean and the Hipparchian spheres (op. cit., pp. 9-10) NOTES ARISTOTLE 251 269 Cf. Neugebauer, Ex. Sci., pp. 103ff. 270 ‘Babylonian’ is used as a convenient generic term for the distinctive culture of the Tigris and Euphrates valleys, which was dominated at different times by Akkadians, Kassites, Assyrians, Persians, and finally Macedonians and Greeks in the Seleucid period 271 Cf. the omen series of texts collectively known as ‘Enuma Anu Enlil’ discussed by E. F. Weidner in Archiv für Orientforschung 14, 1942 and 17, 1954 272 Cf. Van der Waerden, Anf., pp. 56f. 273 Allauthorities agree that these ‘ways’ are bands of a certain width (variously estimated) parallel to the equator, and not lines delimiting zones as in the Greek concept of ‘arctic’ and ‘antarctic’ circles - cf. C. Bezold, A. Kopff and F. Boll, ‘Zenit- und Aequatorialgestirne am babylonischen Fixsternhimmel’, Sitzber. d. Heidelb. Akad. d. Wiss., phil.-hist. Kl., Abh. II, 1913, pp. 3-59; E. F. Weidner, ‘Ein babylonisches Kompendium der Himmelskunde’, Amer. Journ. Sem. Lang. and Lit. 40, 1924, pp. 186-208, and ‘Der Tierkreis und die Wege am Himmel’, Arch. f. Orientf. 7(4), 1931, pp. 170ff.; J. Schaumberger, 3. Ergänzungshefie zur Sternkunde und Sterndienst in Babel, Kugler, 1935, pp. 321f. 274 Rome, 1950 = Teil 4, Bd. 2 of the Sumerisches Lexikon, ed. P. A. Deimel 275 Particularly striking is the fact that the Babylonians designated the ‘horn’ (ie. the claws) of the Scorpion as ZI.BA.AN.NA/zibanîtu, meaning ‘Balance, Scales’ (Gössmann, p. 72), just as the Greek astronomers differentiated the Claws(Xnaat, Latin Chelae) from the rest of the constellation and later called them the Balance (Zoy66, Latin Libra) - the latter name hat is consistently seems to be post-Hipparchian, for in the Comm. in Arat.X used except in one passage (iii, 1, 5), which Manitius regards as spurious on other grounds as well (p. 303, note 41). Ptolemy (Synt. viii, 1, ad init.) uses, Xnrat for the figure, but Zuyós for the sign — cf. Bouché-Leclercq, p. 141 276 Van der Waerden, Anf., pp. 67-8 277 Op. cit., pp. 256-57; but Van der Waerden himself admits that this does not hold for Aries, Cancer, and Aquarius, and his arguments for Virgo (cf. Webb, The Names of the Stars, p. 33, ‘the assumption that, because the Greek Virgin carries a Corn-Ear in her hand, the Babylonian Corn-Ear must have been carried in the hand of a Virgin, though apparently taken for granted by all Assyriologists, is of course ridiculous’), Sagittarius, and Capricornus are extremely flimsy, depending largely in the last two cases on representations of the figures in the Dendera zodiac, which since it dates from the Roman period in Egypt, is hardly convincing evidence that 27 oo This is against the view supported by Webb (see above, pp. 159-60) certain names (including the Triangle) are obviously appropriate for certain star-groups; Van der Waerden (p. 68) specifically comments on the likeness of these particular stars to a plough! 279 Cf. Van der Wacrden, p. 68 and diagram p. 66

EARLY GREEK ASTRONOMY TO NOTES ARISTOTLE 280 The Seleucid era began in 312 BC; after this there is a long series of texts (the latest being dated to ap 75) which show Babylonian mathematical astronomy at its highest level of development - see ©. Neugebauer, Astronomical Cuneiform Texts, 3 vols., 1955. There is no doubt at all, as we shall see, that the results obtained and (to some extent) the methods used by the Babylonians during this period were known to the Greek astronomers from at least the time of Hipparchus (second century Bc) onwards. The disputed questions are when and how these results and methods were transmitted to Greece, and what influence the earlier stages of Babylonian astronomy had on its Greek counterpart, and again when and how this influence was exerted 28 le] Aristophanes fr. 163, nöXog 768° Eoriv; elta méatyy Mıog TETpATTALI Even here it is not altogether impossible for néX06 to have the same meaning as in Birds 179f., namely ‘region of the sky’ 282 In which case it would be similar to the ‘scaphe’ (ox&6n) mentioned by Cleomedes (Cycl. Theor. i, 10, 54f.) as being used by Eratosthenes for his famous measurement of the earth. Vitruvius in his chapter on sun-dials 253 and consists (apart from inferences drawn from Greek literary sources) of a single Demotic text, written in the first century AD but apparently based on an original of the late-sixth or early-fifth century Bc, which contains a number of eclipse omens arranged by the months in which they take place, groups of three months being assigned to four separate terrestrial regions, and also a concordance of Egyptian and Babylonian names for the months. However, since the contents of the text obviously belong to the pre-scientific stage of astronomy and there is no mention of the planets or the fixed stars, Van der Waerden is forced to assume a later blooming of Egyptian observational astronomy (op. cit., p. 133), for which, needless to say, there is no evidence at all 289 See Bouché-Leclercq, L’astrol. grecque, p. 93, note 2 290 In the Philolaic system and perhaps by Democritus - see pp. 65f.; 82 291 See the Venus tablets of Ammizaduga in the astrological omen series ‘Enuma Anu Enlil’ - Van der Waerden, Anf., pp. 34ff. 292 Published in Late Babylonian Astronomical and Related Texts, 1955, (Brown University Studies 18), by A. J. Sachs as facsimiles of the original copies made by Pinches and Strassmaier — no translations are given (ix, 8) speaks of ‘a hemisphere hollowed out of a square’ (hemicyclium excavatum ex quadrato) which was supposed to have been invented by 293 Van der Waerden, Anf., p. 105 Berosus (on whom see note 306, below); but this must have been a later type because he describes it as ‘cut away to suit the latitude’ (ad enclimaque 294 See the standard work by O. Neugebauer, Astronomical Cuneiform Texts, 3 vols. 1955, where all the Seleucid material is dealt with succisum), and this presupposes greater theoretical knowledge than either 295 Cf. Van der Waerden, Anf., p. 166 Berosus or Eratosthenes could have possessed - see CQ ns. 5, 1955, pp. 296 ACT, vol. ii, p. 280 297 Cf. Neugebauer, Proc. Amer. Philos. Soc. 98, 1954, p. 64: ‘But there is no trace of any definition of the vernal point as the intersection of ecliptic and equator (which nowhere appears in Babylonian astronomy)’ 298 Cf. Van der Waerden, Anf., pp. 104-05 299 ACT, vol. ii, p. 281 300 Neugebauer, Journ. Cuneif. Stud. 2, 1948, pp. 209ff. 301 Neugebauer, Journ. Amer. Orient. Soc. 70, 1950, pp. 1-8; of Van der Waerden, Anf., pp. 115-16 302 Van der Waerden, Arch. f. Orientf. 16, 1953, p. 223 303 A. Sachs, Journ. Cuneif. Stud. 2, 1948, pp. 289-90; Van der Waerden, 248f. Vitruvius goes on to say that the invention of the ‘scaphe or hemisphere’ was attributed to Aristarchus 283 For common misconceptions concerning the use of sun-dials in antiquity, see JHS 86, 1966, p. 29 284 Cf. Diels, Antike Technik, 3rd ed., 1924, pp. 162-63 285 Cf. Neugebauer, Proc. Amer. Philos. Soc. 107, 1963, p- 533 286 Cf. Weidner, Amer. Journ. Sem. Lang. and Lit. 40, 1924, pp. 198f.; Neugebauer, Isis 37, 1947, pp. 37-43; Van der Waerden, Anf., pp. 80-1 287 Neugebauer, Ex. Sci., pp. 81; 85-6. Van der Waerden claims (op. cit., p. 88) that the division of day and night into twelve equal periods each is attested by the numbers on an ivory prism of the Assyrian period (thus before 630 BC); but his interpretation of this text (following Fotheringham in The Observatory, No. 703, 1932, p. 338) is far from secure, and on his own admission the meaning of half of it remains unknown 288 To explain the frequent Greek references to Egyptian astronomical observations, Van der Waerden suggests that in the period from 630 to 480 Bc (during part of which Egypt came under Babylonian rule) Babylonian astronomical ideas strongly influenced the local Egyptian astronomy, to the extent of causing a resurgence of observational activity, and that this was how Eudoxus came to profit from his stay in Egypt (Anf., pp. 130f.). The evidence for such a supposition is extremely thin, loc. cit., p. 222, note 25 304 Fotheringham remarks that this puts Ptolemy in a better position than any modern astronomer as regards the length of observation series available to him (The Observatory, No. 51, 1928, pp. 312-13) 305 On this see especially Neugebauer, Proc. Amer. Philos. Soc. 107, 1963, pp. 534-35 306 The Babylonian priest Berosus (or Berossos), who founded a school in the island of Cos and wrote in Greek a history of his own country (see the fragments edited by P. Schnabel, Berossos und die bab.-hell. Lit., Leipzig, 1923), is often cast in the role of intermediary between Babylonian and Greek science (cf. Neugebauer, Ex. Sci., p. 157). Unfortunately, the

EARLY GREEK ASTRONOMY TO extant fragments do not bear this out, and what little astronomy they contain (e.g. fr. 16-26 on the phases of the moon) bears no relation to contemporary Babylonian lunar theory (Neugebauer, Proc. Amer. Philos. Soc. 107, 1963, p. 529). Berosus dedicated his Babyloniaca to Antiochus I (281-261 Bc) and is thus, anyway, too late for Eudoxus 307 Proc. Amer. Philos. Soc. 107, 1963, pp. s29ff. 308 Neugebauer, Ex. Sci., pp. 102; 140. Van der Waerden thinks differently - see below 309 Cf. ACT, vol. i, p. 11, ‘All that can be said with safety at present is that the methods for computing lunar and planetary ephemerides were in existence c. 250 BC. Their previous history is unknown to me’ 310 Journ. Cuneif. Stud. 6, 1952, pp. 54ff. It should be noted that Sachs’ treatment depends on the assumption ‘that the planetary data refer to signs of the 311 zodiac, not constellations’ (p. $5) Even Van der Waerden admits that there is no trace of the zodiac as such 312 in these texts - Anf., p. 77 (see also below) Chiefly in his book Die Anfänge der Astronomie (= Erwachende Wissenschaft II), Noordhoff, Groningen, 1966, which sums up the results of his earlier papers on the subject 313 Op. cit., pp. 171-72; 201-03 314 See JHS 86, 1966, p. 29 315 On which see above, p. 43 and CQ 9, 1959, pp. 294ff. 316 NOTES ARISTOTLE See his highly misleading account of Pythagorean astronomy in Die Astronomie der Pythagoreer, Amsterdam, 1951 317 To the examples mentioned above, add his unquestioning acceptance of Boker’s untenable theory that the Eudoxan-Aratean sphere is only accurate for a date about -1,000 Bc (see above, p. 162 and note 265) 318 According to the Ars Eudoxi(see above, p.88, note 109), Eudoxus estimated the number of days from the autumnal equinox to the winter solstice as 92 and from the winter solstice to the vernal equinox as 91; but unfortunately the papyrus is defective with regard to his estimates of the other two astronomical seasons (cols. 22-3). Since it is certain that in the Eudoxan solar theory the sun’s longitudinal motion is assumed to be uniform (see above, p. 181), Heath is probably right in supposing that Eudoxus made the lengths of the seasons 91 days each, with an additional day for autumn 255 Greek astronomers expended great ingenuity to reconcile the erratic behavior of the planets with their presumed circular motion’ 322 Proclus in his Comment. in Euclid. i expressly draws attention to the fact that several of the theorems were included because of their usefulness in astronomy (pp. 268-69 ed. Friedlein). The earliest extant Greek mathematical treatise, Autolycus’ On the Moving Sphere, dated to the last decades of the fourth century Bc, already contains propositions relating to the sphere which are merely stated without proof, and were therefore presumably taken from a still earlier textbook on ‘sphaeric’ which contained the proofscf. Heath, Hist. of Greek Maths., vol. i, pp. 349-50 323 Neugebauer, Ex. Sci., p. 110 324 Delambre, for example, in his still indispensable Histoire de Pastronomie ancienne, 2 vols., 1817, nowhere mentions the planetary scheme, and only deals with Eudoxus’ other astronomical work in the course of a chapter on Aratus (tom. i, ch. 4, pp. 61-74), although he has a brief section (tom. i, pp. 301-10) on Simplicius’ in De Caelo. Delambre evidently did not know of Eudoxus’ mathematical work, since he says (p. 131), ‘ . rien ne prouve qu’il fat géomètre’ 325 L. Ideler, Abh. d. Berlin. Akad., hist.-phil. KL, 1828, pp. 189-212, and 1830, pp. 49-88; E. F. Apelt, Abh. d. Fries’schen Schule, Heft 2, Leipzig, 1849; T. H. Martin, Mém. de l’Acad. des Inscript. et Belles-Lettres, tom. 30, pt. 1, 1881, pp. 153-302; G. V. Schiaparelli, ‘Le sfere omocentriche di Eudosso, di Callippo e di Aristotele’, Pubblic. del R. Osserv. di Brera in Milano 9, 1875 — German trans. by W. Horn, Abh. z. Gesch. d. Math., Heft 1, Leipzig, 1877. pp. 101-98. Martin states (pp. 160-61) that his own work was completed before Schiaparelli’s, and that the reading of the latter’s description has not caused him to make any changes in his own views, which, as we shall see, differ from Schiaparelli's in one important respect 326 J. L. E. Dreyer, A History ofAstronomy from Thales to Kepler, Dover repr., 1953, pp. 89-103; T. L. Heath, Aristarchus of Samos, pp. 193-211 327 In describing the rest of Eudoxus’ system, it will henceforth be taken for granted that each sphere is affected by the rotations of the spheres enveloping it; for economy of words only the individual rotations will be mentioned 328 Simplic., p. 495,4 ed. Heib., éyxexdpévog mods tov Sid pEsay róv CepStev rooobrov, Écov Y nAelorn Kate TARTOG TH GERN Tapagmpnots ylyvaraı to make the total up to 365 (Heath, Arist., p. 200), thus making no use of . thy tetcyy Sì [ün&dero] Sid To wh Ev cote adtote tod Cadraxod onuelois Boperorérnv te Kol votimt&étyy dalveodar yivouévny, &AAX uerarinreuwv TO toLadta onueta thy Codtov del Ext tà npomyobneva the discovery by Meton and Euctemon of the inequality of the seasons (see below, p. 88) 319 E. F. Weidner, Arch. f. Orientf. 7(4), 1931, p. 171; O. Neugebauer, Isis 37, 1947, p. 38 320 Kugler, Sternkunde u. Sterndienst in Babel, vol. i, 1907, p.13; vol. ii, 1909-10, 329 chy perérroow ravréraoiv datyny ylveodaı Kad’ Ékaorov uva, p. 495, pp. 77-8; of. Neugebauer, Ex. Sci., p. 169 Cf. T. W. Africa, Science and the State in Greece and Rome, 1968, Pp. 37: ‘Hamstrung by the dogma that celestial motion was perfect and circular, 330 ta fact, its changes in declination (from the equator) are much greater than 321 its changes in latitude, but Eudoxus probably failed to distinguish between the two — cf. Martin, op. cit., p. 217

NOTES Martin (pp. 214-15) suggests the sidereal or tropical month of about 27} days, but there is no evidence and little likelihood that this was known to Eudoxus 332 Whatever speed was assigned to the third sphere (and conjecture is fruitless) could easily have been compensated by increasing slightly the speed of the second sphere 333 E.g. W. D. Ross, Aristotle’s Metaphysics, vol. ii, 1924, pp. 385ffare the two diametrically opposite points where the mean lunar orbit intersects the ecliptic 334 The nodes Who clearly indicates in Met. A 8, 1073b26-7 that the second sphere for all the planets and the sun and moon represents their direct (eastwards) motion along the ecliptic 336 Namely, the slow rotation of the poles of the lunar orbit round the poles of the ecliptic. The only evidence adduced for Eudoxus’ knowledge of this period is a remark by Ptolemy that the eclipse period of 223 lunations was known ‘roughly’ to ‘the still older astronomers’ (6Aocyepéorepov uèv the true values (on the heliocentric system) can be made 346 The Ars Eudoxi actually gives the figure of 116 days for the synodic period of Mercury (col. 5, p. 16 ed. Blass), but there is no knowing whether 335 ody of Erı marardtepor. . . Syyrota Edewv uvas usv &rotehovpsvovs oxy, Almag. iv, 2, p, 270, 1ff. ed. Heib.), and since he counts Hipparchus as taXatdg (ili, I, p. 191, 17f.), raraıörepog is taken as referring to Eudoxus. This is very tenuous, and anyway the context makes it clear that of ¿m mahaérepor here refers to the Babylonian astronomers (oi XaXSatkot — op. cit., p. 270, 20), whose results Hipparchus discussed 337 Cf. Delambre, tom. i, pp. 73; 122; 125 257 Mercury and Venus were the same as the sun’s, i.e. 1 year (see note 174), because these planets are never seen far from it. In fact, this assumption results from the very large parallax effects caused by the earth’s rotation in the case of the inferior planets, whereas for the superior planets (at their much greater distances from the sun) such effects are far less noticeable. On the geocentric hypothesis one is bound to give Mercury and Venus sidereal periods equal to that of the sun, and no valid comparison with this was in fact derived from Eudoxus or a later source 347 It should be emphasized that, in this part of his reconstruction, Schiaparelli is demonstrating his own ingenuity rather than that of Eudoxus (as Martin points out — op. cit., p. 225 note 1). There is no evidence that Eudoxus used the figures given by Schiaparelli and, to judge from the inaccuracy of much of the rest of his astronomical work, it would seem highly improbable that he knew the correct values 348 The logic of this last assertion is questionable, since in fact the maximum latitudes are approximately 24° for Saturn and 14° for Jupiter 349 If indeed he assumed any as regards the inclinations and the dimensions of the ‘hippopedes’. It is by no means impossible that he contented himself with showing the theoretical possibility of explaining retrograde motion and stationary points by means of the ‘hippopede’, without actually 338 Martin realized this clearly (op. cit., especially pp. 216-21) and his treatment assigning any parameters to the systems apart from the sidereal and of the Eudoxan system is sensible apart from a tendency to accept data derived from the Ars Eudoxi as genuinely Eudoxan when there is no proof of this; Lasserre also notes the uncritical assumption of a mistake on the part of Simplicius (Die Fragmente des Eudoxos von Knidos, 1966, p. 202), but gives no discussion of the issues involved 339 This is so on both Schiaparelli’s and Simplicius’ interpretations synodic periods 350 Cf. Dreyer, pp. 380ff. 351 It does not seem that Eudoxus regarded his sets of spheres as anything other than mathematical abstractions; there is no evidence that he speculated on the material of which they were comprised or the connection between them or the power that moved them. As we shall see, Aristotle was concerned with all these things. According to Archimedes (Aren. 9, 340 Eb862 Tolvuv Kai roig mod abrod Tpeis 6 Aoc ¿Sóxer kivetobar kivhoets, p. 493, ITf. 341 times that of the moon; how he arrived at this figure we do not know - in reality the ratio is about 400:1 Hayduck; Chalcid., Comm. in Tim. 77, p. 125 ed. Waszink; Mart. Cap. viii, 849 (287 G), p. 315 ed. Eyssenhardt; also 863 (293 G), p. 322 ed. Eyssenhardt 352 Kol Sorel pdrtota révrov abtyY rreplodog rois barvouévois suubmvelv, The mathematical details are best studied in Schiaparelli or Heath (who also gives a modern solution, using analytic geometry, by N. Herz); cf. also Neugebauer, Scripta Math. 19, 1953, pp. 226-29 343 Since the figure is described on the surface of a sphere, Schiaparelli calls it (somewhat misleadingly) a ‘spherical lemniscate’ 344 Comm. in Eucl. i, ed. Friedlein, Teubner, pp. 127, 1; 128, 5 345 The ancient astronomers regularly assumed that the sidereal periods of 342 ed. Heib., vol. ii, p. 220) Eudoxus supposed the sun’s diameter to be nine Theon Smyrn., pp. 135 ed. Hiller (apparently from Adrastus — cf. p. 129); 173; 194; Pliny, Nat. Hist. ii, 67; Alex. Aphrod., in Met. 8, p. 703 ed. loc. cit. ad fin. On the ‘parapegmata’, see above, pp. 84f. 354 Latitudinal zones on the terrestrial sphere in which, for practical purposes, such data as the length of the longest day, the ratios of the gnomon to its shadow at stated times, and the appearance of the night sky remained the same for all observers in the same ‘clima’ - see on the development of this concept CQ 5, 1955, pp. 248f.; CQ 6, 1956, pp. 243ff.; GEH, pp. 1s4ff. 355 Vitruvius (ix, 8) says in connection with sun-dials that Eudoxus (or, according to some sources, Apollonius) invented the ‘spider’ (arachne).

NOTES What this was is not certain, but it is not unlikely that Eudoxus investigated the shadows cast by a gnomon, and the lines and circles marking these may have suggested the term (cf. Diels, Antike Technik, 3rd ed., 1924, pp. 160-61 and diagram on p. 163). Later, the movable disc (representing the ecliptic) of the planispheric astrolabe was called the ‘spider (GFH, pp. 197; 201), but Eudoxus certainly did not know this instrument 356 Ptolemy says (Phas, p 67, 5 ed. Heib.) that Callippus made observations in the Hellespont 357 Sosigenes (a Peripatetic philosopher of the second century AD — not the astronomer of the same name who helped Julius Caesar reform the calendar; Simplicius makes it clear that Sosigenes derived most of his information from Eudemus’ History ofAstronomy, on which cf. CQ 9, 1959, pp. 301f) ap. Simplic. p. 504, 17, od phy al ye riv repl EüSoËov o@ Covet tà durvöneva, ody Eas TÀ borepov KatarnpbevTa, BAN addì TÀ PS TEPOV yvoodévra ral In’adrav Ekelvov nıorevßevre 358 Loc. cit 36-7, 1% bawwöueva el wearer tug dmodbcerv — a perfectly regular and straightforward use of &rodiSopr in the sense of ‘account for’, ‘explain’ (see LSJ s.v.). Unfortunately, Sosigenes (followed by all later commentators) preferred the far less accurate, if more picturesque, phrase ck dawopeva odtew, Le. ‘to preserve (agreement with) the facts of observation’. Kranz (Rhein. Mus. 100, 1957, p. 128) is wrong in supposing that the phrase was first used by Heracleides Ponticus, a pupil of Plato; the passage he quotes from Simplicius in support of this is clearly an indirect quotation and describes Heracleides’ views in Simplicius’ own words — in De Caelo ii, 13 p. 519 ed. Heib., év 6 Kévtp@ Sè odcav chy Av Kal wr riwvovpévnv, tov SÈ odpavdy Mpepodvta ‘HpaxAetdnc è Tlovtixds Órro0éuevos cptewv Hero rà parvbpeva. Sosigenes’ phrase, in its literal English translation of ‘to save (preserve) the appearances’ with all the ambiguities inherent in the expression, has led to the misleading idea that the Greek astronomers were concerned mainly with distorting the results of observation to make them fit into preconceived, theoretical schemes. The whole history of Greek astronomy, which shows a steady development from the naiveties of the Pre-Socratics, through the Pythagoreans and Plato, to the system of Eudoxus, and finally to the HipparchianPtolemaic system of epicycles and eccentrics, demonstrates how false this idea is; at each stage, as new and more accurate observations were accumulated, older theories were dropped in favour of newer ones which seemed to provide a more complete explanation of astronomical facts 359 p. 497, 17 ed. Heib. 360 Cols. 22-3; these values are a considerable improvement on those of Euctemon (cf. p. 88) and, compared with the true figures for 330 BC, are less than half a day out - cf. Schiaparelli, p. 46 361 The mathematical details are given by Schiaparelli (op. cit.), whom Heath (Arist., pp. 213-16) follows closely. It must again be emphasized (cf. note 259 347) that the values assumed by Schiaparelli are entirely conjectural, as indeed is the mode of operation of the additional spheres, since we have no information on these points from the ancient sources 362 Geminus, Isag. 8, 58-60; cf. p. 189 above 363 As explicitly stated by Hipparchus ap. Ptol., Almag. iii, 1, p. 207, 11 ed. Heib. 364 E.g. Almag. ili, 1; iv, 10; v, 3; vi, 5; vii, 3, et al. 365 Cf. Van der Waerden, JHS, 80, 1960, p. 170; Ginzel, RE, Bd. 10(2), 1919, col. 1663 366 Ed. W. K. C. Guthrie, Loeb, repr. 1960; P. Moraux, Budé, 1965 367 De Caelo ii, 10, 291429-32, mepl dì ig táleos adbt&v [av &ctpwy], dv uèv tpdnov Exaotov Keita (vl. kieras) TH tà uèv elvas mpórepa tà D botepa, Kal mie Eyer mpdg Ama voló dnootTHLAcL, dx Tv mepl dotporoyiav dempsicdo: cf. 291b10 and Met. A 8, 1073b3-6 368 W. D. Ross, Aristotle’s Physics, 1936, Introd., pp. xv-xviü 369 W. D. Ross, Aristotle's Metaphysics, 1924, Introd., pp. xxiv-xxix 370 Op. cit., pp. xxix note 1; 382; 384. It is fair to point out that the difference in styles has also been given the opposite interpretation, i.e. that the fuller style is earlier than the more concise one (e.g. by F. Blass in Rhein. Mus. 30, 1875, pp. 481-505). P. Merlan (Traditio 4, 1946, pp. I-30), on the other hand, sees 1074431-38 as an essential part of the argument of this chapter, which he finds ‘logically and satisfactorily organized’ (op. cit., p. 14) 371 Cf. Moraux, Introd., pp. lxiv-lxv; cxxivff. 372 Thus various attempts have been made to trace specifically Aristotelian doctrines, such as those of the fifth element and the Unmoved Mover, back to the lost, early dialogue De Philosophia (of which we have fragments, ed. V. Rose, Teubner, pp. 24-40), and to discover a line of development between this (presumed to be still strongly under Platonic influence) and Aristotle’s later ideas; but the very divergent conclusions reached by different scholars (for references, see Moraux, pp. li-lv) do not inspire much confidence 373 Except Aristarchus and Seleucus, who undoubtedly put forward at least tentatively a heliocentric hypothesis - see Heath, Arist., pp. 301ff. 374 For the astronomical opinions of many of the Pre-Socratics, Aristotle’s is the only evidence that can be considered to any degree reliable - see above, Chapter II 375 In the whole work, Aristotle records only one detailed astronomical observation (that of an occultation of Mars by the moon, ii, 12, 29243-6, chy yap sehjvyy Ewedxauev — hence presumably observed by Aristotle himself — dıxöropov uèv obouv, breAModaay St Tüv dorépov toy Tod ”Apeog, x.7.2.), and this is neither dated by him (modern calculations show that it was probably the occultation of 4 May 357 Bc - cf. Guthrie ad loc., Loeb, p. 205) nor reported in the form that a practising astronomer would use (compare the manner in which similar occultations by the moon of

the Pleiades are reported by Ptolemy from Timocharis, 283 BC, and Agrippa, AD 92, in Almag. vii, 3, ed. Heib., vol. ii, p. 25, 15f. and p. 27, If). Aristotle adds that similar observations have been made by the Egyptians and the Babylonians (see above, p. 167) NOTES 261 that the stars do rotate since it is in their nature to do so (Hypoth. Planet. ii, p. 131, of. ed. Heib., vol. ii, Claud. Ptol. Op. astron. min. - this second book of the Planetary Hypotheses is extant only in an Arabic translation of which Heiberg gives a German version by L. Nix) — but he throws no further 376 Cf. Met. A 8, 1073b9-10, mAetoug yap Ékaorov dépetar uric as TAKVO— uévov Lorea. I follow Cherniss’ interpretation (Aristotle’s Criticism of Plato and the Academy, 1944, App. VIII, pp. 547f.) which is surely correct. Aristotle has at the back of his mind those like Heracleides Ponticus who light on any actual observations of this alleged phenomenon 384 This is not stated explicitly, but seems a necessary inference from his were able to account for the daily risings and settings by postulating a rotating earth and a fixed outer sphere, but he insists that this is not sufficient, since any planetary body must have more than one individual motion; but, if the earth is given the requisite number of motions, then other phenomena will be produced which are contrary to the facts of observation. This seems preferable to assuming (with Heath, Arist., p. 241, and Guthrie, op. cit., pp. 242-43) that Aristotle was unaware of the alternative explanation of the daily revolution (a highly improbable assumption, 6 hoc . . . Heath (Arist., p. 235) attempts a defence of Aristotle which since Heracleides was also a pupil of Plato), and was referring only to a double motion of the earth, one component of which he infers must be in the plane of the ecliptic 377 See above, pp. 136f. 378 On tporat, see p. 116 379 «vprós, 297b28; cf. Meteor. ii, 7, 365432, &¢ odong [tHe yñc] xupräs al obarpoeıdoög — strictly, this proves only the curvature of the earth’s surface, but taken in conjunction with the other arguments it serves as 00] proof of the sphericity 380 The examples he gives, that stars seen in Egypt and Cyprus are invisible previous words, since he is evidently using ¿orpov as a general term to denote all the celestial bodies - cf. 290414-15, póvos SE Soket rüv ¿oro carries little conviction 385 This is an essential presupposition for the theory of unmoved movers (sce below), and Aristotle takes great pains in arguing against the proponents of a plurality of worlds, the Atomists 386 ai0ñp, which he derives from det Beiv, ‘always running’ (of. Plato, Crat. 410b), because it is in continual motion, criticizing Anaxagoras’ use of the term to denote fire (De Caelo i, 3, 270b22-5; ef. Meteor. i, 3, 339b22). Yet in Phys. iv, 4, 212b21 Aristotle himself uses it as a synonym for nip. For ai8p in Homer, see above p. 30 387 1074a7-8, todtov Sì póvas où Set dvediyOñvar dv ale cd karoréro terayuévoy déperat. Actually, as Sosigenes notes (ap. Simpl., p. 503, 28), without discussing the point, the moon also requires counteracting spheres; for Aristotle’s own explanation in the Meteorologica of such phenomena as comets, shooting stars, and the Milky Way (on which see below) envisages the outer layer of the sublunary sphere as being carried round in the same way as the fixed stars — so that there is the same need for the motions of the moon’s individual spheres to be cancelled out as in the cases of the other planetary bodies (cf. Heath, Arist., p- 219) further north and that those continuously visible in the north are seen, further south, to rise and set (2983-6), are almost certainly taken from Eudoxus - cf. p. 155 388 1074a12-14, el Sè tH cedqyy ve Kal TH NAO wh rpoorıdeln tug Bc elnonev 381 The figures cited by Guthrie (Loeb, pp. 254-55) from Prantl are completely 389 107443, elg td adtd dnoxahıorkons tH Oosı. Sosigenes spells this out — and inexplicably wrong (except the last one), and it is incredible that they should continue to be repeated (e.g. by J. H. Randall, Aristotle, p. 160, note 21). For the conversion of stades into miles, the best assumption is to take 8.72 stades as equivalent to 1 English mile or (which gives roughly the same result) 10 stades as equivalent to 1 geographical or nautical mile (= 1.152 Eng. miles) - on the value of the stade, see GFH, pp. 42-6 | 382 De Caelo ii, 11, 291b13, h Sì dios oddtv KAöywmg odiè UdTHY moret: cf. ii, 8, 289625; 290431. This is the keynote of all Aristotle’s natural philosophy | he is a teleologist Kıynosız, al näoaı opaípar Zoovrart Exmrá ve Kat TEOOAPÁKOVTO speaking of the last of Saturn's counteracting spheres, he says (ap. Simpl., P. 502, 17) orpadhoereı ody obtasg éuoiwc KIVOUUÉVN TH drchovel, où uévror kal thy TE eer ris émhavodc, mepl &Arous otpehouévy rékouc kal ob tobe Ts Amiavodg — cf. Pp. 498, 5-7 390 The same error vitiates the results of an ingenious paper by N. R. Hanson, ‘On Counting Aristotle’s Spheres’, Scientia, 98, 1963, pp. 223-32, who tries to prove that a 55-sphere system cannot work, but that “The required observations can be generated either within a system of 49 spheres, or within one comprising 61 spheres — the latter being preferable from an 383 It is difficult to imagine what gave rise to this curious notion, which (as far “Aristotelian” point of view’ (p. 223); later he suggests that either 50 or as I know) does not appear in any other ancient source. Simplicius in his 54 or 62 or 66 spheres would suffice (p. 232)! Hanson agrees that ‘ss commentary (pp. 454-56 ed. Heib.) is obviously (and not surprisingly) unhappy about Aristotle’s arguments in the whole of this section; he quotes spheres is all right [sic] if only we assume that each new« [the first sphere in each set] absolutely has the motion of the fixed stars’ (p. 229), but he regards the passage in the Timaeus, and refers approvingly to Ptolemy’s opinion this as incompatible with Aristotle’s ‘unified mechanically-articulated

NOTES 263 as produced by uniform expansion from the centre, or by uniform concosmology’. Yet this assumption does according to all our evidence traction from the circumference’ underlie Eudoxus’ original scheme (cf. Met. A 8,1073b18-19, &v Thy uèv Tpórnv thy Tüv émhavdv éotpwv elvaı) and Hanson rightly points out that ‘Aristotle is explicit in adapting [sic] en bloc Eudoxus’ technique for his 399 Ross (Arist. Met., p. cxxxiv) says, ‘This, however, is an incautious expression which should not be pressed. Aristotle’s genuine view undoubtedly is own cosmology’ (p. 226). His ideas about the connections postulated that the prime mover is not in space’, and he cites in support De Caelo 279418. Yet this passage does not altogether bear out Ross’ opinion. Aristotle is explaining (27946ff.) that there cannot be any bodily mass Aristotle) seems an excellent example of the dangers of forcing a spurious scientific rigidity on the modes of ancient astronomical thought. However, outside the heavens, for the world (6 más xéou0c) is made up of all the between the spheres by Aristotle go well beyond what we are entitled to infer from Aristotle’s words, and the whole paper (which out-Aristotles available matter (6A) and there is only one world; ‘outside the heaven, there is neither place nor void nor time (0888 témog od82 Kévov odSé Hanson is probably more correct than he realizes in saying (p. 229) that, if 55 spheres are insisted upon, ‘Aristotle’s entire cosmology becomes a childish re-scaling of the Eudoxan calculation technique’ - although xeóvos atly Ew rod obpavod) . . . and therefore neither are the things there born in place (dıörep od” Ev róxo ráxel méburev), nor does time make them grow old, nor is there any change at all in any of the things ‘childish’ seems unnecessarily harsh especially the last sentence, Gore oharpoerdng dv ely nica 287a5-11, 391 | révra yao &rtetat Kal ouvex% ¿ori tate ohatpatc that are posited to lie beyond the outermost revolution (rüv bate thy ¿Eotáro rerayuevav bopdv), but changeless and unaffected they continue to lead the best and most self-sufficient life throughout all eternity’ - and Aristotle goes on to stress the ideas of immortality and divinity which men have always connected with the notion of eternity. Thus there are 392 odpavós in all three of the senses which Aristotle defines in De Caelo i, 9, 278b8ff. (namely, the outer circumference of the world, the celestial regions, and the whole universe) is conceived of as ‘body’ (0% ua); cf. ii, 3, 286a10-12 393 ii, 12, 29346-8, &v roXaïc yap ohatpats Y rerevrala chatpa Evdcdey tvn at least conceptual entities ££ rod odpavod — and what better place could there be for the notional first mover or movers? Cf. W. Theiler in JHS 77 (1), 1957, pp. 127-31, who cites two passages in Sextus Empiricus pipetat, Ékdorn Sì odhatow oué te tryydver ov 394 See De Gen. et Corr. ii, 10, 336a31ff., 310 Kal odgh POT bopà abría ¿ori yevécews Kal dIopdc, ¿AN $ xarà tov AoËdv «óxdov, and the whole of this chapter; also Meteor. i, 9, 346b21-4; ii, 4, 361a12-14; of. Met. A 5, (Hyp. iti, 218 and Adv. Math. x, 33) for Aristotle’s view of god répas rob odpavod. There is no need at all to assume ‘an incautious expression’ on Aristotle’s part. In fact, the eternity of the whole heaven (including all 1071413, . . . bonep &vOodnov alrıov tk te OTOLLELA . . . Kal mapa time and infinity) is described in this passage of the De Caelo in terms that recall those applied later to the prime mover (it is ‘deathless and divine’ radra è hoc ka 6 Aokds xbxdoc, where Ross’ note (p. 365) to the effect that it was Hipparchus who first called the ecliptic 6 éxAeuntixdg is wrong — the latter term is not found until Achilles Tatius in the third century AD and the source of existence and life for all other things, 279428-30; cf. Met. A 7, 1072b14 and 28-30); the reason why the latter is not actually mentioned by name here is presumably because Aristotle had not yet (its appearance in Cleomedes, Cycl. Theor. ii, 5, p. 206, 26 ed. Ziegler, is an interpolation), whereas Hipparchus and Ptolemy always use the phrases 5 AoËdc KdKAOS or 6 Sk pécav róv Codlav xóxdos (as does Aristotle himself - see above and A 8, 1073b19), restricting éxAeinrikéc to the elaborated this concept (cf. Cherniss, Arist. Crit. Pl. and Acad., App. X, p- 588). P. Merlan in Apeiron, Monash University, Australia, 1, 1966, meaning ‘pertaining to eclipses’ 395 &hrroug yee Has Kab cedhvy kivobvrar kivhoeus À THY TAaVOpEVOY &otowv Evia, 291035 396 Phys. vii, 2, 243a32-4, where the mover is said to be ¿ya the moved and ¿uo is defined as ‘nothing being in between them’ (&rı oddév ¿ori aby wera£d) — a similar definition of ¿pa is given in v, 3, 226b21; cf. viii, 1, 242b59-63 397 258b10-11, évéyrn elvat vi dtdiov 6 mpdtov Kuveî, elte Ev elte melo. Later Aristotle says that it is better to envisage only one unmoved first mover, on the principle of the economy of hypotheses (25946-13); but, as we shall see, he has to abandon this position with regard to the movers of the planetary spheres 398 As Ross explains (Arist. Phys., pp. 727-28), ‘the sphere may be regarded / pp- 3-13, has an interesting analysis of this passage; his main thesis, that Aristotle’s theology is basically polytheistic, is probably correct; less convincing is his insistence that Aristotle’s views on the fifth element and the unmoved mover or movers are self-contradictory - on this apparent contradiction, see further above, p. 213 400 1071520, Ett rolvuv rabras Set tas odctac elvar dvev Lane: didiove yao det, elmep ye Kai dAdo ti dtdiov. Evépyerat po — note the plural, which anticipates the prime movers of the planetary spheres mentioned later; hence the plural ¿vépyeror (found in two ss) seems better than the singular of the Oxford text (cf. Merlan, loc. cit., p. 11 note 1) 401 kivel Sé de épouevov, 1072b3. For both desire (ëpeËtc) and thinking (vénotc) are types of movement in Aristotle’s view (cf. 1072430, vob¢ Sè und ro vontod kuveïtou), as is explained in De Anima iii, 10

EARLY GREEK ASTRONOMY TO ARISTOTLE 402 1072b26-30; cf. Nic. Eth. x, 8, 1178b21-2 403 It is difficult to see how to reconcile this statement with the dvertrrovoar NOTES 408 obaipaı 404 This is the very puzzling passage 1074431-8 (see above, p. 195). One may 15; Dox. Gr., p. 343), that every star was a world by itself, with its own earth and bodies as fiery stones (see above, pp. 58f. and Heath, Arist., p. 246 note 1) This comet is mentioned three times by Aristotle (343b1; b18; 344534), always with the epithet ‘great’ (6 péyas). It is possible that it was an appearance of what is now known as Halley’s comet, which in its 76- or agree with Merlan (Traditio 4, 1946, p. 13) that Aristotle is arguing against views such as those attributed to Heraclides Ponticus (Aét. ii, 13, 265 75-year period would have been due to appear about 370 Bc 409 This is a common phenomenon in naked-eye observation, and its precise air; but why does he, immediately after stressing the plurality of prime movers (and since these are 55 or 47 in number, how is it that they do not description by Aristotle confirms that he himself had experience of it. The star in question is either è or e Canis maioris 410 If this is what is referred to in Meteor. i, 5 as Ideler, Heath, and Lee assume; partake of matter by Aristotle’s own reasoning?), relapse into speaking E. W. Webster (in the Oxford translation, vol. iii, 1931, ad loc.) thinks of ‘the first unmoved mover’ (tò rp&roy kıyvoöv éxivnrov dv, 437) as if it rather of ‘phenomena of cloud coloration’ - cf. Lee, p. 36. The aurora is were the only one? A possible explanation perhaps (which I have not seen rarely seen except in extreme northern or southern latitudes round the suggested elsewhere) is that Aristotle regarded the prime mover of the outer heaven as a primum inter paria; there is only one basic principle of AII celestial movement (944) for our one, unique universe, but this principle manifests itself in a number of independent prime movers of which the 412 first (activating the sphere of the fixed stars) is commonly used as the exemplar, since the daily revolution of the heavens from east to west is the only revolution common to all the celestial bodies. Such an explanation (which cannot here be developed in detail) might serve to account for the earth’s north or south magnetic poles And therefore rises and sets with the heavens - hence the moon also should have been endowed with counteracting spheres (see note 387) See pp. 29f. for this concept in Homer 413 Aristotle’s ‘explanation’ is even less convincing than usual. He seems to regard the Milky Way as that part of the sphere of the fixed stars which contains the greatest number of bright stars (346a17/f. - hence presumably emphasis that Aristotle lays (both here and in De Caelo i, 8 and 9 - see the appellation “greatest circle’); but the fixed stars form the outermost sphere of the whole universe, and it is difficult to see how this can be above, p. 199) on the idea of one world only; more than one world would entail more than one set of unmoved movers, and more than one principle regarded as in close enough contact with the outer stratum of the sublunary region to ignite it. Perhaps he would invoke the concept of circular motion would be utterly incompatible with his whole philoof the counteracting planetary spheres (see above) to meet this point. sophical system It is interesting that the text refers to a diagram (önoypabn) and a globe (cpaîpa) on which stars might be marked (346a32f.) - no doubt as 405 1074a38-b14, esp. b2, Oeot té eloıv odor Kal mepréyer td Oslo thy SAny ¿vou and bo, 6t1 Oeobc dovro tag mph ras obolus elvas, Debes dv elpjobar voutoetev. If we regard a31-38 as a long parenthesis (sce above, p. 195), the antecedent of 08 ot will be the divine celestial bodies mentioned in a30; but even if we do not so regard it, the lack of a specifically expressed. visual aids to accompany the lecture (cf. Lee, p. 67 note b) 414 See pp. 84f. 415 6 31% navrös pavepds (kôwAoc), 362b2 — but this, as Aristotle must have antecedent need not prevent its referring to the prime movers which have known (cf. De Caelo ii, 14, 297b31f.), properly refers to the limit of the circumpolar stars at a particular latitude, which changes with the observer’s been the subject of discussion (Merlan - op. cit., p. 14 - thinks of a gesture towards the heavens when the passage was read aloud). It seems likely that locality. Poseidonius and Strabo rightly criticize Aristotle for defining a by tv dexatov Kab rauraralcoy (br) and tv meatov (br4) Aristotle is apparent in the chapter on winds (ii, 6), where in the circular diagram means the ancient Egyptians and Babylonians (cf. De Caelo ii, 12, 29247-9), who undoubtedly had an astral religion from very early times; but there winter sunset and sunrise, equinoctial sunset and sunrise, and the north is no evidence for star gods in early Greek belief zone by a variable circle (Str. C 95 - see GFH, p. 166). The same confusion based on the eight commonly used reference points (namely, summer and 406 This and the last two books (iii and iv) of De Caelo deal with the four and south poles - see Lee, p. 187), a chord connecting the points where two northerly winds blow is described as ‘nearly corresponding to the elements, their mutual transformations, and the general principles of the wholly visible circle, but not accurately’ (4 dè tod IK Sikperpog Bobretat processes of generation and decay - cf. H. D. P. Lee, Meteorologica, Loeb, 1952, p. x 407 This occurrence was known to Anaxagoras, who is even supposed to have pèv «ora Tov Suk mavrdc elvaı daivduevoy, odx dkpiBot Dé) 416 This is because of his insistence that motion must start from the right, therefore east must be the right-hand side, and the motion of the heavens predicted it (DK 59 Art and 12; Diog. Laert. ii, 10), but this is simply a must be from right to left. However, when we face south (as in the northern picturesque inference derived from his well-known views of the celestial hemisphere we must in order to face the sun), the motion of the heavens

NOTES 267 is clearly from our left (east) to our right (west), on the normal supposition that we are standing up with our heads in the direction of the visible north 430 The question cannot be argued in detail here, but cf. the views of Merlan pole; but this does not accord with the right’s being the start of the motion — 431 Cf. Moraux, p. xlii and lxxxviii and the authorities referred to in his notes 432 This itself is incompatible with the description in ii, 4 (see above, p. 203) air has no business to be in the celestial regions at all, and the only planetary spheres immediately beneath which there is air are those of the moon (cf. hence we have to suppose that our feet are towards the north pole and our head towards the south, which is therefore the upper pole. This whole chapter shows Aristotle at his least convincing in an astronomical context. Wicksteed (Loeb Physics, pp. Ixii-Ixiii) has a good note on this passage, and correctly points out that in terrestrial maps east is on the right, but in celestial maps (e.g. Norton’s Star Atlas) east is on the left. For Pythagorean views on the supremacy of the right and Plato’s connection of this with the east, see above p. 121 417 From what we are told of Aristotle’s relations with Callippus, Met. A 8 can hardly have been written before 330 Bc and probably later - see pp. 190 and 194 418 E.g. Met. A 9, 992432; cf. his sharp criticism in De Caelo iii, 7 of Plato’s elemental triangles as described in the Timaeus - see Solmsen, Arist. Syst. Phys. World, 1960, pp. 259f. 419 Cf. Merlan in Traditio 4, 1946, p. 5, who draws attention to the tripartite classification mentioned in Phys. ii, 7, 198429, whereof astronomy belongs to the second part which is concerned with ‘things that are in motion but are indestructible’ 420 See p. 199; cf. Met. A 8, 1050622, where Aristotle assures us that there is no need to fear that the heavens will become tired! 421 E.g. ii, 6, 288427-b7; 288b22-30; iv, 3, 311a9-12; cf. i, 8, 277b9-12 and Guthrie ad loc. 422 The controversy has centred on De Caelo i, 9, 279433-b3; ii, 1, 284a18-b4; ii, 3, 286410-12; iii, 2, 300b1 8-22; iv, 2, 309b17-24 - all these passages have been thought to be inconsistent with the concept of a prime mover - as well as on the passages mentioned above. Cherniss (loc. cit.) cites most of the relevant literature; cf. Moraux, p. xliii-xlv 423 For the stars do not vary their distances from each other — 288b10-12; ef 28945-7 424 287a23-4, h tod odpavod dopà . . . udvy ovveyhs Kat duarye cal &t8r0¢ 425 dvopalla... dvaparlav: peraBàXor. . . peraBdXder; &Suvania . .. adbvatov (288426; 288b5; 288621) 426 As Cherniss points out, op. cit., App. X, pp. 581-82; cf. Moraux, p. xlv 427 Cf. Met. © 8, 1050b21, obk Lori Kara Súvayr xivovievov &AN D rroBiv rot 428 287b27-8, dvd yen ydp cal tobto Y dpyhv elvar Y elvas ad rod Loy y 429 The passages cited by Ross (Met. A 4, 1070634; 7, 1072513; 10, 10764) are simply general expressions of the universal influence of the prime mover of the outer heaven to which, in a sense, everything in the celestial regions is subject, since it is the cause of all risings and settings. As mentioned above (note 404), Aristotle seems to use this as an exemplar or typical prime mover cited above, note 399 o Meteor. i, 3 and 4; above, pp. 199; 203) 433 This is part of his argument against the Pythagorean ‘harmony of the spheres’ 434 291b2, Exaorov ydp dvtupépetat TH obpavé Katà tov adrod KbKAov— this, of course, refers to motion along the zodiac in the opposite direction (i.e. west to east) to the daily rotation 435 Thus Saturn has the longest sidereal period (about 293 years) and the moon the shortest (about 274 days) 436 Cf. Moraux, p. cii, ‘Les théories proprement astronomiques du De Caelo ne paraissent ni très claires ni très cohérentes’; cf. pp. cxxv-cxxvi 437 E.g. De Caelo ii, 3, 286a4-7; 5, 287b31-28842; 12, 291b25-8; 202a14-18; Met. A 8, 1073b13-17 438 Hence, of course, the comparative success of the Greeks in the two fields, mathematics and astronomy, which make least use of the controlled experiment 439 And Ptolemy was just as convinced of the divine nature of the heavens and the celestial bodies as ever Plato and Aristotle were (cf. Almag. i, 1, p. 6, 23 ed. Heib., and the famous epigram in the Palatine Anthology, ix, 577) 440 Summa Theol. i, 50, 3-4; cf. P. Duhem, Le système du monde, tom. v, 1917, | p. 530ff441 See P. Wicksteed, The Reactions between Dogma and Philosophy, 1920, pp. 442 an we know nothing for certain of how Eudoxus or Callippus made their observations. It is a reasonable assumption that they made use of celestial globes and the gnomon, but we can only guess at the type of sighting instrument they employed, if indeed they used any — it is remarkable what can be achieved by simply using the fingers of the outstretched arm to gauge the relative positions of celestial objects 443 Author of two extant treatises, On the Moving Sphere and On Risings and Settings, which (with Euclid’s Phainomena) are the earliest mathematically based works on astronomy that have come down to us — but there is no actual mention of the theory of concentric spheres in these works