IV

ANAXIMANDER

ANAXIMANDER of Miletus (born probably in 611/10, died soon after 547/6 B.C.), son of Praxiades, was a fellow citizen of Thales, with whom he was doubtless associated as a friend if not as a pupil. A remarkably original thinker, Anaximander may be regarded as the father or founder of Greek, and therefore of western, philosophy. He was the first Greek philosopher, so far as is known, who ventured to put forward his views in a formal written treatise.1,² though possibly that title was given to it, not by Anaximander himself, but only by later writers.³ The amount of thought which went to its composition and the maturity of the views stated in it are indicated by the fact that it was not till the age of 64 that he gave it to the world.⁴ The work itself is lost, except for a few lines amounting in no case to a complete sentence.

Anaximander boldly maintained that the earth is in the centre of the universe, suspended freely and without support,⁵ whereas Thales regarded it as resting on the water, and Anaximenes as supported by the air. It remains in its position, says Anaximander, because it is at an equal distance from all the rest (of the heavenly bodies).⁶ Aristotle expands the explanation thus:⁷ ‘for that which is located in the centre and is similarly situated with reference to the extremities can no more suitably move up than down or laterally, and it is impossible that it should move in opposite directions (at the same time), so that it must necessarily remain at rest.’ Aristotle admits that the hypothesis is daring and brilliant, but argues that it is not true: one of his grounds is amusing, namely, that on this showing a hungry and thirsty man with food and wine disposed at equal distances all round him would have to starve because there would be no reason for him to stretch his hand in one direction rather than another8 (presumably the first occurrence of the well-known dilemma familiar to the schoolmen as the ‘Ass of Buridan’).

According to Anaximander, the earth has the shape of a cylinder, round, ‘like a stone pillar’;⁹ one of its two plane faces is that on which we stand, the other is opposite;¹⁰ its depth, moreover, is one-third of its breadth.¹¹

Still more original is Anaximander’s conception of the origin and substance of the sun, moon, and stars, and of their motion. As there is considerable difference of opinion upon the details of the system, it will be well, first of all, to quote the original authorities, beginning with the accounts of the cosmogony.

‘Anaximander of Miletus, son of Praxiades, who was the successor and pupil of Thales, said that the first principle (i.e. material cause) and element of existing things is the Infinite, and he was the first to introduce this name for the first principle. He maintains that it is neither water nor any other of the so-called elements, but another sort of substance, which is infinite, and from which all the heavens and the worlds in them are produced; and into that from which existent things arise they pass away once more, “as is ordained; for they must pay the penalty and make reparation to one another for the injustice they have committed, according to the sequence of time”, as he says in these somewhat poetical terms.’¹²

‘Anaximander said that the Infinite contains the whole cause of the generation and destruction of the All; it is from the Infinite that the heavens are separated off, and generally all the worlds, which are infinite in number. He declared that destruction and, long before that, generation came about for all the worlds, which arise in endless cycles from infinitely distant ages.’13

‘He says that this substance [the Infinite] is eternal and ageless, and embraces all the worlds. And in speaking of time he has in mind the separate (periods covered by the) three states of coming into being, existence, and passing away.’¹⁴

‘Besides this (Infinite) he says there is an eternal motion, in the course of which the heavens are found to come into being.’¹⁵

‘Anaximander says eternal motion is a principle older than the moist, and it is by this eternal motion that some things are generated and others destroyed.’¹⁶

‘He says that (the first principle or material cause) is boundless, in order that the process of coming into being which is set up may not suffer any check.’¹⁷

‘Anaximander was the first to assume the Infinite as first principle in order that he may have it available for his new births without stint.’¹⁸

‘Anaximander . . . said that the world is perishable.’¹⁹

‘Those who assumed that the worlds are infinite in number, as did Anaximander, Leucippus, Democritus, and, in later days, Epicurus, assumed that they also came into being and passed away, ad infinitum, there being always some worlds coming into being and others passing away; and they maintained that motion is eternal; for without motion there is no coming into being or passing away.’²⁰

‘Anaximander says that that which is capable of begetting the hot and the cold out of the eternal was separated off during the coming into being of our world, and from the flame thus produced a sort of sphere was made which grew round the air about the earth as the bark round the tree; then this sphere was torn off and became enclosed in certain circles or rings, and thus were formed the sun, the moon, and the stars.’21

‘The stars are produced as a circle of fire, separated off from the fire in the universe and enclosed by air. They have as vents certain pipe-shaped passages at which the stars are seen; it follows that it is when the vents are stopped up that eclipses take place.’²²

‘The stars are compressed portions of air, in the shape of wheels, filled with fire, and they emit flames at some point from small openings.’²³

’The moon sometimes appears as waxing, sometimes as waning, to an extent corresponding to the closing or opening of the passages.’²⁴

Further particulars are given of the circles of the sun and moon, including the first speculation about their sizes:

‘The sun is a circle 28 times the size of the earth; it is like a wheel of a chariot the rim of which is hollow and full of fire, and lets the fire shine out at a certain point in it through an opening like the tube of a blow-pipe; such is the sun.’²⁵

‘The stars are borne by the circles and the spheres on which each (of them) stands.’²⁶

‘The circle of the sun is 27 times as large as the earth and that of the moon is 19 times as large as the earth.’27

‘The sun is equal to the earth, and the circle from which the sun gets its vent and by which it is borne round is 27 times the size of the earth.’²⁸

‘The eclipses of the sun occur through the opening by which the fire finds vent being shut up.’²⁹

’The moon is a circle 19 times as large as the earth; it is similar to a chariot-wheel the rim of which is hollow and full of fire, like the circle of the sun, and it is placed obliquely like the other; it has one vent like the tube of a blowpipe; the eclipses of the moon depend on the turnings of the wheel.’³⁰

‘The moon is eclipsed when the opening in the rim of the wheel is stopped up.’³¹

‘The sun is placed highest of all, after it the moon, and under them the fixed stars and the planets.’³²

We are now in a position to make some comments. First, what is the nature of the eternal motion which is an older principle than water and by which some things are generated and others destroyed? Teichmülier held it to be circular revolution of the Infinite, which he supposed to be a sphere, about its axis;³³ Tannery adopted the same view.³⁴ Zeller³⁵ rejects this for several reasons. There is no evidence that Anaximander conceived the spherical envelope of fire to be separated off by revolution of the Infinite and spread out over the surface of its mass; the spherical envelope lay, not round the Infinite, but round the atmosphere of the earth, and it was only the world, when separated off, which revolved; it is the world too, not the Infinite, which stretches, at equal distances, and therefore in the shape of a sphere, round the earth as centre. Lastly, a spherical Infinite is in itself a gross and glaring contradiction, which we could not attribute to Anaximander without direct evidence. Tannery36 gets over the latter difficulty by the assumption that the Infinite was not something infinitely extended in space but qualitatively indeterminate only, and in fact finite in extension. This is rather an unnatural interpretation, especially in view of what we are told of the ‘infinite worlds’ which arise from the Infinite substance. The idea here seems to be that the Infinite is a boundless stock from which the waste of existence is continually made good.³⁷ With regard to the ‘infinite worlds’ Zeller³⁸ held that they were an infinity of successive worlds, not an unlimited number of worlds existing, or which may exist, at the same time, though of course all are perishable; but in order to sustain this view Zeller was obliged to reject a good deal of the evidence. Burnet³⁹ has examined the evidence afresh, and adopts the other view. In particular, he observes that it would be very unnatural to understand the statement that the Boundless ‘encompasses the worlds’ of worlds succeeding one another in time; for on this view there is at a given time only one world to ‘encompass’. Again, when Cicero says Anaximander’s opinion was that there were gods who came into being, rising and setting at long intervals, and that these were the ‘innumerable worlds’⁴⁰ (cf. Aëtius’s statement that, according to Anaximander, the ‘innumerable heavens’ were gods⁴¹), it is more natural to take the long intervals as intervals of space than as intervals of time;⁴² and, whether this is so or not, we are distinctly told in a passage of Stobaeus that ‘of those who declared the worlds to be infinite in number, Anaximander said that they were at equal distances from one another’, a passage which certainly comes from Aëtius.⁴³ Neuhäuser,⁴⁴ too, maintains that Anaximander asserted the infinity of worlds in two senses, holding both that there are innumerable worlds co-existing at one time and separated by equal distances, and that these worlds are for ever, at certain (long) intervals of time,45 passing away into the primordial Infinite, and others continually succeeding to their places.⁴⁶

The eternal motion of the Infinite would appear to have been the ‘separating-out of opposites’,⁴⁷ but in what way this operated is not clear. The term suggests some process of shaking and sifting as in a sieve.⁴⁸ Neuhäuser⁴⁹ holds that it is not spatial motion at all, but motion in another of the four Aristotelian senses, namely generation, which takes the form of the ‘separating-out of opposites’, condensation and rarefaction incidentally playing a part in the process.

As regards the motion by which the actual condition of the world was brought about (the earth in the centre in the form of a flat cylinder, the sun, moon, and stars at different distances from the earth, and the heavenly bodies revolving about the axis of the universe), Neuhäuser⁵⁰ maintains that it was the motion of a vortex such as was assumed by Anaxagoras, the earth being formed in the centre by virtue of the tendency of the heaviest of the things whirled round in a vortex to collect in the centre. But there is no evidence of the assumption of a vortex by Anaximander; Neuhäuser relies on a single passage of Aristotle, which however does not justify the inference drawn from it.⁵¹

We come now to Anaximander’s theory of the sun, moon, and stars. The idea of the formation of tubes of compressed air within which the fire of each star is shut up except for the one opening is not unlike Laplace’s hypothesis with reference to the origin of Saturn’s rings.52 A question arises as to how, if rings constituting the stars are nearer than the circles of the sun and moon, they fail to obstruct the light of the latter. Tannery⁵³ suggests that, while of course the envelopes of air need not be opaque, the rarefied fluid within the hoops, although called by the name of fire, may also be transparent, and not be seen as flame except on emerging at the opening. The idea that the stars are like gas-jets, as it were, burning at holes in transparent tubes made of compressed air is a sufficiently original conception.

But the question next arises, in what position do the circles, wheels, or hoops carrying the sun, moon, and stars respectively revolve about the earth? Zeller and Tannery speak of them as ‘concentric’, their centres being presumably the same as the centre of the earth; and there is nothing in the texts to suggest any other supposition. The hoops carrying the sun and moon ‘lie obliquely’, this being no doubt an attempt to explain, in addition to the daily rotation, the annual movement of the sun and the monthly movement of the moon. Tannery raises the question of the heights (‘hauteurs’) of these particular hoops, by which he seems to mean their breadths as they would be seen (if visible) from the centre. Thus, if the bore of the sun’s tube were not circular but flattened (like a hoop), in the surface which it presents towards the earth, to several times the breadth of the sun’s disc, it might be possible to explain the annual motion of the sun by supposing the opening through which the sun is seen to change its position continually on the surface of the hoop. But there is nothing in the texts to support this. Zeller⁵⁴ feels difficulty in accepting the sizes of the hoops as given, on the supposition that the earth is the centre. For we are told that the sun’s circle or wheel is 27 or 28 times the size of the earth, while the sun itself is the same size as the earth; this would mean that the apparent diameter of the sun’s disc would be a fraction of the whole circumference of the ring represented by 1/28π, that is, the angular diameter would be about 360°/88, or a little over 4°, which is eight times too large, and would be too great an exaggeration to pass muster even in those times. Zeiler therefore wonders whether perhaps the sun’s circle should be 27 times the moon’s circle, which would make it 513 times the size of the earth. But the texts, when combined, are against this, and further it would make the apparent diameter of the sun much too small. According to Anaximander, the sun itself is of the same size as the earth; therefore, assuming d to be the diameter of the sun’s disc and also the diameter of the earth, the circumference of the sun’s hoop would be 513πd, so that the apparent diameter of the sun would be about 1/1600th part of its circle, or less than half what it really is. Teichmüller55 and Neuhäuser⁵⁶ try to increase the size of the sun’s hoop 3·1416 times, apparently by taking the diameter of the hoop to be 28 times the circumference of the earth, ‘because the measurement clearly depended on an unrolling’; but this is hardly admissible; the texts must clearly be comparing like with like. Sartorius⁵⁷ feels the same difficulty, and has a very interesting hypothesis designed to include provision for the sun’s motion in the ecliptic as well as the diurnal rotation. He bases himself on a passage of Aristotle which, according to a statement of Alexander Aphrodisiensis made on the authority of Theophrastus, refers to Anaximander’s system.

Aristotle speaks of those who explain the sea by saying that

‘at first all the space about the earth was moist, and then, as it was dried up by the sun, one portion evaporated and set up winds and the turnings of the sun and moon, while the remainder formed the sea’;⁵⁸

and again he says in another place:

‘The same absurdity also confronts those who say that the earth, too, was originally moist, and that, when the portion of the world immediately surrounding the earth was warmed by the sun, air was produced and the whole heaven was thus increased, and that this is how winds were caused and the turnings of the heaven brought about’59

It is on these passages that Zeller⁶⁰ grounds his view that the heavens are moved by these winds and not by the eternal rotational movement of the Infinite about its axis assumed by Teichmüller and Tannery; accordingly, Zeller cannot admit that the word in these passages is used in its technical sense of ‘solstices’.⁶¹ Sartorius, however, clearly takes the to refer specially to the solstices (so does Neuhäuser⁶²), and he shows how the motions of the sun could be represented by two different but simultaneous revolutions of the sun’s wheel or hoop. Suppose the wheel to move bodily in such a way that (1) its centre describes a circle in the plane of the equator, the centre of which is the centre of the earth, while (2) the plane of the wheel is always at right angles to the plane of the aforesaid circle, and always touches its circumference; lastly, suppose the wheel to turn about its own centre at such speed that the opening representing the sun completes one revolution about the centre of the wheel in a year, and suppose the centre of the wheel to describe the circle in the plane of the equator at uniform speed in one day.

In the figure appended, E represents the earth, the C’s are positions of the centre of the sun’s hoop or wheel;

S₁ represents the sun’s position at the vernal equinox;

S₂ represents the sun’s position at the summer solstice;

S₃ represents the sun’s position at the autumnal equinox;

S₄ represents the sun’s position at the winter solstice.

Fig. 2.

At the winter solstice the sun is south of the equator, at the summer solstice north of it, and the diameter of the wheel corresponds to an angle at E which is double of the obliquity of the ecliptic, say 47°. Now, as the diameter of the sun’s wheel is 28 times the diameter of the earth, i.e. of the sun itself (which is the same size as the earth), the angular diameter of the sun at E will be about 47°/28 or 1°41′. This is still far enough from the real approximate value , but it is much nearer than the 4° obtained from the hypothesis of a hoop with its centre at the centre of the earth.

Let us consider what would be the distance of the sun from the earth on the assumption that the sun’s diameter (supposed to be equal to that of the earth) subtends at E an angle of . If d be the diameter of the earth, and D the distance of the sun from the earth, we shall have approximately

or

But Sartorius’s hypothesis is nothing more than an ingenious guess, as the texts give no colour to the idea that Anaximander intended to assign a double motion to the sun, nor is there anything to suggest that the hoops of the sun and moon moved in any different way from those of the stars, except that they were both ‘placed obliquely’.

Fig: 3.

The hypothesis of concentric rings with centres at the centre of the earth seems therefore to be the simplest.

Neuhäuser,63 in his attempted explanation of Anaximander’s theory of the sun’s motion, contrives to give to the technical meaning of solstices, while keeping the ring concentric with the earth. The flat cylinder (centre O) is the earth, N.P. and S.P. are the north and south poles, the equator is the circle about AA' as diameter and perpendicular to the plane of the paper. Neuhäuser then supposes the plane of the sun’s circle or hoop to be differently-inclined to the circle of the equator at different times of the year, making with it at the summer solstice and at the winter solstice angles equal to the obliquity of the ecliptic in the manner shown in the figure, where the circle on AA' as diameter in the plane of the paper is the meridian circle and SS' is the diameter of the sun’s ring at the summer solstice, BB' the diameter of the sun’s ring at the winter solstice. Between the extreme positions at the solstices the plane of the sun’s hoop changes its inclination slightly day by day, its section with the meridian plane moving gradually during one half of the year from the position SS' to the position BB' and during the other half of the year from BB' back to SS'. As it approaches the summer-solstitial position, it is prevented from swinging further by the winds, which are caused by exhalations, and which by their pressure on the sun’s ring force it to swing back again. The exhalations and winds only arise in the regions where there is abundant water. Neuhäuser supposes that Anaximander had the Mediterranean and the Black Sea in mind, and that their positions sufficiently ‘correspond’ (?) to the summer-solstitial position SS' to enable the winds to act as described. There is no sea in such a position as would enable winds arising from it to repel the sun’s ring in the reverse direction from BB' to SS' consequently Neuhäuser has to suppose that the ring has an automatic tendency to swing towards the position SS' and that it begins to go back from BB' of itself, as soon as the force of the wind which repelled it from SS' ceases to operate. There is, however, no evidence in the texts to confirm in its details this explanation of the working of Anaximander’s system; on the contrary, there seems to be positive evidence against it in the phrase ‘lying obliquely’, the breadth therefore; used of the hoops of the sun and moon, which suggests that the hoops remain at fixed inclinations to the plane of the equator instead of oscillating, as Neuhäuser’s theory requires, between two extreme positions relatively to the equator.

In any case Anaximander’s system represented an enormous advance in comparison with those of the other Ionian philosophers in that it made the sun, moon, and stars describe circles, passing right under the earth (which was freely suspended in the middle), instead of moving laterally round from the place of setting to the place of rising again.

We are told by Simplicius that

‘Anaximander was the first to broach the subject of sizes and distances; this we learn from Eudemus, who however refers to the Pythagoreans the first statement of the order (of the planets) in space.64

This brings us back to the question of the sizes of the hoops of the sun and moon as given by Anaximander. We observe that in one passage the sun’s circle is said to be 28 times as large as the earth, while in another the circle ‘from which it gets its vent’ is 27 times as large as the earth. Now, on the hypothesis of concentric rings, we, being in the centre, of course see the inner circumference at the place where the sun shines through, the sun’s light falling, like a spoke of the wheel, towards the centre. The words, then, used in the second passage, referring to the circle from which the sun gets its vent, suggest that the ‘27 times’ refers to the inner circumference of the wheel, while the ‘28 times’ refers to the outer;⁶⁵ the breadth therefore of the sun‘s wheel measured in the direction from centre to circumference is equal to once the diameter of the earth. A like consideration suggests that it is the outer circumference of the moon’s hoop which is 19 times the size of the earth, and that the inner circumference is 18 times the size of the earth; nothing is said in our texts about the size of the moon itself. Nor are we told the size of the hoops from which the stars shine, but, as they are in Anaximander’s view nearer to the earth than the sun and moon are, it is perhaps a fair inference that he would assume for a third hoop or ring containing stars an inner circumference representing 9 times the diameter of the earth; the three rings would then have inner circumferences of 9, 18, 27, being multiples of 9 in arithmetical progression, while 9 is the square of 3; this is appropriate also to the proportion of 1 : 3 between the depth of the disc representing the earth and the diameter of one of its faces. These figures suggest that they were not arrived at by any calculation based on geometrical constructions, but that we have merely an illustration of the ancient cult of the sacred numbers 3 and 9.66 3 is the sacred number in Homer, 9 in Theognis, 9 being the second power of 3. The cult of 3 and its multiples 9 and 27 is found among the Aryans, then among the Finns and Tartars, and next among the Etruscans (the Semites connected similar ideas with 6 and 7). Therefore Anaximander’s figures really say little more than what the Indians tell us, namely that three Vishnu-steps reach from earth to heaven.

The story that Anaximander was the first to discover the gnomon⁶⁷ (or sun-dial with a vertical needle) is incorrect, for Herodotos says that the Greeks learnt the use of the gnonion and the polos from the Babylonians.⁶⁸ Anaximander may, however, have been the first to ‘introduce’⁶⁹ or make known the gnomon in Greece, and to show on it ‘the solstices, the times, the seasons, and the equinox’.⁷⁰ He is said to have set it up in Sparta.⁷¹ He is also credited with constructing a sphere to represent the heavens,⁷² as was Thales before him.⁷³

But Anaximander has yet another claim to undying fame. He was the first who ventured to draw a map of the inhabited earth.⁷⁴ The Egyptians had drawn maps before, but only of particular districts;⁷⁵ Anaximander boldly planned out the whole world with ‘the circumference of the earth and of the sea‘⁷⁶ Hecataeus, a much-travelled man, is said to have corrected Anaximander’s map, so that it became the object of general admiration. According to another account, Hecataeus left a written description of the world based on the map. In the preparation of the map Anaximander would of course take account of all the information which reached his Ionian home as the result of the many journeys by land and sea undertaken from that starting-point, journeys which extended to the limits of the then-known world; the work involved of course an attempt to estimate the dimensions of the earth. We have, however, no information as to his results.77

Anaximander’s remarkable theory of evolution does not concern us here.⁷⁸

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¹ Themistius, Orafzones, 36, p. 317 C (Vors. i², p. 12. 43).

² Ibid.; Suidas, s. υ.

³ Zeller, Philosophie der Griechen, i⁵, p. 197.

⁴ Diog. L. ii. 2 (Vors. i², p. 12. 7–10).

⁵ Hippol. Refut. i. 6. 3 (D. G. p. 559. 22; Vors. i², p. 14. 5).

⁶ Ibid.; cf. Plato’s similar view Phaedo 108 E–109 A.

⁷ De caelo ii. 13, 295 b 10–16. It is true that Eudemus (in Theon of Smyrna, p. 198.18) is quoted as saying that Anaximander held that ‘the earth is suspendedfreely and moves about the centre of the universe’; but there mustclearly be some mistake here; perhaps Kivctrat should be (‘lies’).

⁸ Aristotle, De caelo ii. 13, 295 b 32.

⁹ Hippol. Refut. i. 6. 3 (D. G. p. 559. 24; Vors. i², p. 14. 6); Aët. iii. 10. 2 (D. G. p. 376; Vors. i² p. 16. 34).

¹⁰ Hippol., loc. cit.

¹¹ Ps. Plut. Stromat. 2 (D. G. p. 579. 12; Vors. i², p. 13. 34).

¹² Simplicius, in Phys. p. 24. 13 (Vors. i², p. 13. 2–9). The passage is from Theophrastus’s Phys. Opin., and the words in inverted commas at all events are Anaximander’s own. I follow Burnet (Early Greek Philosophy, p. 54) in making the quotation begin at ‘as is ordained’; Diels includes in it the words just preceding ‘and into that from which . . . .’

¹³ Ps. Plut. Stromat. 2 (D.G. p. 579; Vors. i², p. 13. 29 sq.). This passage again is from Theophrastus.

¹⁴ Hippol. Refut. i. 6. 1 (D. G. p. 559; Vors. i², pp. 13. 44–14. 2).

¹⁵ Ibid. i. 6. 2.

¹⁶ Hermias, Irris. 10 (D. G. p. 653; Vors. i², p. 14. 21).

¹⁷ Aët. i. 3. 3 (D. G. p. 277; Vors. i², p. 14. 29).

¹⁸ Simplicius on De caelo, p. 615. 13 (Vors. i², p. 15. 24). In this passage Simplicius calls Anaximander a ‘fellow citizen and friend ‘of Thales ; these appear to be the terms used by Theophrastus, to judge by Cicero’s equivalent ‘popularis et sodalis’ (Acad. pr. ii. 37. 118).

¹⁹ Aët. ii. 4. 6 (D. G. p. 331; Vors. i², p. 15. 33).

²⁰ Simplicius, in Phys. p. 1121. 5 (Vors. i², p. 15. 34–8).

²¹ Ps. Plut. Stromat, loc. cit.

²² Hippol. Refut. i.6. 4 (D. G. pp. 559, 560; Vors. i², p. 14. 8).

²³ Aët. ii. 13. 7 (D. G. p. 342; Vors. i², p. 15. 39).

²⁴ Hippol., loc. cit.

²⁵ Aët. ii. 20. I (D. G. p. 348; Vors. i², p. 16. 8).

²⁶ Aët. ii. 16. 5 (D.G. p. 345; Vors. i², p. 15. 43. This sentence presents difficulties. It occurs in a collection of passages headed ‘Concerning the motion of stars’, and reads thus: . If means , each of the stars, the expression , ‘on which each of them stands’ or ‘is fixed’, is certainly altogether inappropriate to Anaximander’s system; it suggests Anaximenes’ system of stars ‘fixed like nails on a crystal sphere’; I am therefore somewhat inclined to suspect, with Neuhäuser (Anaximander Milesius, p. 362 note), that the words (if not also) are wrongly transferred from later theories to that of Anaximander. It occurred to me whether could be , ‘each of the circles’; for it would be possible, I think, to regard the circles as ‘standing’ or ‘being fixed’ on (imaginary) spheres in order to enable them to revolve about the axis of such spheres, it being difficult to suppose a wheel to revolve about its centre when it has no spokes to connect the centre with the circumference.

Diels (‘Ueber Anaximanders Kosmos’ in Archiv für Gesch. d. Philosophie, x, 1897, p. 229) suggests that we may infer from the word ‘spheres’ here used that the rings are not separate for each star, but that the fixed stars shine through vents on one ring (which is therefore a sphere); the planets with their different motions would naturally be separate from this. I doubt, however, whether this is correct, since all the rings are supposed to be like wheels; they are certainly not spheres. But no doubt the Milky Way may be one ring from which a multitude of stars flame forth at different vents: this may indeed be the idea from which the whole theory started (Tannery, op. cit., p. 91; Burnet, Early Greek Philosophy, p. 69).

²⁷ Hippol, Refut, i. 6. 5 (A G. p. 560; Vors. i², p. 14. 12, and ii. I², p. 653).

²⁸ Aët. ii. 21. 1 (D.G. p. 351; Vors. i², p. 16. 11).

²⁹ Aët. ii. 24. 2 {D. G. p. 354; Vors. i², p. 16. 13).

³⁰ Aët. ii. 25. 1 (D. G. p. 355; Vors. i², p. 16. 15).

³¹ Aët. ii. 29. 1 (D. G. p. 359; Vors. i², p. 16. 19).

³² Aët. ii. 15. 6 (D. G. p. 345 Î Vors. i², p. 15. 41).

³³ Teichmüller, Studien zur Gesch. der Begriffe Berlin, 1874, pp. 25 sqq.

³⁴ Tannery, op. cit., pp. 88 sqq.

³⁵ Zeller, i⁵, p. 221.

³⁶ Tannery, op. cit., pp. 146, 147.

³⁷ Burnet, Early Greek Philosophy, p. 55.

³⁸ Zeller, i⁵, pp. 229–36.

³⁹ Burnet, Early Greek Philosophy, pp. 62–6.

⁴⁰ Cicero, De nat. deor. i. 10. 25 (Vors. i², p. 15. 27).

⁴¹ Aét. i. 7. 12 {D. G. p. 302; Vors. i², p. 15. 26).

⁴² Probably, as Burnet says, Cicero found in his Epicurean source.

⁴³ Aët. ii. 1. 8 (D. G. p. 329; Vors. i², p. 15. 32).

⁴⁴ Neuhäuser, Anaximander Milesius, pp. 327–35.

⁴⁵ , Simpl. in Phys. p. 24. 20 (Vors. i², p. 13. 9).

⁴⁶ Cf. Simpl. in Phys. p. 1121. 5 (Vors. i², p. 15. 34–8, quoted above, p. 26).

⁴⁷ , Aristotle, Phys. i. 4, 187 a 20.

⁴⁸ Burnet, Early Greek Philosophy, p. 61.

⁴⁹ Neuhäuser, Anaximander Milesuts-, pp. 305–15.

⁵⁰ Neuhäuser, Anaximander Mileshis, pp. 409–21.

⁵¹ The passage is Aristotle, De caelo ii. 13, 295 a 9 sqq. It is there stated that ‘if the earth, as things are, is kept by force where it is, it must also have come together (by force) through being carried towards the centre by reason of the whirling motion; for this is the cause assumed by everybody on the ground of what happens in fluids and with reference to the air, where the bigger and the heavier things are always carried towards the middle of the vortex. Hence it is that all who describe the coming into being of the heaven say that the earth came together at the centre; but the cause of its remaining fixed is still the subject of speculation. Some hold . . .’ Now Neuhäuser paraphrases the passage thus: ‘All philosophers who hold that the world was generated or brought into being maintain that the earth is not only kept by force in the middle of the world, but was, at the beginning, also brought together by force. For all assign as the efficient cause of the concentration of the earth in the middle of the world a vortex , arguing from what happens in vortices in water or air.’ It is clear that Aristotle says no such thing. He says that the philosophers referred to assert that the earth comes together at the centre, but not that they hold that it is kept there by force; indeed he expressly says later (295 b 10–16) that Anaximander regarded the earth as remaining at the centre without any force to keep it there. Again ‘everybody’ is not ‘all philosophers’, but ‘people in general’. Lastly, the tendency of the heavier things in a vortex to collect at the centre might easily suggest that the earth had come together in the centre because it was heavy, without its being supposed that a vortex was the only thing that could cause it to come together.

⁵² Tannery, op. cit., p. 88.

⁵³ Ibid. p. 92.

⁵⁴ Zeller, i⁵, pp. 224, 225.

⁵⁵ Teichmüller, Studien zur Geschichte der Begriffe, 1874, pp. 16, 17.

⁵⁶ Neuhäuser, Anaximander Mileshis, p. 371.

⁵⁷ Sartorius, Die Entwicklung der Astronomie bei deft Griechen bis Anaxagorasund Empedokles, pp. 29, 30.

⁵⁸ Aristotle, Meteorologica ii. 1, 353 b 6–9. A note of Alexander (in Meteor. p. 67. 3; see D.G. p. 494; Vors. i², p. 16. 45) explains the passage thus: ‘For, the space round the earth being moist, part of the moisture is then evaporated by the sun, and from this arise winds and the turnings of the sun and moon, the meaning being that it is by reason of these vapours and exhalations that the sun and moon execute their turnings, since they turn in the regions where they receive abundant supplies of this moisture; but the part of the moisture which is left in the hollow places (of the earth) is the sea.’

⁵⁹ Aristotle, Meteorologica ii. 2, 355 a 21.

⁶⁰ Zeller, i⁵, p. 223.

⁶¹ Zeller (i⁵, pp. 223, 224) has a note on the meanings of the word . Evenin Aristotle it does not mean ‘solstice’ exclusively, because he speaks of of the stars’ (De caelo ii. 14, 296b 4), ‘ of the sun and moon’ (Meteor, ii. 1, 353 b 8), and ‘ of the heaven’ (according to the natural meaning of , 355 a 25). It is true that could be used of the moon in a sense sufficiently parallel to its use for the solstices, for, as Dreyer says (Planetary Systems, p. 17, note 1), the inclination of the lunar orbit to that of the sun is so small (5°) that the phenomena of ‘turning-back’ of sun and moon are very similar. But the use of the word by Aristotle with reference to the stars and the heaven shows that it need not mean anything more than the ‘turnings ‘or revolutions of the different heavenly bodies. Zellers view is, I think, strongly supported by a passage in which Anaximenes is made to speak of stars ‘executing their turnings’ ( Aët. ii. 23. 1, D. G. p. 352) and the passage in which Anaximander himself is made to say that the eclipses of the moon depend on ‘the turnings of its wheel’ (Aët. ii. 25. 1, D. G. p. 355 b 22).

⁶² Neuhäuser, op. cit., p. 403.

⁶³ Neuhäuser, pp. 405–8 and Fig. 2 at end.

⁶⁴ Simplicius on De caelo, p. 471. 4, ed. Heib. (Vors. i², p. 15. 47). Simplicius adds : ‘Now the sizes and distances of the sun and moon as determined up to now were ascertained (by calculations) starting from (observations of) eclipses, and the discovery of these things might reasonably be supposed to go back as far as Anaximander.’ If by ‘these things’ Simplicius means the use of the phenomena of eclipses for the purpose of calculating the sizes and distances of the sun and moon, his suggestion is clearly inadmissible. On Anaximander’s theory eclipses of the sun and moon were caused by the stopping-up of the vents in their respective wheels through which the fire shone out; moreover, the moon was itself bright and was not an opaque body receiving its light from the sun, notwithstanding the statement of Diogenes Laertius (ii. 1; Vors. i², pp. 11. 40–12. 1) to the contrary; it is clear, therefore, that Anaximander’s estimates of sizes and distances rested on no such basis as the observation of eclipses afforded to later astronomers.

⁶⁵ Diels, ‘Über Anaximanders Kosmos’ in Archiv für Gesch. d. Philosophie x, 1897, p. 231; cf. Tannery, p. 91.

⁶⁶ Diels, loc. cit., p. 233.

⁶⁷ Diog. L. ii. I (Vors. i², p. 12. 3).

⁶⁸ Herodotus, ii. 109.

⁶⁹ , Suidas (Vors. i², p. 12. 18).

⁷⁰ Euseb. Praep. Evang. x. 14. II (Vors. i², p. 12. 24).

⁷¹ Diog. L. ii. 1.

⁷² Ibid. ii. 2.

⁷³ Cic. De rep. i. 14. 22.

⁷⁴ Agathemerus (from Eratosthenes), i. 1 (Vors. i², p. 12. 36).

⁷⁵ Gomperz, Griechische Denket, i³, pp. 41, 422.

⁷⁶ Diog. L. ii. 2 (Vors. i², p. 12. 5).

⁷⁷ On Anaximander’s map see Berger, Geschichte der wissenschaftlichen Erdkunde der Griechen, 2 ed., 1903, pp. 35 sqq.

⁷⁸ See Plut. Symp. viii. 8. 4 (Vors. i², p. 17. 24); Aët. v. 19.4 (D. G. p. 430; Vors. i², p. 17. 18); Ps. Plut. Stromat. 2 (D. G. p. 579); Hippol. Refut. i. 6. 6 (D. G. p. 560). According to Anaximander, animals first arose from slime evaporated by the sun; they first lived in the sea and had prickly coverings; men at first resembled fishes.