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DISTURBING THE HEARTH: ARISTARCHUS’ HELIOCENTRIC UNIVERSE AS COURT PARRHÊSIA

Published online by Cambridge University Press:  21 September 2026

Joshua David McDermott Open the ORCID record for Joshua David McDermott [Opens in a new window]
Joshua David McDermott*
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University of Sydney
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joshua.mcdermott@sydney.edu.au
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Abstract

Aristarchus of Samos’ heliocentric model of the universe has usually been treated by modern scholars as an astronomical controversy somehow removed from the ideological concerns of the Ptolemaic court in which it was produced. This traditional approach has not fully accounted for the contemporary reception of the astronomer’s work, which included accusations of disruption, and even impiety, by scholarly rivals. Consideration of Aristarchus’ astronomy as an expression of scientific parrhêsia (frank speech) for his royal patron may help account for the hostile response. This article identifies spatializing techniques of displacement and diminution within Aristarchus’ astronomy. It proposes that such ideologically disruptive effects function as powerful expressions of parrhêsia intended to place sobering limits on potentially excessive claims to universal kingship promoted in more propagandistic court astronomical treatises.

Keywords

astronomyparrhêsiaAristarchus of SamosHellenistic courtHellenistic kingshippropagandacourt sciencePtolemies

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The Classical Quarterly , First View , pp. 1 - 16
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© The Author(s), 2026. Published by Cambridge University Press on behalf of The Classical Association

INTRODUCTION

In mid third century b.c.e. Alexandria, the renowned astronomer Aristarchus of Samos produced a radical new treatise which removed the earth from its place at the centre of the universe. Instead, he argued that it was we who revolved around the sun. Further, he expanded the size of the universe, almost beyond comprehension. His thesis was evidently shocking to some, becoming a byword for turning the universe ‘upside down’.Footnote 1 The Stoic philosopher Cleanthes of Assos went further, arguing that ‘the Greeks ought to lay an action for impiety against [Aristarchus] on the ground that he was disturbing the hearth of the universe’.Footnote 2 Was this just a dogmatic or technical rejection, as it has often been presented?Footnote 3 Or were there also ideological concerns at play? We may gain a fuller understanding of Aristarchus’ controversial work, and Cleanthes’ virulent response, by considering the treatise within its context, as a work produced by and for the sympotic court of the Ptolemies.

Recent scholarship has emphasized the concerns of sympotic court culture in the production of Hellenistic court science.Footnote 4 Well-patronized scientists are increasingly being recognized for their roles as ‘friends of the king’ (philoi tou basileôs).Footnote 5 Their scientific treatises and devices were intended as gifts to entertain and delight their royal patrons.Footnote 6 To this end, scientific treatises could function not only as wonders (thaumata), but also as gifts of praise (epainos), communicating propaganda as an expression of performative friendship.Footnote 7

As we will see, astronomers, like geographers, could use spatializing gestures to emphasize the king’s centrality, power and pretensions of hyperbolic imperial reach. The privileged role of the court philos also provided an avenue, however, and even a certain expectation, to place limits on excessive imperial claims. A true philos in the sympotic tradition would not simply ‘praise everything you say or do, but … [would also] criticize your mistakes’.Footnote 8 Tactful frank speech (parrhêsia) from a loyal philos was seen as a vital antidote to the delusions and distortions of the much-feared court flatterer (kolax).Footnote 9 The frank speech should, ideally, be welcomed by a cultivated monarch as a gift from a friend.Footnote 10

Aristarchus’ heliocentric model, and Cleanthes’ response, may be better understood if we consider the treatise as an expression of scientific parrhêsia. We will first look at the astronomical court propaganda to which the text was responding, namely, royal claims of centrality, hyperbolic reach and total imperial control (1). We will then see how Aristarchus’ use of spatial techniques challenges these claims. Elements which may function as spatial displacement will be identified, and we will investigate the challenges these pose to imperial ideology (2). This will be followed by considering the impact of juxtapositions and associated diminution upon the king’s place in the cosmos (3). I argue that these effectively place limits on imperial ideology. With these effects established, we will be better equipped to revisit the accusation of asebeia directed towards Aristarchus by Cleanthes (4). The accusation can be better understood not only as a philosophical rejection of the model, but also as part of sympotic court discourse; a defence of the imperial astronomy needed for the ideology of universal kingship to effectively function. This article will show how astronomy, just like other texts produced at court, could function as expressions of parrhêsia. By looking at the interaction between the scientific treatise and royal imperial ideology, we may glimpse how astronomy was intended to function: as weighty paideia within Hellenistic court discourse.

LIFE AND SOURCES

Aristarchus of Samos probably flourished at Alexandria during the reign of Ptolemy II Philadelphus (reigned 282–246), possibly into the reign of Ptolemy III (reigned 246–222/1).Footnote 11 He was a pupil of Strato of Lampsacus, known as the physikos, tutor to Ptolemy II and philos to the divine queen Arsinoë II.Footnote 12 Strato appears to have been something of a successful parrhêsiastês himself, having used geological observations and innovative hypotheses to challenge the divine origins of the Ptolemy-legitimizing oracle at Siwa oasis.Footnote 13 Our one clear date for Aristarchus’ astronomy is his observation of the summer solstice in 280/79.Footnote 14 According to Vitruvius, he also designed two types of sundials, the hemispherical skaphê and the disc-with-plane.Footnote 15 Such grand mechanisms tended to function in equal parts as performance and science, not only invaluable for autoptic observation, but also allowing demonstrations to evoke wonder.Footnote 16 While dating his treatise On the Sizes and Distances of the Sun and Moon is uncertain, the heliocentric model must date before 232, when his ardent critic, Cleanthes, died.Footnote 17 Knorr, however, has persuasively argued that Aristarchus’ model was probably proposed several decades earlier,Footnote 18 which places Aristarchus’ model late in the reign of Ptolemy II, when the regime’s seemingly limitless thalassocratic reach faced its first serious challenges.Footnote 19

Our sources for Aristarchus’ heliocentric model survive only in a handful of fragments.Footnote 20 The most important of these is found in the proem of Archimedes’ The Sand Reckoner, a letter-treatise written to his patron, Gelon of Syracuse. In this near contemporary source, Archimedes introduces Aristarchus’ heliocentric model. Archimedes himself rejects it, yet he none the less uses Aristarchus’ massive universe to show the almost limitless potential of his sand-reckoning formula.Footnote 21 The other main mathematical source is Aristarchus’ On the Sizes and Distances of the Sun and Moon surviving in Pappus of Alexandria’s Little Astronomy.Footnote 22 The calculations for the sizes of these bodies (mostly) match those recorded in Archimedes’ account of Aristarchus’ works, suggesting that both ultimately come from the same text, although the heliocentricity is not apparent in Pappus’ version. Other fragments are more explicit: heliocentrism can be found in Aëtius’ Tenets, Sextus Empiricus’ Against the Physicists, and Plutarch’s Platonic Questions and On the Face in the Moon.Footnote 23 These last four fragments are less technical in nature, emphasizing the disruptive concerns raised by Aristarchus’ new model. Finally, via a papyrus fragment from an anonymous second-century c.e. commentary on Odyssey 20, we find a brief reference to Aristarchus’ identification of a correlation between eclipses and the lunar month, and a natural ‘earthen’ moon.Footnote 24 From these few sources Aristarchus’ cosmology has been pieced together by Schiaparelli, Heath, Neugebauer and others, earning him the somewhat anachronistic title ‘the ancient Copernicus’.Footnote 25 These readings provide important insights into the nature of Aristarchus’ model and how it was understood in dialogue with other Hellenistic scientists. But the astronomer’s work is yet to be considered within the sympotic court context where it was penned. How well do Aristarchus’ technical treatises align with the ideology of his royal patron? These same fragments which provide a glimpse into his scientific concerns may also reveal something of his astronomical parrhêsia. To establish this, we must first look at the works it contradicted: the astronomy of empire.

1. THE SPATIAL PROPAGANDA OF EMPIRE: CENTRALITY, REACH AND CONTROL

Court astronomers and geographers could design models of the cosmos which supported the claims of Hellenistic kings to universal empire. These spatial expressions of total kingship provided the court with hyperbolic imperial reach and an all-pervading centripetal pull on the map which were otherwise denied them by stubborn geopolitical realities.Footnote 26

On Earth, the Ptolemies’ waterborne vectors touched the edge of the oikoumenê. In court panegyric, Theocritus’ thalassocratic tour extends from Alexandria to the Aegean, the vector territorializing through imperial movement so that ‘the entire land and sea’ (θάλασσα δὲ πᾶσα καὶ αἶα) was Ptolemy’s.Footnote 27 These naval vectors would be extended in the periplous of Ptolemy II’s admiral, Timosthenes of Rhodes, to the farthest ports,Footnote 28 and even further still in the Adulis stele, where Ptolemy III, ‘having become master of all the country this side of the Euphrates’, would go on to apparently conquer eastern lands.Footnote 29 Similarly ambitious vectors reached to the southern edge of the habitable zone, more certain on the map than in reality, bringing thaumata and resources to the Alexandrian centre from the periphery.Footnote 30 The imperial map unambiguously asserted the ‘long … arm’ of the Ptolemies.Footnote 31

In the heavens, Ptolemaic reach knew no limit. This is most vividly seen with the ostensible discovery of a new constellation, Coma Berenices, by the astronomer Conon of Samos in 246.Footnote 32 According to Callimachus, the astronomer’s careful observations of ‘the lines … where [the stars] are carried’ provided the scientific proof of a miracle.Footnote 33 Queen Berenice’s sacrificial lock of hair, recently having disappeared from the altar at the temple of Aphrodite-Arsinoë at Zephyrion, has been raised to ‘the abodes of the gods’, transformed into ‘a new constellation among the ancient stars’.Footnote 34 The apotheosis lends itself elegantly to royal ideology, associating the queen’s lock with Isis, Aphrodite and, crucially, the cult of the divine Ptolemaic queen, Arsinoë II.Footnote 35 The discovery communicates that Ptolemaic reach extends to the firmament on the outer sphere of the cosmos, reinforcing both the divine nature of the royal couple and the universal nature of their empire.Footnote 36 For his critics, this performance was scientific kolakeia, the scholar distorting space only to gain royal ‘favour’.Footnote 37 None the less, the epainos proved an ideological triumph: the expression of imperial reach in its ultimate form.

Centrality was another key feature of the imperial map: the king’s court was to be the physical and ideological epicentre of the universe. Political geographers have long been aware of the power of cartographical centrality as a means of expressing spatial power, with those on the periphery consigned to a subordinate status.Footnote 38 This is apparent in ancient imperial models where the king at centre commands attention over a subordinate periphery.Footnote 39 For the Ptolemies, Alexandria pulled resources and people with seeming inevitability to the capital, seen in royal grand processions, court poetry and geographical treatises.Footnote 40 For the more mobile Seleucids, Patrocles and Demodamas constructed geographies which none the less emphasized the movement of resources from periphery to core.Footnote 41 The centre ground spoke powerfully to the significance of the true empire over would-be challengers on the periphery.

Centrality in astronomy can be observed in Aratus of Soli’s Phaenomena, which depicts the heavens revolving around a stable and certain imperial centre. Produced under the lavish patronage of Antigonus II Gonatas,Footnote 42 the poem is designed to appeal to multiple audiences, and is ostensibly a celebration of Zeus Kosmokratôr.Footnote 43 As Strootman argues, however, it may also function as an allegory for universal kingship.Footnote 44 Having established early in the poem an all-pervading (μεσταί) divine omnipotence in the cities, countryside, roads, harbours and seas of the earth (2–17), our gaze is soon directed to the heavens, where we encounter stars spinning (19–21). But far from out of control, these stars, we are assured, follow (ἕλκονται) carefully drawn paths for eternity under the direct control of the divine ruler.Footnote 45 Further, the axis for the heavens is pointedly fixed (ἄρηρεν) in the earth.Footnote 46 We return to the earth (21–4), where we find the earth at ‘equipoise’ the ultimate centre-point. Indeed, it ‘wheels the heaven itself around [it]’.Footnote 47 The earth is central, stable and, subsequently, a powerful anchor around which an orderly cosmos can revolve. The poem may function as pious Stoic parable and didactic text, but it also functions as potent astronomical propaganda. The universe is steered by the divine king, seated firmly on the terrestrial centre.

Aristarchus’ antagonist, Cleanthes, produced his own astronomical propaganda in his Hymn to Zeus, a paean which likewise asserts centrality and control.Footnote 48 The scholar’s hyperbole speaks to imperial concerns: ‘This whole universe, spinning around the earth, truly obeys you wherever you lead, and is readily ruled by you.’Footnote 49 The entirety of the universe spins about us in a secondary, and explicitly deferent, position. The planets and stars are simplified, becoming ‘great and the small lights’ governed by a universal force which ‘permeates everything’.Footnote 50 The central position is privileged, the universe reduced to a cowered servant of the ‘highest king’.Footnote 51 Astronomy is recruited here as a muscular assertion of the universal kingship from the centre.Footnote 52

Like imperial geography, astronomy could express the power of divine universal kingship. As seen in Aratus’ and Cleanthes’ astronomy, it provided the powerful centre-ground through which one could govern the cosmos. But it could also do more: gestures of hyperbolic reach, like those of Conon, were the ultimate expressions of this power, shaping the very heavens. Centrality, control and reach: these were the watchwords of the imperial map which Aristarchus’ astronomy would disrupt.

2. UNTETHERING THE HEARTH: DISPLACEMENT IN ARISTARCHUS’ ASTRONOMY

The earth, the ‘hearth of the gods’, would be powerfully displaced in Aristarchus’ astronomy, challenging any sense of centre.Footnote 53 To Gelon, Archimedes explains (Archim. The Sand Reckoner 5, from Heiberg [n. 21], 218.10–18):

ὑποτίθεται γὰρ τὰ μὲν ἀπλανέα τῶν ἄστρων καὶ τὸν ἅλιον μένειν ἀκίνητον, τὰν δὲ γᾶν περιφέρεσθαι περὶ τὸν ἅλιον κατὰ κύκλου περιφέρειαν, ὅς ἐστιν ἐν μέσῳ τῷ δρόμῳ κείμενος, τὰν δὲ τῶν ἀπλανέων ἄστρων σφαῖραν περὶ τὸ αὐτὸ κέντρον τῷ ἁλίῳ κειμέναν τῷ μεγέθει ταλικαύταν εἶμεν, ὥστε τὸν κύκλον, καθ᾿ ὃν τὰν γᾶν ὑποτίθεται περιφέρεσθαι, τοιαύταν ἔχειν ἀναλογίαν ποτὶ τὰν τῶν ἀπλανέων ἀποστασίαν, οἵαν ἔχει τὸ κέντρον τᾶς σφαίρας ποτὶ τὰν ἐπιφάνειαν.

His [Aristarchus’] hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the track, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface (transl. Heath [n. 18], 222, adapted)

The account is striking for its inversions, something especially shocking for a non-specialist audience. The march of the sun which, through the will of gods, gave order to the days and seasons, has now been brought to a halt.Footnote 54 The stars too, with their formerly vital movement, are now also emphatically stationary (μένειν ἀκίνητον), contradicting court poets and priesthood alike.Footnote 55 This is in sharp contrast to the chariot-riding Helios we see associated with those imperial conquerors par excellence, Alexander and Demetrius, moving swiftly across the oikoumenê with their stellar philoi in tow.Footnote 56 Instead of moving with the imperial speed of Helios over the landscape, the sun here has drawn to an eerie standstill.

Worryingly, it is the earth, demoted to a satellite, which now does all the moving.Footnote 57 Aëtius explains this model with typical succinctness, telling us that ‘Aristarchus makes the sun stand still together with the fixed stars, while he moves the earth in the circle of the sun’.Footnote 58 Similarly, Sextus Empiricus seems to refer to Aristarchus and his followers, who ‘rejected the motion of the Universe, but … held that the earth moves’.Footnote 59 The salient feature of this model for later critics was evidently the earth’s relocation to a peripheral and subordinate position. The effect of displacement for an imperial map has been well established by political geographers, the centre of the map speaking to imperial power.Footnote 60 But in Aristarchus’ astronomy, we see geographic displacement on a cosmic scale. His critics were right to complain of the universe being turned ‘upside down’.

Destabilization of the earth denies a court audience their assumed sense of control. In Archimedes’ account, Aristarchus’ earth is described as on a track, with the sun sitting in the middle of it (ἐν μέσῳ τῷ δρόμῳ κείμενος). Tracks, as the audience knew, are potentially hazardous. Yet we have now, almost Phaethon-like, assumed the reins that rightfully belong to the sun.Footnote 61 Our novel sense of motion sickness is then compounded by the axial rotation of the earth.Footnote 62 In On the Face in the Moon, Plutarch’s Lucius distances himself from Aristarchus’ model, in which ‘the earth revolves in an inclined circle, while rotating at the same time about its own axis’.Footnote 63 In Platonic Questions Plutarch goes further, describing Aristarchus’ earth as ‘turning and whirling about’, like a spinning top.Footnote 64 The passive whirling (ἀνειλουμένην) denies us what von Erhardt and von Erhardt-Siebold call a ‘double constraint’ of centrality and rest.Footnote 65 We are disoriented in this more chaotic universe. Like Strato, perhaps, Aristarchus is emphasizing greater, detached forces—‘mindless’ nature—in the driver’s seat, while we hang on.Footnote 66 The court audience could be forgiven for feeling queasy. The double displacement conspires against the imperial centre, ‘disturbing the hearth of the universe’, as Cleanthes would put it.Footnote 67 The stable universe so integral for claims of universal kingship is thoroughly confounded, as is a court audience’s sense of agency.

With our place in the universe now more confused, we are in greater need than ever of portents to guide us. But we are denied these too, astrological readings losing coherency in Aristarchus’ model, with its stationary sun and stars. Stationary geocentricity had long been axiomatic for Hellenistic astrology, with careful observations of the ascendent, mid-heaven, setting point and under-earth position of celestial bodies allowing astrologers to anticipate the influence of celestial movements upon our world.Footnote 68 Dorotheus of Sidon considered the movement of the sun, just like the movement of the planets, to shape events at court. Trines formed with sun and planets would warn of political intrigue or worse.Footnote 69 The stars, too, in their geocentric orientation, directly impact the earth. For example, Sirius’ summertime ascent, something long known to bring hardship, could also predict political turmoil, if its rise occurred in particular astrological houses.Footnote 70 The Roman-era papyrus P.Cairo 31222 shows predictions of immediate concern for an Egyptian king: if Sothis (Sirius) rises when Jupiter is in Sagittarius, there will be rebellions and failed invasions, but if it rises when Mars is in Gemini, then the king of Egypt will go forth, quashing foreigners.Footnote 71 Such imperial concerns are echoed in the late antique compilation of Hephaestion of Thebes.Footnote 72 As portents, the movements of the sun and stars directly spoke to the court audience. The fixed heavens of Aristarchus undermine court astrology: the stars tell us nothing.

For the Ptolemies, such stillness of the stars is especially unnerving, challenging their position as facilitating harmony between the earth and the heavens. This relationship is on full display in the Canopus decree (238), the new intercalary day explicitly associating the new year and ubiquitous feasting to celebrate the divine royal couple, Ptolemy III and Berenice II, on the day ‘when the star of Isis rises’ (τῇ ἡμέρᾳ ἐν ᾗ ἐπιτέλλεται τὸ ἄστρον τὸ τῆς Ἴσιος).Footnote 73 The arrival of the star of Isis, a deity interwoven with Ptolemaic ideology via the potent Arsinoë II, ushers in the flood.Footnote 74 The innovation of the calendar has been implemented, we are told, by the Theoi Euergetai, who set right (διωρθῶσθαι καὶ ἀναπεπληρῶσθαι) not only our understanding of the seasons, but our relationship with the movements of the heavens (τὴν ὅλην διακόσμησιν).Footnote 75 In the Canopus decree, the divine royal couple’s accurate calculation of the movement of stars, especially the star of Isis, is integral to good order here on earth.

The effect of Aristarchus’ radical model for a court audience is disturbing. The sun and planets appear to have their own relationships from which the earth’s significance is demoted. The stars are now defined by their relationship with the sun (περὶ τὸ αὐτὸ κέντρον τῷ ἁλίῳ), their gaze no longer focussed on the earth. Human beings have been sidelined. If Conon’s astrology functioned as propagandistic praise, then Aristarchus’ astronomy is functioning here as parrhêsia, distancing its readers from a sense of imperial centrality and control. The divine king and queen, and their court, are diminished with sobering displacement. They are no longer on stable ground from which to order the cosmos.

3. SIZE MATTERS: ELEVATION, JUXTAPOSITION, DIMINUTION

Aristarchus presented a universe many times expanded, the court audience’s place in the cosmos relatively diminished and hyperbolic claims of universal kingship tacitly undermined. Size mattered in the Hellenistic court. Giant war ships, barges and even grain ships communicated power in terms of sheer scale, defying merely practical concerns.Footnote 76 Political geographers have shown how physical diminution can impact claims to imperial power. Relative size on the map communicates relative significance, or lack thereof.Footnote 77 Hellenistic scholars were keenly aware of this; imperial propaganda could diminish and even neuter the perceived threat of rival empires.Footnote 78 What may appear to be a powerful empire in one map can, if we zoom out, be exposed as something less significant. In court astronomy, such a juxtaposition can pose a profound challenge to court pretensions of universal kingship.

Aristarchus’ relative juxtaposition begins with the earth and sun. Using the moon, earth and sun in a right triangle and measuring the earth’s shadow on the moon, he measured the relative sizes of these objects.Footnote 79 The sun is measured as ‘greater than 18 times but less than 20 times the diameter of the moon’.Footnote 80 In our Pappus source, we get a similar ratio of between 19:3 and 43:6.Footnote 81 This makes the sun over 300 times greater in volume than the earth, more than doubling the difference in size when compared to Eudoxus’ former measurements.Footnote 82 This, in itself, significantly diminishes the earth. But as Carman observes, not all the measurements add up. Specifically, the sixth hypothesis, which claims ‘that the moon subtends one fifteenth part of a sign of the Zodiac’ (IE 2°), powerfully expresses the sun’s relative size but is an exaggerated measurement.Footnote 83 This may not be just an honest error: it features prominently in the treatise’s opening hypotheses (the part a lay audience can easily follow), but is not a mistake that the apparently gifted mathematician has made elsewhere.Footnote 84 It has been argued that this exaggeration was Aristarchus’ rebuttal of Epicurean cosmology, which proposed that the sun was essentially ‘no bigger than it appears’,Footnote 85 although there is nothing in the text that shows this to be the motivation. The effect on a lay audience, though, is certainly apparent: this is a universe where the sun dwarfs our world.

Yet it is the space beyond the sun and moon, the distance to the fixed stars, which diminishes the earth most powerfully. This we find in The Sand Reckoner. We are fortunate that Archimedes needs, and thus preserves, his own summary of Aristarchus’ massive universe, which is compared to significantly older models.Footnote 86 As we saw earlier, Aristarchus’ universe ‘is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface’. The passage appears to have Aristarchus literally proposing an infinite universe, with the ratio of the earth’s orbit to the stars being like comparing a sphere’s centre point (which has no substance) to its surface.Footnote 87

Archimedes is quick to dismiss this as ‘impossible’ (ἀδύνατον) and relegates it to poor expression on Aristarchus’ part (The Sand Reckoner 6.22–7):

ἐκδεκτέον δὲ τὸν Ἀρίσταρχον διανοεῖσθαι τόδε· ἐπειδὴ τὰν γᾶν ὑπολαμβάνομες ὥσπερ εἶμεν τὸ κέντρον τοῦ κόσμου, ὃν ἔχει λόγον ἁ γᾶ ποτὶ τὸν ὑφ’ ἁμῶν εἰρημένον κόσμον, τοῦτον ἔχειν τὸν λόγον τὰν σφαῖραν, έν ᾇ ἐστιν ὁ κύκλος, καθ’ ὃν τὰν γᾶν ὑποτίθεται περιφέρεσθαι, ποτὶ τὰν τῶν ἀπλανέων ἄστρων σφαῖραν.

We must however take Aristarchus to mean this: since we conceive the earth to be, as it were, the centre of the universe, the ratio which the earth bears to what we describe as the ‘universe’ is the same as the ratio which the sphere containing the circle in which he supposes the earth to revolve bears to the sphere of the fixed stars (transl. Heath [n. 18, page 222]).

Archimedes’ understanding is that Aristarchus intended to produce an extremely large but finite universe, suitable for The Sand Reckoner’s purpose. If taken figuratively, as most scholars have argued it should be, Aristarchus aimed to express something far greater than this, ‘an almost inconceivable expansion of the universe’ in mathematical analogy.Footnote 88 Certainly, Neugebauer thought it was supposed to be a near-infinite, but ultimately finite universe, which effectively accounts for the lack of yearly parallax and associated movement of the fixed stars.Footnote 89 The alternative is to take Aristarchus at face value, in which we are dealing with an infinitely small earth in an infinitely large universe, like what the Epicureans proposed.Footnote 90 Which of these Aristarchus meant remains uncertain, but the effect on a lay audience is effectively the same: the world has been shrunk to an infinitesimal degree.

Considering the work as a sympotic expression of parrhêsia allows us to account for this unfathomably large universe. Modern geographers have shown how extreme elevation can encourage us to question the significance of geopolitical space.Footnote 91 Court geographers could use elevation to express geographical parrhêsia at court, showing the oikoumenê claimed by the king to be a proportionately less significant portion of the world than a non-specialist audience may have otherwise imagined.Footnote 92 We see a similar technique at play in Aristarchus’ astronomy; the earth, indeed the oikoumenê claimed by the king, becomes little more than a speck. The Ptolemaic claim to rule the entire oikoumenê appears from this vantage point as quaintly parochial. Without directly targeting the regime, the model provides a sobering sense of perspective to dampen claims of absolute and universal kingship.

4. SYMPOTIC SPARRING: PARRHÊSIA AS ‘IMPIETY’

Having identified the ideologically disruptive aspects in Aristarchus’ court astronomy, we are perhaps better equipped to consider the accusations of asebeia. The accuser, Cleanthes, was scholarch of the Stoa in Athens (263–232) and produced significant treatises, including his lost Against Aristarchus.Footnote 93 What we know of his life is essentially from Diogenes Laërtius, who is keen to emphasize Cleanthes’ humility, resilience and lack of worldly ambition.Footnote 94 But even Laërtius’ account betrays significant connections with the Antigonid and Ptolemaic courts. Antigonus II Gonatas apparently ‘attend[ed] his lectures’.Footnote 95 Patronage is explicit and presented without comment; ‘we are also told that Antigonus made him a present of three thousand drachmas’.Footnote 96 Such lavish patronage may interrupt Diogenes Laërtius’ thematic concerns of poverty, but is perfectly appropriate for a philos ‘worthy of his art’.Footnote 97 Diogenes Laërtius also tells us that Cleanthes was in correspondence with the Ptolemies and sent one of his students, Sphaerus, to the Alexandrian court. Cleanthes appears to have been in Alexandria at some point, at least long enough to be abused by the court poet Sositheus, and for Tarn, it was the Ptolemaic link which was the strongest.Footnote 98 Perhaps all we can say with confidence is that the scholar had an explicit reputation for flattery and significant connections with both the courts of the Antigonids and the Ptolemies.Footnote 99

We can see how Aristarchus’ model posed a direct challenge to Cleanthes’ propagandistic praise. In Cleanthes’ Hymn to Zeus, we have seen that the ‘supreme king’ (ὕπατος βασιλεύς) was master of the universe from a terrestrial vantage point.Footnote 100 His account of this mastery evokes martial themes, ‘everything trembles’ (πάντ’ ἐρρίγασιν) coerced ‘under the blow’ (ὑπὸ πληγῆς) of his thunderbolt, much as a foreign army might tremble in one of Theocritus’ panegyrics.Footnote 101 This perhaps evokes a sense of the ‘spear-won’ victories of Alexander and the Successors which presage a universal empire.Footnote 102 In Cleanthes’ astronomy, the king’s martial might has, indeed, conquered the entire universe.

Aristarchus’ work places profound limits on such royal ideology. As we have seen, the divine king is displaced, his world spinning uncertainly, undermining claims of centrality and control of the oikoumenê, let alone the universe. The king’s domain is diminished by the sheer size of the cosmos as presented by Aristarchus. It is certainly in opposition to the divine and omnipotent kingship propagated by philosophers like Cleanthes. If Aristarchus’ astronomy may be understood as asebeia, as Cleanthes claims, then it is not merely a problem for a Stoic Zeus, but has unavoidable consequences for the ideology of universal kingship. Our tiny, off-centre vantage point provides no place for a divine king to exert influence. The world of his royal patrons had, indeed, been turned ‘upside down’.

Accusations of impiety, particularly those which challenged royal ideology, posed a danger for otherwise successful poets and scholars. The controversial poet, Sotades of Maroneia, openly mocked Ptolemy II Philadelphus’ incestuous marriage to his divine sister-queen. He was hunted down and summarily executed for his faux pas.Footnote 103 This tactless humiliation was impiety of the highest order, undermining the foundations of the Ptolemaic ruler cult in direct terms. Jokes which challenged universal kingship could be seen in other courts too, with equally fatal consequences.Footnote 104 Such rudeness could not be understood as the parrhêsia of a true philos.

Cleanthes’ accusations of impiety against Aristarchus may speak to the fierce court rivalry between philoi, the scholar taking offence on the king’s behalf. Insults against rival philoi were an intrinsic part of the sympotic court, sometimes with devastating consequences for the recipient.Footnote 105 But for a scientist like Aristarchus, such an accusation is defensible in a way that Sotades’ or Daphitas’ jokes were not. Much like his mentor Strato, Aristarchus could draw on the venerable authority of science to challenge imperial ideology without causing offence.Footnote 106 The sympotic king, as a famous ‘lover of truth’, could meet the limits of their royal ideology in the form of a scholar.Footnote 107 As Euclid stubbornly insisted to an earlier Ptolemy, there is ‘no royal road’, no escape for the divine king, from the sobering limits of science.Footnote 108

CONCLUSION

The heliocentric model appears to have done more than challenge scientific orthodoxy, making waves as it did in an ideologically charged court environment. From the sources, we can conclude the following: (1) Aristarchus’ model departed from the more orthodox astronomical propaganda, which emphasized imperial centrality, reach and control. (2) The astronomer’s use of displacement, juxtaposition and associated diminution necessarily disrupts this orthodox imperial cosmology. (3) Court parrhêsia can help us understand how such an ideologically unorthodox text could be produced, let alone published, at court.

Court astronomy cannot be divorced from its sympotic court context. As we have seen, these scholars were court philoi, whose relationships with kings were fundamental to their work. As well as showcasing scientific discoveries on one hand, the same works also needed to function as a performance. Astronomy could function as powerful expressions of propagandistic praise, demonstrating the superlative power of their friend and patron, the king. It could also work as sober parrhêsia, however, a distinctly sympotic type of paideia where true friends were expected to speak frankly to one another, when no one else would dare. Aristarchus’ astronomy provides the means for a philos to say through science what would be tactless to deliver in more explicit words.

The astronomical parrhêsia expressed by Aristarchus did not, it seems, end entirely with his work. In the mid second century b.c.e., the astronomer Seleucus, who hailed from the important royal city of Seleucia-on-the-Tigris and who studied with the eminent Chaldean astronomers, may have tried to prove (ἀποφαινόμενος) Aristarchus’ model,Footnote 109 perhaps through the development of heliocentric tables.Footnote 110 Furthermore, this Seleucus identified ‘irregularities’ in the phenomena; the tides are caused by the earth’s rotation combined with the moon’s revolution.Footnote 111 In Seleucus’ works, Strato’s interest in tides and Aristarchus’ heliocentricity seem to have come together, developing a world where nature, not imperial agency, is in control. If this eminent astronomer was, as is entirely possible, a court philos, then this work is a timely message for his increasingly precarious Seleucid patrons. Court astronomy evidently continued to function as important parrhêsia from philos to king: the monarch’s power did, after all, have limits.

Footnotes

*

This article was made possible with funding via the Paulette Isabel Jones Career Award from the University of Sydney. Thanks to Julia Kindt for insights; to Paul McKechnie for advice concerning Egyptian astrology under the Ptolemies; and to CQ’s reader for valuable suggestions.

References

1 Plut. De fac. 922F λαβεῖν παρ᾿ ὑμῶν ἄνω τὰ κάτω τοῦ κόσμου ποιούντων.

2 His argument is summarized by Plutarch: De fac. 923A–B ὥσπερ Ἀρίσταρχον ᾤετο δεῖν Κλεάνθης τὸν Σάμιον ἀσεβείας προσκαλεῖσθαι τοὺς Ἕλληνας ὡς κινοῦντα τοῦ κόσμου τὴν ἑστίαν. Although no longer extant, Cleanthes’ Against Aristarchus is listed among the philosopher’s works (Diog. Laert. 7.5.174); for this work see T.L. Heath, Aristarchus of Samos: The Ancient Copernicus (Oxford, 1913), 304; C.C. Carman, ‘The first Copernican was Copernicus: the difference between pre-Copernican and Copernican heliocentrism’, AHES 72 (2018), 1–20, at 6; E. Rosen, ‘Aristarchus of Samos and Copernicus’, BASP 15 (1978), 85–93, at 90; and further below.

3 Heath (n. 2), 308. For dogmatic rejection see R. von Erhardt and E. von Erhardt-Siebold, ‘Archimedes’ Sand-Reckoner: Aristarchos and Copernicus’, Isis 33 (1942), 578–602, especially (595 n. 45) the ‘incompatibility with certain physical and cosmological doctrines of Plato and Aristotle’. For technical rejection see G. Sarton, Hellenistic Science and Culture in the Last Three Centuries B.C. (New York, 1959), 59; A.D. Gregory, ‘Astronomy’, in G. Irby (ed.), A Companion to Science, Technology, and Medicine in Ancient Greece and Rome (Malden, MA / Oxford / Chichester, 2016), 96–113, at 109.

4 ‘Science’ at court involves technical works of geography, astronomy, mathematics, engineering and medicine ‘produced for the entertainment of the court’: M. Berrey, Hellenistic Science at Court (Berlin and Boston, 2017), 1–16, at 5. According to R. Strootman, The Birdcage of the Muses, Patronage of the Arts and Sciences at the Ptolemaic Imperial Court, 305–222 BCE (Leuven / Paris / Bristol, CT, 2017), 112, through ‘successful demonstration … a technician could win esteem and praise from courtiers and king’, and royal symposia were settings where ‘treatises were read, inventions demonstrated’ for elite audiences (page 113). See also R. Strootman, Courts and Elites in the Hellenistic Empires: The Near East after the Achaemenids, c. 330 to 30 BCE (Edinburgh, 2014), 161–3.

5 E.g. R. Strootman, ‘The Hellenistic royal court. Court culture, ceremonial and ideology in Greece, Egypt and the Near East, 336–30 BCE’ (Diss., University of Utrecht, 2007), 216–20; Strootman (n. 4 [2017]), 135–46; P.J. Kosmin, The Land of the Elephant Kings: Space, Territory, and Ideology in the Seleucid Empire (Cambridge, MA, 2014), 67; Berrey (n. 4), 8, 72–85; M.S. Visscher, Beyond Alexandria: Literature and Empire in the Seleucid World (New York, 2020), 17–25.

6 Gift exchange at the royal symposion: for court philoi, ‘gift-exchange was the principal mechanism underlying social relations at court’: Strootman (n. 4 [2014]), 145, 146–50; Strootman (n. 4 [2017]), 69–73; Berrey (n. 4), 117–25.

7 As wonder: K. Tyberg, ‘Wonder-making and philosophical wonder in Hero of Alexandria’, SHPS 34 (2003), 443–66; Berrey (n. 4), 182–3, 186–7, 208–9; Strootman (n. 4 [2017]), 112. As propaganda: M. Leventhal, ‘Eratosthenes’ letter to Ptolemy: the literary mechanics of empire’, AJPh 138 (2017), 43–84, at 77–9; P.J. Kosmin, ‘The politics of science: Eratosthenes’ geography and Ptolemaic imperialism’, OTerr 15 (2017), 85–96, at 91–4; Visscher (n. 5), 25–70. As praise: Strootman (n. 4 [2017]), 139–42.

8 Isoc. 2.28 ὅ τι ἂν λέγῃς ἢ ποιῇς ἐπαινοῦντας, ἀλλὰ τοὺς τοῖς ἁμαρτανομένοις ἐπιτιμῶντας.

9 The figure of the court kolax (flatterer) features as a threat to successful kingship in Peri basileias (On Kingship) didactic treatises produced for Hellenistic courts. These now survive in fragments (e.g. Ath. Deipn. 6.249c–252f; Onesikritos BNJ 134 T 7; Plut. Vit. Phoc. 30.1; Plut. Apophthegmata regum atque imperatorum 188F; Letter of Aristeas 270) and many survive only as titles (e.g. Diog. Laert. 5.1.22; 5.2.42, 5.3.59, 6.1.18, 7.6.178). For Peri basileias literature see O. Murray, ‘Aristeas and Ptolemaic kingship’, JThS 18 (1967), 337–71, at 358; as serving didactic and propagandistic function: Strootman (n. 4 [2017]), 136.

10 LSJ s.v. παρρησία A1; parrhêsia as quality at court for philoi ‘as counsellors for rulers’: Strootman (n. 4 [2017]), 137–8; reception by royal audience: Berrey (n. 4), 94–5, 99, 104–6; as a ‘mirror’ for the king: R. Waterfield, The Making of a King: Antigonus Gonatas of Macedon and the Greeks (Chicago, 2021), 216–17. Geography as parrhêsia in early Hellenistic courts: J.D. McDermott, ‘Bending space: praise and parrhēsia in Hellenistic court geography’ (Diss., University of Sydney, 2023), 88–128, 165–88; cf. in imperial Rome: Z.M. Tan, ‘Subversive geography in Tacitus’ Germania’, JRS 104 (2014), 182, 197–202. Parrhêsia had a long tradition among Greek elite: in Homer: Il. 1.68–92; E.T.E. Barker, Entering the Agon: Dissent and Authority in Homer, Historiography and Tragedy (Oxford, 2009), 41–7. This is not to be confused with ‘measureless speech’ of insubordination: Hom. Il. 2.211, 46; P. Cartledge, Ancient Greek Political Thought in Practice (Cambridge, 2009), 33–6; T. Roberts, Athens on Trial: The Anti-Democratic Tradition of Western Thought (Princeton, 1997), 49–50. At the aristocratic symposion: Thgn. 93–9; ‘originally a typical aristocratic ideal’, Strootman (n. 4 [2014]), 173; L. O’Sullivan, ‘Parrhêsia and censorship in the polis and the symposium: an exploration of Hyperides Against Philippides 3’, in H. Baltussen and P.J. Davis (edd.), The Art of Veiled Speech: Self-Censorship from Aristophanes to Hobbes (Philadelphia, 2015), 42–73, at 47. Cf. parrhêsia in the polis: R. Benitez, ‘Parrhesia, ekmarturia and the Cassandra dialogue in Aeschylus’ Agamemnon’, Pages on C.P. Cavafy. Modern Greek Studies 11 (2003), 334–46, at 340; K.A. Raaflaub, ‘Aristocracy and freedom of speech in the Greco-Roman world’, in I. Sluiter and R.M. Rosen (edd.), Free Speech in Classical Antiquity (Leiden, 2004), 41–61, at 46–9. Foucault argues for democratic origins, migrating to court: M. Foucault (transl. G. Burchell), The Courage of the Truth (The Government of the Self and Others II) (Basingstoke and New York, 2011), 57.

11 Heath (n. 2), 299; G. Huxley, ‘Aristarchus of Samos and Graeco-Babylonian astronomy’, GRBS 5 (1964), 123–131, at 123, 130.

12 Ἀρίσταρχος Σάμιος μαθηματικός, ἀκουστὴς Στράτωνος …: Aët. 1.15.5 (J. Mansfeld and D.T. Runia [edd.], Aëtius, Placita [Cambridge, MA and London, 2023]). Strato’s biography: F1 (R. Sharples, ‘Strato of Lampsacus: the sources, texts, and translations’, in M.-L. Desclos and W.W. Fortenbaugh [edd.], Strato of Lampsacus: Text, Translation, and Discussion [Abingdon and New York, 2011], 5–229); for Strato as Ptolemy II’s tutor, see Diog. Laert. 5.3.58; letters to Arsinoë: 5.3.60.

13 Strato F 54; cf. Ptolemaic divine kingship affirmed by the oracle of Siwa: Diod. Sic. 20.100.3–4; McDermott (n. 10), 84–5, 109–12.

14 50th year, 1st Callippic cycle: Ptol. Alm. 3.1 (J.L. Heiberg and F.J. Boll, Claudii Ptolemaei Opera quae exstant omnia, vol. 1 [Leipzig, 1898], 203 lines 7–12). Toomer associates this observation with Aristarchus’ ‘school’ (G.J. Toomer, Ptolemy’s Almagest [London, 1984], 137 n. 19) while Heath (n. 2), 299 is more direct.

15 Vitr. De arch. 9.8.1.

16 E.g. Eratosthenes’ mesolabos used mechanical display to double the cube: Leventhal (n. 7), 62–6; Conon’s astronomical performance: S. West, ‘Venus observed? A note on Callimachus, Fr. 110’, CQ 35 (1985), 61–66, at 65; skaphê as later public display in Alexandria: Ptol. Alm. 3.1 (J.L. Heiberg and F.J. Boll [n. 14], 195 lines 3–9).

17 Diog. Laert. 7.5.176.

18 W.R. Knorr, ‘Archimedes and the elements: proposal for a revised chronological ordering of the Archimedean corpus’, AHES 10 (1978), 211–290, at 237–8, 271–2. Contra: T.L. Heath, The Works of Archimedes (London, 1897), lxxx.

19 Ptolemaic imperial ideology has been traditionally depicted as a ‘tortoise’, limited in ambition: E.R. Bevan, The House of Ptolemy (Chicago, 1927), 23; G. Hölbl, A History of the Ptolemaic Empire (New York, 2001), 28. However, with increasing use of non-Polybian sources, it is now more commonly understood as universal in ambition, emulating Alexander as an ‘imperialist’ regime much like other early Hellenistic courts: I. Worthington, Ptolemy I: King and Pharaoh of Egypt (Oxford, 2016), 83–6; C. Marquaille, ‘The foreign policy of Ptolemy II’, in P. McKechnie and P. Guillaume (edd.), Ptolemy II Philadelphus and his World (Leiden and Boston, 2008), 39–64, at 41–2; H. Hauben, ‘Callicrates of Samos and Patroclus of Macedon, champions of Ptolemaic thalassocracy’, in K. Buraselis, M. Stefanou and D.J. Thompson (edd.), The Ptolemies, the Sea, and the Nile: Studies in Waterborne Power (Cambridge, 2013), 39–65, at 39–42 (on imperial pretensions), 61–2 (practical limits).

20 Heath (n. 2), 301–6.

21 For Archimedes’ The Sand Reckoner, I follow J.L. Heiberg’s text: Archimedis Opera omnia, cum commentariis Eutocii (Leipzig, 1913), 2.216–58 and Heath (n. 18), 221–32, unless otherwise indicated.

22 Pappus, Syn. 6.69–73. MS transmission, earliest being the ninth century Vaticanus graecus 204: C.C. Carman and R. Buzón, Aristarchus of Samos: On the Sizes and Distances of the Sun and Moon: Greek Text, Translation, Analysis, and Relevant Scholia (London, 2023), 21–8; appendix 2 at 297; Heath (n. 2), 317–27.

23 Aët. 2.24.7 (n. 12); Sext. Emp. Adv. phys. 2.173–4 (R.G. Bury, Sextus Empiricus, Against Physicists. Against Ethicists [Cambridge, MA and London, 1936]); Plut. De fac. 922F–923B (n. 2); Plut. Quaest. Plat. 1006C (H. Cherniss [ed.], Plutarch, Moralia [Cambridge, MA and London, 1976]).

24 P.Oxy. 3710 cols. 2.33–3.19; A.V. Lebedev, ‘Aristarchus of Samos on Thales’ theory of eclipses’, Apeiron 23 (1990), 77– 85, at 77–80; attributed to ‘scribe A5’: W.A. Johnson, Bookrolls and Scribes in Oxyrhynchus (Toronto, 2004), 20–1, 61.

25 Heath (n. 2), iv (‘the real originator of the Copernican hypothesis’) and 301; G.V. Schiaparelli, I precursori di Copernico nell’antichità (Milan, 1873), 2, 41–2, 47–8; O. Neugebauer, ‘Archimedes and Aristarchus’, Isis 34 (1942), 4–6; A History of Ancient Mathematical Astronomy, Part Two (Berlin, 1975), 635; Gregory (n. 3), 109.

26 Competing claims of universal kingship: Plut. Demetr. 15.3; Plut. Pyrrh. 12.2; for Lund ‘universal power’ is integral to the ruler cult: H.S. Lund, Lysimachus: A Study in Early Hellenistic Kingship (London, 1992), 170; for Ptolemaic claims: Call. Hymn 4; ‘universalizing discourse of empire’: M. Brumbaugh, The New Politics of Olympos: Kingship in Kallimachos’ Hymns (New York, 2019), 162–90, at 167–71; ‘universal saviors and benefactors’: Y. Suto, ‘Common savior and benefactor of all: popular conception of kingship in Ptolemaic Egypt’, Orient 59 (2024), 79–90, at 79, 88–9; in the footsteps of Alexander: Worthington (n. 19), 84–6. Antecedents to universal kingship: Shulgi A (2.4.2.01) 1–6; Achaemenid claims, e.g. DB 1; XPf 2; XV 2; XE 2; DPh 1: A.A. Kuhrt, The Persian Empire: A Corpus of Sources from the Achaemenid Period (London and New York, 2007), 141, 244, 301; R. Strootman, ‘Hellenistic imperialism and the ideal of world unity’, in H. Drake and C. Rapp (edd.), The City in the Classical and Post-Classical World: Changing Contexts of Power and Identity (Cambridge and New York, 2014), 38–61, at 39 (‘universalistic pretensions’), 40–3.

27 θάλασσα δὲ πᾶσα καὶ αἶα | καὶ ποταμοὶ κελάδοντες ἀνάσσονται Πτολεμαίῳ, Theoc. Id. 17.91–2 (transl. N. Hopkinson, Theocritus, Moschus, Bion [Cambridge, MA and London, 2015]); Brumbaugh (n. 26), 174 notes the ‘universalizing’ ideology inherent in such claims.

28 Timosth. FGrHist 2051 F 11 = Plin. HN 6.5.15 (D. Meyer, ‘Timosthenes of Rhodos (2051)’, in H.-J. Gehrke and F.K. Maier [edd.], Jacoby Online. Die Fragmente der Griechischen Historiker Continued, Part V [Leiden, 2013]); as periphery: ἔσχατος πλοῦς, Strabo 11.2.16.

29 κυριεύσας δὲ τῆς τε ἐντὸς Eὐφράτου | χώρας πάσης, OGIS 54.14.13–14 (transl. E.R. Bevan, The House of Ptolemy [Chicago, 1927], 192–3). Strootman (n. 26), 44 emphasizes ‘the oikoumenê as an empire, united under the rule of a single great king’ as ‘core element’ of Ptolemies’ imperial ideology.

30 Red Sea vector: Ptol. II: Diod. Sic. 3.18.4; Strabo 16.4.5–7; I.Cair. 22183.21–4; Ptol. III: Bab-el-Mandeb: Strabo 16.4.13–14. The slower hybrid sea-road-Nile route was used in reality, however: S.E. Sidebotham and R.E. Zitterkopf, ‘Routes through the eastern desert of Egypt’, Expedition 37 (1995), 39–51, at 40–2; M.A. Woźniak, S.E. Sidebotham, M. Osypińska, A. Carannante and J.K. Rądkowska, ‘Ptolemaic Berenike: resources, logistics, and daily life in a Hellenistic fortress on the Red Sea coast of Egypt’, AJA 125 (2021), 247–281, at 247–9. For Alexandria as geographic, cosmological centre: Dio. Chrys. 32.36; centripetal pull in epigrammatic poetry: Posidippus, epigrams on stones 7; 11.2; 12.1–2; 16; 19–20 A.–B.; see A. Kuttner, ‘Cabinet fit for a queen: the Λιθικά as Posidippus’ gem museum’, in K. Gutzwiller (ed.), The New Posidippus: A Hellenistic Poetry Book (Oxford, 2005), 141–63, at 159–60; Alexandria’s centripetal pull in Timosthenes’ geography, see Timosth. FGrHist 2051 F 1; F. Prontera, ‘Timosthenes and Eratosthenes: sea routes and Hellenistic geography’, in K. Buraselis, M. Stefanou and D. Thompson (edd.), The Ptolemies, the Sea and the Nile: Studies in Waterborne Power (Cambridge, 2013), 207–17, at 208; ‘a place designed as a centripetal force towards which everything converges’, C. Marquaille (n. 19), 51; C. Jacob, ‘Mapping the mind: the Earth from ancient Alexandria’, in D. Cosgrove (ed.), Mappings (London, 1999), 24–49, at 33.

31 Polyb. 5.34.9 (transl. W.R. Paton, Polybius, The Histories [Cambridge, MA and London, 1923]).

32 Catull. 66.1; D.L. Selden, ‘Alibis’, ClAnt 17 (1998), 289–412, at 328.

33 Scientific surveillance: πάντα τὸν ἐν γραμμαῖσιν ἰδὼν ὅρον ᾗ τε φέρονται, Call. Aet. F 110a H.; Catullus 66.1, following Callimachus: omnia qui magni dispexit lumina mundi (‘he who scanned all the lights of the vast sky’, transl. Cornish); scientific and mythical allusion: K. Gutzwiller, ‘Callimachus’ Lock of Berenice: fantasy, romance, and propaganda’, AJPh 113 (1992), 359–85, at 373–4.

34 Cat. 66.63–4 uuidulam a fluctu cedentem ad templa deum me | sidus in antiquis diua nouum posuit.

35 Isis: S. Jackson, ‘Callimachus: Coma Berenices: origins’, Mnemosyne 54 (2001), 1–9, at 5–6; Aphrodite: G.L. Huxley, ‘Arsinoe Lokris’, GRBS 21 (1980), 239–44, at 241; Arsinoë II: Gutzwiller (n. 33), 363, 365–7.

36 Exaggerated reach expressed in geography: D. Dueck, ‘The geographical narrative of Strabo of Amasia’, in K.A. Raaflaub and R.J.A. Talbert (edd.), Geography and Ethnography: Perceptions of the World in Pre-Modern Societies (Malden MA and Oxford, 2010), 236–51, at 245; Strootman (n. 26 [2014]), 45–52; Strootman (n. 4 [2017]), 145–6; Visscher (n. 5), 62.

37 Fellow philos, Eratosthenes: Conon mathematicus cupiens inire gratiam regis dixit crinem inter sidera uideri collocatum et quasdam uacuas a figura septem stellas ostendit quas esse fingeret crinem (‘Conon, in the hope of gaining the king’s favour, claimed to have seen the lock set among the stars; and he pointed to seven stars that did not belong to any constellation, saying that these must surely be the hair’, Hyg. Poet. astr. 2.24.1004–7: G. Viré [ed.], Hygini De astronomia [Leipzig, 1992], 70; transl. R. Hard, Constellation Myths [Oxford, 2015], 70. For commentary: 71–2). For possible politics of Eratosthenes’ omission of Conon’s discovery, see K. Geus, Eratosthenes von Kyrene: Studien zur hellenistischen Kultur und Wissenschaftsgeschichte (Munich, 2002), 206–23, at 222.

38 For centrality and periphery as propaganda in political maps: S. Speier, ‘Magic Geography’, Social Research 8 (1941), 310–30, at 313–4; H. Lefebvre (transl. D. Nicholson-Smith), The Production of Space (Oxford and Cambridge, MA, 1974), 84; ‘divinely appointed to the centre of the universe’: J.B. Harley, ‘Maps, Knowledge, and Power’, in D. Cosgrove and S. Daniels (edd.), The Iconography of Landscape (Cambridge, 1988), 277–312, at 290; J.B. Harley, ‘Deconstructing the map’, in T. Barnes and J.S. Duncan (edd.), Writing Worlds: Discourse, Text and Metaphor in the Representation of Landscape (London, 1992), 231–47, at 236–7.

39 Neo-Babylonian mappa mundi: BM 92687; map, obv.: cf. Euphrates and Babylon intersecting at centre (13) with subordinate places (2–5, 8, 10, 11–12), and peripheral regions (18–22; text: 8); W. Horowitz, ‘The Babylonian Map of the World’, Iraq 50 (1988), 147–65, at 148–9; R. Rochberg, ‘The expression of terrestrial and celestial order in Ancient Mesopotamia’, in R.J.A. Talbert (ed.), Ancient Perspectives: Maps and Their Place in Mesopotamia, Egypt, Greece, and Rome (Chicago, 2019), 9–46, at 32–4.

40 For Ptolemy II’s grand procession as depicting Ptolemaic geographical order: Callixenus BNJ 627 F 2; E.E. Rice, The Grand Procession of Ptolemy Philadelphus (Oxford, 1983), 48, 84–110. For Ptolemaic centripetal geography: n. 30.

41 Visscher (n. 5), 33–45.

42 Suda α 3745 Adler; Vit. Arat.

43 Presented at a symposion for an elite audience: E. Mass, Aratea (1892, Berlin), 317–19; M. Erren, Die Phainomena des Aratos von Soloi. Untersuchungen zum Sach-und Sinnverständnis (Wiesbaden, 1967), 10–15. Although Bing identifies ‘inclusive discourse’ for multiple audiences (elite and non-elite): P. Bing, ‘Aratus and his audiences’, in P. Mitsis and J.S. Clay (edd.), Mega nepios: il destinatario nell’epos didascalico = The Addressee in Didactic Epic (Pisa, 1993), 99–109, at 100.

44 Strootman (n. 5 [2007]), 230–2; (n. 4 [2017]), 140; A. Schiesaro, ‘Aratus’ myth of Dike’, MD 37 (1996), 9–25, at 20–3. Later use as imperial propaganda: H. Zehnacker, ‘D’Aratos à Aviénus: astronomie et idéologie’, ICS 14 (1989), 317–29, at 321–4. Zeus and universal kingship: Theoc. Id. 17.1, with Erren (n. 43), 16–17; and Call. Hymn 1.

45 Cf. Zeus delegating control: Call. Hymn 1.73–80; M. Fantuzzi and R. Hunter, Tradition and Innovation in Hellenistic Poetry (Cambridge, 2004), 353.

46 Arat. Phaen. 21–2 αὐτὰρ ὅ γ᾿ οὐδ᾿ ὀλίγον μετανίσσεται, ἀλλὰ μάλ᾿ αὕτως | ἄξων αἰὲν ἄρηρεν (‘but the Axis shifts not a whit, but unchanging is for ever fixed’; transl. Mair).

47 Arat. Phaen. 22–3 ἔχει δ᾿ ἀτάλαντον ἁπάντη | μεσσηγὺς γαῖαν, περὶ δ᾿ οὐρανὸν αὐτὸν ἀγινεῖ.

48 Cleanthes fr. 537 von Arnim = Stob. Ecl. 1.1.12. Text and translation follow J.C. Thom, Cleanthes’ Hymn to Zeus: Text, Translation, and Commentary (Tübingen, 2005), 40–1. For Davidson, it is both ‘a pious submission to the world-order’ and materialism which gives ‘unity’ to the system: W.L. Davidson, The Stoic Creed (Edinburgh, 1907), 27–8, 229. ‘All-pervading reason’ in control of ‘the entire universe’: A.D. Rossi, ‘Cleanthes’ hymn to Zeus’, CB 53 (1976), 1–2, at 1. As expression of universal power: Thom (this note), 20–4. Textual issues: J.D. Meerwaldt, ‘Cleanthea I’, Mnemosyne 4 (1951), 40–69, at 66–9; J.D. Meerwaldt, ‘Cleanthea II’, Mnemosyne 5 (1952), 1–12, at 1–3. Cf. Aratus: Zehnacker (n. 44), 317.

49 Cleanthes fr. 537.3–4 = Thom, lines 7–8 σοὶ δὴ πᾶς ὅδε κόσμος ἑλισσόμενος περὶ γαῖαν | πείθεται ᾗ κεν ἄγῃς, καὶ ἑκὼν ὑπὸ σεῖο κρατεῖται.

50 Cleanthes fr. 537.8–9 = Thom, lines 12–13 ᾧ σὺ κατευθύνεις κοινὸν λόγον, ὃς διὰ πάντων | φοιτᾷ μειγνύμενος μεγάλῳ μικροῖς τε φάεσσι. For conjecture and emendations, see Thom (n. 48), 36 n. 13, and also 32.

51 Cleanthes fr. 537.10 = Thom, line 14 ὕπατος βασιλεὺς διὰ παντός.

52 Themes of ‘universal rule’: Thom (n. 48), 22.

53 Theon of Smyrna, Expositio rerum mathematicarum ad legendum Platonem utilium (ed. Hiller [Leipzig, 1878], 200 lines 7–12) γῆν μὲν χρὴ οἴεσθαι μένειν, ἑστίαν τοῦ θεῶν οἴκου κατὰ τὸν Πλάτωνα (‘we must suppose the earth, the Hearth of the House of the Gods according to Plato, to remain fixed’, transl. Heath).

54 Solar movement: Hes. Theog. 758–61; Hom. Od. 12.379–83; omniscience: 12.323.

55 Ordered celestial motions: Ap. Rhod. 1.496–500; K. Poulheria, ‘Empedoclean echoes in Apollonius Rhodius’ Argonautica’, Hermes 122 (1994), 309–19, at 309–10; see also stellar motion: Hom. Il. 18.485–9; Od. 5.271–81; Arat. Phaen. 19–44. For stellar movement and the Nile flood, Theoi Euergetai cult, see n. 74 below. Followed by the science: Cic. Nat. D. 2.97.

56 Most vividly associated with Demetrius: Ithyphallic hymn (BNJ 76 F 13), where Demetrius is explicitly associated with Helios (ὅμοιον ὥσπερ … ἥλιος), outshining his stellar philoi (11–2) and more distant deities (15–20); cf. dancing astral bodies yielding to Helios’ path: Julian. Or. 4.135A–B, 146C–D; life-giving movement of Helios across the entire oikoumenê: 146D–147A. For Demetrius similarly ‘riding on the world’ (ἐπὶ τοῦ προσκηνίου ἐπὶ τῆς οἰκουμένης ὀχούμενος), see BNJ 76 F 14; ‘Helios-like’ (ἡλιόμορφος): F 10; Helios-like cloak (Plut. Demetr. 41.4–5); cf. Helios’ cloak: Valerius Flaccus, Argon. 4.92–5. L. O’Sullivan, ‘Le roi soleil: Demetrius Poliorcetes and the dawn of the Sun-King’, Antichthon 42 (2008), 78–99. Alexander’s oikoumenê-wide conquest attributed to Helios: Diod. Sic. 17.89.3; Curt. 9.1.1; A.F. Stewart, Faces of Power (Berkeley, 1993), 179–80.

57 Neugebauer (n. 25), 6.

58 Aët. 2.24.7 Ἀρίσταρχος τὸν ἥλιον ἵστησι μετὰ τῶν ἀπλανῶν, τὴν δὲ γῆν κινεῖ περὶ τὸν ἡλιακὸν κύκλον καὶ κατὰ τὰς ταύτης ἐγκλίσεις σκιάζεσθαι.

59 Sext. Emp. Adv. phys. 2.174 οἵ γε μὴν τὴν τοῦ κόσμου κίνησιν ἀνελόντες τὴν δὲ γῆν κινεῖσθαι δοξάσαντες, ὡς οἱ περὶ Ἀρίσταρχον τὸν μαθηματικόν.

60 Centrality: C. Leuenberger and I. Schnell, ‘The politics of maps: constructing national territories in Israel’, Social Studies of Science 40 (2010), 803–42, at 835 n. 1; Harley (n. 38 [1992]), 236; Harley (n. 38 [1988]), 290.

61 eget moderamine certo: Ov. Met. 2.67; cf. Pl. Tim. 22c–d.

62 In contrast to earlier geo-central axial rotation: W.H. Stahl, ‘The Greek heliocentric theory and its abandonment’, TAPhA 76 (1945), 321–32, at 323–5; P.T. Keyser, ‘Heliocentrism in or out of Heraclides’, in W.W. Fortenbaugh and E. Pender (edd.), Heraclides of Pontus: Discussion (New Brunswick, NJ, 2009), 205–35, at 213–14.

63 Plut. De fac. 923A μένειν τὸν οὐρανὸν ὑποτιθέμενος ἐξελίττεσθαι δὲ κατὰ λοξοῦ κύκλου τὴν γῆν ἅμα καὶ περὶ τὸν αὑτῆς ἄξονα δινουμένην.

64 Plut. Quaest. Plat. 1006C ἀλλὰ στρεφομένην καὶ ἀνειλουμένην νοεῖν, ὡς ὕστερον Ἀρίσταρχος καὶ Σέλευκος ἀπεδείκνυσαν.

65 von Erhardt and von Erhardt-Siebold (n. 3), 598.

66 Strato F 19A (= Cic. Nat. D. 1.35) quae causas gignendi augendi minuendi habeat sed careat omni et sensu et figura.

67 Plut. De fac. 923A ὡς κινοῦντα τοῦ κόσμου τὴν ἑστίαν.

68 J. Evans, ‘The astrologer’s apparatus: a picture of professional practice in Greco-Roman Egypt’, JHA 35 (2004), 1–44, at 1.

69 Dorotheus, Carmen astrologicum 2.14 (D.E. Pingee [transl.], Carmen astrologicum [Leipzig, 1976]).

70 Sirius: Ap. Rhod. 3.957; Nic. Ther. 200–9, 367–9; Hom. Il. 22.28–31; Hes. Op. 585–8.

71 Political turmoil: P.Cairo 31222.6 (ed. and transl. G.R. Hughes, ‘A Demotic astrological text’, JNES 10 [1951], 256–64, at 258–9). Into Asia: P.Cairo 31222.9–10.

72 Hephaestion, Apotelesmatics 1.23 lines 4–11 (D. Pingree [ed.], Hephaestionis Thebani Apotelesmaticorum [Leipzig, 1973]). Petosiris-Nechepso traditionally predating Hipparchus: P. Keyser, ‘On cometary theory and typology from Nechepso-Petosiris through Apuleius to Servius’, Mnemosyne 47 (1994), 625–51, at 642 n. 70.

73 OGIS 56A.36 (PHI 218980); D. Clayman, Berenice II and the Golden Age of Ptolemaic Egypt (Oxford and New York, 2014), 167.

74 OGIS 56A.37–8 (PHI 218980) ἄγεται καὶ ἡ συναγωγὴ τῶν καρπῶν καὶ ἡ τοῦ | ποταμοῦ ἀνάβασις γίνεται.

75 OGIS 56A.45–6 (PHI 218980) ὅπως ἅπαντες εἰδῶσιν διότι τὸ ἐλλεῖπον πρότερον περὶ τὴν σύνταξιν τῶν ὡρῶν καὶ τοῦ ἐνιαυτοῦ καὶ τῶν νομιζο|μένων περὶ τὴν ὅλην διακόσμησιν τοῦ πό<λ>ου διωρθῶσθαι καὶ ἀναπεπληρῶσθαι συμβέβηκεν διὰ τῶν Eὐεργετῶν θεῶν.

76 Gigantic Hellenistic warships ‘intended for display’: L. Casson, Ships and Seamanship in the Ancient World (Princeton, 2014 [1971]), 97–140, at 98. Barges ‘built to impress, not for practical ends’: D.J. Thompson, ‘Hellenistic royal barges’, in K. Buraselis and D.J. Thompson (edd.), The Ptolemies, the Sea and the Nile: Studies in Waterborne Power (Cambridge, 2013), 185–96, at 193; Sen. Ben. 7.20.3 lusorias et cubiculatas et alia ludibria regum in mari lasciuientium mittam. Examples vary: for hyper-galleys, barges, grain ships: Ath. Deipn. 5.203e–209e; for possible extant depiction of hyper-galley on tour: L. Basch, ‘The Isis of Ptolemy II Philadelphos’, The Mariner’s Mirror 71 (1985), 129–51, at 146–9.

77 For juxtaposition used to express relative significance in geopolitical maps see Speier (n. 38), 318–9; H. Soffner, ‘War on the visual front’, The American Scholar 11 (1942), 465–76, at 469–72; M. Monmonier, How to Lie with Maps (Chicago and London, 1991), 94–9, 102, fig. 7.11.

78 Patrocles’ geography depicted a reduced and encircled India for the Seleucids: Visscher (n. 5), 32–4; McDermott (n. 10), 144–51; contra Kosmin’s ‘amarna’ geography (n. 5), 31–6, 48–51.

79 C.C. Carman, ‘Two problems in Aristarchus’s treatise On the Sizes and Distances of the Sun and Moon’, AHES 68 (2014), 35–65, at 36.

80 Archim. Arenarius 3, from Heiberg (n. 21), 220.22–5: Ἀριστάρχου δὲ πεπειραμένου δεικνύειν, ὅτι ἐστὶν ἀ διάμετρος τοῦ ἁλίου τᾶς διαμέτρου τᾶς σελήνας μείζων μὲν ἢ ὀκτωκαιδεκαπλασίων, ἐλάττων δὲ ἢ εἰκοσαπλασίων, ‘Aristarchus tried to prove that the diameter of the sun is greater than 18 times but less than 20 times the diameter of the moon’ (transl. Heath); repeated by Plutarch, De fac. 925C–D.

81 Aristarchus of Samos, On the Sizes and Distances of the Sun and Moon, Prop. 3 (ed. Heath [n. 2], 352.10–2).

82 Heath (n. 2), 310.

83 Aristarchus of Samos, On the Sizes and Distances of the Sun and Moon, Prop. 6 (Heath [n. 2], 352 lines 14–15) τὴν σελήνην ὑποτείνειν ὑπὸ πεντεκαιδέκατον μέρος ζῳδίου; Carman (n. 79), 58; cf. J. Evans, The History and Practice of Ancient Astronomy (New York, 1998), 22.

84 Contra 0.5° Archim. Arenarius 10–11 (Heiberg [n. 21], 222.3–11); Aristarchus’ mathematical skill: Vitr. De arch. 1.1.17, 9.2.3; and modern praise: J.L. Berggren and N. Sidoli, ‘Aristarchus’s On the Sizes and Distances of the Sun and the Moon: Greek and Arabic texts’, AHES 61 (2007), 213–54, at 231.

85 Aët. 2.21.5 τηλικοῦτον ἡλίκος φαίνεται, ἢ μικρῷ τινι μείζω (that is, the size of a human foot: 4); Heath (n. 2), 61; Carman (n. 79), 55–6.

86 Archim. Arenarius (Heiberg [n. 21], 218.1–2): διότι καλεῖται κόσμος ὑπὸ μὲν τῶν πλείστων ἀστρολόγων); J. Wietzke, ‘Speaking wit to power: reconsidering royal patronage through Archimedes’ Sand-reckoner’, ClAnt 41 (2022), 129–79, at 149–50. Archimedes compares it to 6th–5th c. model favoured by Anaximander, Empedocles, Leucippus: von Erhardt and von Erhardt-Siebold (n. 3), 580.

87 Euc. 1 def. 1, 16; 3 def. 4 (J.L. Heiberg [ed.], Euclidis Elementa [Leipzig, 1883]). Heron Definitiones def. 7 (J.L. Heiberg [ed.], Heronis Alexandrini Opera quae supersunt omnia, vol. 4 [Berlin, 1912]). P. Tannery, Recherches sur l’histoire de l’astronomie ancienne (Paris, 1893), 99.

88 Sarton (n. 3), 57; Heath (n. 2), 308–10; von Erhardt and von Erhardt-Siebold (n. 3), 585, 592.

89 Neugebauer (n. 25), 5–6; cf. von Erhardt and von Erhardt-Siebold (n. 3), 582. Contra: Carman (n. 2), 2.

90 An ‘unreal and confusing’ assertion: von Erhardt and von Erhardt-Siebold (n. 3), 590; Epicurean universe: Diog. Laert. 10.45.

91 Satellite photography, distancing effects: D. Wood, The Power of Maps (New York, 1992), 49–51, 55–6; J.B. Harley, ‘Silences and secrecy: the hidden agenda of cartography in early modern Europe’, Imago Mundi 40 (1988), 57–76, at 71 n. 2.

92 Seen in the geography of Eratosthenes: Eratosth. fr. 25, 30, 31, 34, 44 (D.W. Roller [ed.], Eratosthenes Geography, Fragments Collected and Translated, with Commentary and Additional Material [Princeton and Oxford, 2010]); McDermott (n. 10), 117–19.

93 Diog. Laert. 7.5.174; Carman (n. 2), 6.

94 Diog. Laert. 7.5, especially 169–70.

95 Diog. Laert. 7.5.169 φασὶ δὲ καὶ Ἀντίγονον αὐτοῦ πυθέσθαι ὄντα ἀκροατήν. Stoicism at the Antigonid court: Diog. Laert. 7.1.6; W.W. Tarn, Antigonos Gonatas (Oxford, 1913), 231–3, 235, 248–50; R. Waterfield, The Making of a King: Antigonus Gonatas of Macedon and the Greeks (Chicago, 2021), 214–7.

96 Diog. Laert. 7.5.169 φασὶ δὲ καὶ Ἀντίγονον αὐτῷ τρισχιλίας δοῦναι.

97 Theoc. Id. 17.114 δωτίναν ἀντάξιον ὤπασε τέχνας; Berrey (n. 4), 89–90.

98 Diog. Laert. 7.7.185; Tarn (n. 95), 331. Insulted in person by Sositheus: 7.5.173.

99 Kolakeia: Diog. Laert. 7.5.171.

100 See nn. 48–52.

101 Cleanthes fr. 537.5–7 = Thom, lines 9–11 τοῖον ἔχεις ὑποεργὸν ἀνικήτοις ὑπὸ χερσὶν | ἀμφήκη πυρόεντα ἀειζώοντα κεραυνόν· | τοῦ γὰρ ὑπὸ πληγῆς φύσεως πάντ’ ἔργα … (my transl.). Cf. thunderbolts as blows (ὑπὸ πληγῆς): Plut. Quaest. Plat. 1005Β; trembling: Theoc. Id. 16.76–7, followed by spear-wielding conquest: 78–103.

102 Alexander’s spear-won territory: Diod. Sic. 17.17.1–2; Just. Epit. 11.5.5–11; I. Worthington, Alexander the Great: Man and God (London and New York, 2004), 71, 90. The ‘spear-won’ (δορίκτητος) land of Successors: Diod. Sic. 19.105.4; F.W. Walbank, The Hellenistic World (Cambridge, MA, 1982), 37 (Alexander), 107–8 (Ptolemies), 124 (Seleucids); A.B. Bosworth, The Legacy of Alexander: Politics, Warfare and Propaganda Under the Successors (Oxford, 2002), 213 (Seleucids), 242 (Ptolemies). Claims of universal empire: see n. 26.

103 Sotades apud Ath. Deipn. 14.621a εἰς οὐχ ὁσίην τρυμαλιὴν τὸ κέντρον ὠθεῖς; R. Hunter, ‘“Acting down”: the ideology of Hellenistic performance’, in P. Easterling and E. Hall (edd.), Greek and Roman Actors: Aspects of an Ancient Profession (Cambridge, 2002), 189–206, at 197.

104 E.g. Daphitas and the Attalids: Strabo 14.1.39; Cic. Fat. 3.5.

105 E.g. Stilpo’s razor wit, fatal humiliation for Diodoros ‘Kronos’: Diog. Laert. 2.10.111–2.

106 Strato’s and Eratosthenes’ challenges to Siwa’s divine origins overlap in Strabo: Strat. fr. 54 (= Eratosth. fr. 15 = Strabo 1.3.4).

107 Ptolemy II: Letter of Aristeas 206.

108 Procl. Hypotyp. Prol. II (G. Friedlein [ed.], Procli Diadochi in primum Euclidis Elementorum librum commentarii [Leipzig, 1873], 68.16–7) μὴ εἶναι βασιλικὴν ἀτραπὸν ἐπὶ γεωμετρίαν; P.M. Fraser, Ptolemaic Alexandria (Oxford, 1972), 1.386–7.

109 Plut. Quaest. Plat. 8, 1006C μὴ συνεχομένην καὶ μένουσαν ἀλλὰ στρεφομένην καὶ ἀνειλουμένην νοεῖν, ὡς ὕστερον Ἀρίσταρχος καὶ Σέλευκος ἀπεδείκνυσαν, ὁ μὲν ὑποτιθέμενος μόνον ὁ δὲ Σέλευκος καὶ ἀποφαινόμενος, ‘to have been devised not as confined and at rest but as turning and whirling about in the way set forth later by Aristarchus and Seleucus, by the former only as an hypothesis but by Seleucus beyond that as a statement of fact’ (transl. Cherniss); see Heath (n. 2), 306–7; Sarton (n. 3), 59; Carman (n. 2), 6–7. He ‘studied with Babylonian astronomers and astrologers’: P.T. Keyser, ‘Seleukos’, in P.T. Keyser and G.L. Irby-Massie (edd.), The Encyclopedia of Ancient Natural Scientists (London and New York, 2008), 730; Strabo 16.1.6. For Seleucia-on-the-Tigris’ role as Seleucid royal city and imperial centre: Kosmin (n. 5), 145 (map 5).

110 B.L. van der Waerden, ‘The heliocentric system in Greek, Persian and Hindu Astronomy’, Annals of the New York Academy of Sciences 500 (1987), 525–45, at 528–9; Seleucus’ possible parallax measurements: von Erhardt and von Erhardt-Siebold (n. 3), 598–9. Contra Carman (n. 2), 7 (‘too farfetched’), following O. Neugebauer, A History of Ancient Mathematical Astronomy Part Two (New York / Heidelberg / Berlin, 1975), 697–9.

111 Seleucus argues tides from the moon’s revolution (Aët. 3.17.9): Σέλευκος ὁ μαθηματικὸς ἀντιγεγραφὼς Κράτητι, κινῶν καὐτὸς τὴν γῆν, | ἀντικόπτειν αὐτῆς τῷ δίνῳ φησὶ {καὶ τῇ κινήσει} τὴν περιστροφὴν τῆς σελήνης, ‘Seleucus the astronomer, who wrote against Crates and who, too, moves the earth, says that the revolution of the moon hinders its rotation [sc. of the earth]’ (transl. J. Mansfeld and D.T. Runia [n. 12]). Seleucus’ ‘irregularity’ (ἀνωμαλίαν) of the tide vis-à-vis the moon’s position: Strabo 3.5.9.