Abstract
The article provides a reconstruction of Eudoxus' approach to simultaneous risings and settings in his two works dedicated to the issue: the Phaenomena and the Enoptron. This reconstruction is based on the analysis of Eudoxus’ fragments transmitted by Hipparchus. These fragments are difficult and problematic, but a close analysis and a comparison with the corresponding passages in Aratus suggests a possible solution.
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Notes
‘Seasonal hours’ are obtained by dividing daytime and night time into 12 equal parts each, so that the duration of a seasonal hour changes during the year and depends on latitude. These are the hours usually used by the Greeks in their civil life. However, astronomers, starting from ca. 300 BCE (the first attestation is in PHibeh 1.27, dating to that period) also used ‘equinoctial hours’, which are obtained by dividing the night-and-day combination into 24 parts of equal length.
The parapegmata are calendars sometimes organized by the position of the sun in the zodiacal constellations (or signs) and listing the rising and setting of other fixed constellations as well as weather predictions. We have examples of parapegmata in manuscript form (as e.g. P.Hibeh 1.27, dated to the early third century BCE, or the parapegma at the end of Geminus’ Introduction) and stone parapegmata displayed in public spaces which kept track of cyclical celestial phenomena through movable pegs (e.g. the two parapegmata from Miletus, dating to the second century BCE). Cf. Lehoux 2007, 12-19.
With zodiacal signs, which are a division of the ecliptic into equal arcs of 30 degrees each, and equinoctial hours, things are more precise. Indeed, six zodiacal signs (i.e. 180 degrees on the ecliptic) rise every night. Throughout this paper I will always distinguish between zodiacal signs and zodiacal constellations, since this distinction is at the core of the different approaches of Aratus and Eudoxus (who use zodiacal constellations) and Hipparchus (who uses zodiacal signs).
The sequence ὑποτίθεται … τὰς ἀρχὰς τῶν ζῳδίων ἐπὶ τῆς ἀνατολῆς exactly corresponds to what Hipparchus says of Aratus in 2.2.2 ὑποθέμενος τοίνυν ὁ Ἄρατος ἐπὶ τῆς ἀνατολῆς τὴν ἀρχὴν τοῦ Καρκίνου φησί...[Thus, assuming that the beginning of the Crab is at the point of its rising, Aratus says ...].
Boll 1903, 59-62 (who suggested that the system of Eudoxus is also adopted by Vettius Valens); Martin 2002-2003, I lxxxix (who concluded that ‘Eudoxus’ is actually a later prose summary from Aratus); Dekker 2013, 41-43. As Dekker 2013, 41 also explains: “Hipparchus tells us that, in the treatises he attributes to Eudoxus, the author lists those constellations that either rise or set during the time it takes a zodiacal sign to rise. Aratus constructs his lists differently and mentions those constellations that are rising or setting when a zodiacal sign is beginning to rise. When the two versions are compared it appears that the constellations listed by ‘Eudoxus’ as rising or setting during the rise of a zodiacal sign are actually the same as the ones that are recorded by Aratus as rising or setting when the following zodiacal sign is beginning to rise”.
See Schironi (forthcoming), passim.
See Hipp. 1.2.2 ἀναφέρεται δὲ εἰς τὸν Εὔδοξον δύο βιβλία περὶ τῶν φαινομένων (fr. F 4), σύμφωνα κατὰ πάντα σχεδὸν ἀλλήλοις πλὴν ὀλίγων σφόδρα. τὸ μὲν οὖν ἓν αὐτῶν ἐπιγράφεται Ἔνοπτρον, τὸ δὲ ἕτερον Φαινόμενα. πρὸς τὰ Φαινόμενα δὲ τὴν ποίησιν συντέταχεν [Two books about the visible phenomena are attributed to Eudoxus (fr. F 4), in agreement with each other in almost everything except for a few details. One of them is entitled Enoptron [i.e. Mirror] and the other Phaenomena. And [Aratus] has put together his poem following the Phaenomena].
In fact, even not counting the Pleiades, ο Tau is not the first star of the Bull to rise. See Schironi (forthcoming), at Hipp. 3.3.11.
Phaen. 569–589: When the Crab rises, not the faintest stars lie on both sides [of the Ocean], turning around, some setting and some coming up on the other [side]. The Crown sets and the [Southern] Fish sets along its spine; you would see half of the descending Crown up in the air but the farthest edges [of the horizon] already throw down half of it. But the one who is turned backward [i.e. the Kneeler] is not yet [set] in the other parts up to the lower belly, while the upper parts are borne in the night. The Crab also brings down the wretched Serpent-Bearer from the knees to the shoulders and brings down the Serpent near the neck. The Guardian-of-the-Bear would not then be large on both sides [i.e. above and below the horizon]; [he is] smaller in the day [i.e. above the horizon] and the greater part of him is already at night [i.e. below the horizon]. For the Ocean receives the Plowman as he goes down together with four parts [i.e. four zodiac constellations]; and after he is satiated with light, he occupies more than half of the passing night in the unyoking of his oxen when he sets with the sun going down. Those nights are also named after his late setting. So these [stars] set, and on the opposite side, not at all worthless, but very bright in his belt and both his shoulders, Orion, trusting in the strength of his sword, stretches along the other horn [i.e. limit] [of the Ocean], carrying the entire River.
Phaen. 699–708: Yet much of it [i.e., the Water-Snake] still remains behind, but when the Fishes rise, [night] carries it away entirely together with the Centaur itself. With the Fishes comes the [Southern] Fish, which lies below dark Capricorn itself—not all of it, but a bit of it waits for the twelfth other part. So also the unhappy hands and the knees and the shoulders of Andromeda are all stretched in two directions, some in front and others behind, when both Fishes first show themselves from the Ocean.
For the Enoptron being later than the Phaenomena, see Hipp. 1.3.10 and Schironi (forthcoming), at Hipp. 1.3.5–12.
On the other hand, Martin thinks that ‘Eudoxus’ is later than Aratus, so ‘Eudoxus’ must have changed the system.
See Schironi (forthcoming).
References
Boll, F., 1903, Sphaera: neue griechische Texte und Untersuchungen zur Geschichte der Sternbilder, Leipzig.
Dekker, E. 2013. Illustrating the phaenomena: Celestial cartography in antiquity and the Middle Ages. Oxford.
Lehoux, D. 2007. Astronomy, weather, and calendars in the ancient world: Parapegmata and related texts in classical and Near Eastern societies. Cambridge: UK - New York.
Martin, J., 2002–2003, Aratos, Phénomènes, Paris.
Schironi, F., (forthcoming), Hipparchus of Nicaea, Exegesis of the Phaenomena of Eudoxus and Aratus: Edition, Translation, and Commentary, Abingdon.
Acknowledgements
I would like to thank Fabio Acerbi and Alexander Jones for reading this paper and giving useful comments and suggestions. The figures in this paper were generated using Stellarium, a free open-source planetarium (https://stellarium.org).
Funding
This research was supported by Directorate for Social, Behavioral and Economic Sciences (Grant AGS-1849638).
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Schironi, F. Eudoxus’ simultaneous risings and settings. Arch. Hist. Exact Sci. 77, 423–441 (2023). https://doi.org/10.1007/s00407-023-00309-x
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DOI: https://doi.org/10.1007/s00407-023-00309-x