Hippocrates of Chios's Theory of Comets

Proclus makes Hippocrates a contemporary of Anaxagoras and Oinopides ( Diels H. Kranz W. , Die Fragmente der Vorsokratiker (Hildesheim, 1951), 42.1). For other chronological discussion, see Netz R. , The shaping of deduction in Greek mathematics: A study in cognitive history (Cambridge, 1999), 272–5 (who suggests 440 b.c. as a floruit), and idem, “Eudemus of Rhodes, Hippocrates of Chios and the earliest form of a Greek mathematical text”, Centaurus, xlvi (2004), 2004–86, pp. 244–8. Burkert W. (Lore and science in ancient Pythagoreanism, transl. by Minar E. L. Jr (Cambridge, 1972), 313–14) places Hippocrates's floruit around 430 b.c.

Hippocrates's name is missing from most of usual handbooks and surveys of ancient astronomy.

Goldstein and Bowen deny the use of the “two-sphere” model before the second half of the fourth century b.c. ( Goldstein B. R. Bowen A. C. , “A new view of early Greek astronomy”, Isis, lxxiv (1983), 330–40).

Alexander , In Aristotelis Meteorologicorum libros commentaria , ed. by Hayduck M. (Berlin, 1899); Philoponus J. , In Aristotelis Meteorologicorum librum primum commentarium, ed. by Hayduck M. (Berlin, 1901); Olympiodorus, In Aristotelis Meteora Commentaria, ed. Stüve W. (Berlin, 1900).

There is some evidence that the total sum of the five planets had not been firmly established by the late fifth century. In addition to the Pythagoreans, Democritus ( Diels Kranz , op. cit. (ref. 1), 68A92) suspected that there were more planets, but did not set down their numbers or names.

Tradition reports a rivalry between Parmenides and Pythagoras for the discovery of the identity of the evening and the morning star ( Diels Kranz , op. cit. (ref. 1), 28A1). Empedocles certainly knew of wandering stars (Diels and Kranz, op. cit. (ref. 1), 31A54).

Translations are my own unless otherwise noted.

It is used in this sense at De caelo ii.14 296a35; Meteorologica i.6 343a24; at i.7 344b1 1 in Aristotle's own theory, a comet can fall behind a fixed star or a planet; in the astronomical sense Liddell H. G. Scott R. (A Greek—English lexicon, ninth edn (Oxford, 1968)) do not cite any use earlier than Aristotle.

It may have been used by Democritus ( Diels Kranz , op. cit. (ref. 1), 68A88 “relinqui”).

Lucretius (De rerum natura, ed. and transl. by Bailey C. (Oxford, 1947), v.623–34: “the nearer the several stars are to Earth, the less can they be borne on with the whirl of heaven. For its swift keen strength passes away and is lessened beneath, and so little by little the Sun is left behind (relinqui) with the hindmost signs, because it is much lower than the burning signs. And even more the Moon: The lower her course, the farther it is from the sky and nearer to Earth, the less can she strain on her course level with the signs. Moreover, the weaker the whirl with which she is borne along, being lower than the Sun, the more do all the signs catch her up (adipiscuntur) all around and pass her (praeter feruntur). Therefore, it comes to pass that she seems to turn back more speedily to each several sign, because the signs come back to her”.

is not used by the preSocratics in this sense, but enjoys some limited use later: Ptolemy Almagest vi.6 487.1 and Cleomedes ii.5.129–32 (Todd).

Geminus rejects the notion of ‘lagging’ as properly descriptive of the complexity of planetary motions (xii.14–24), which shows that it represents an pre-Eudoxan stage in theorization. He attributes the model to many philosophers without naming them (xii.19): All the celestial bodies are carried around together by the same motion, but some, because of their size, lag behind the fixed stars. This conception does not place the various bodies in separate orbits nor does it take account of the oblique circle of the zodiac. Plato makes clear (Timaeus 39a4-b2) that this view is most appropriate when one does not distinguish the diurnal from the direct motion, though it can still be used to discuss the relative motions of the planets.

See Knorr W. , “Plato and Eudoxus on the planetary motions”, Journal for the history of astronomy, xxi (1990), 313–29; Bowen A. C. , “Simplicius and the early history of Greek planetary theory”, Perspectives on science, x (2002), 2002–67, p. 158.

There is no evidence that Hippocrates was concerned with retrograde motion. See also Bowen , op. cit. (ref. 13), 150.

As van der Waerden (“The earliest form of the epicycle theory”, Journal for the history of astronomy , v (1974), 175–85; Die Pythagoreer (Munich, 1979), 440–52) has argued, although it is remarkable that he did not cite Hippocrates as evidence in favour of his thesis. I follow the consensus, and reject the early epicycle view.

Meteorologica i.8 345a13–18; Diels Kranz , op. cit. (ref. 1), 41.10.

Diels Kranz , op. cit. (ref. 1), 31A58.

Diels Kranz , op. cit. (ref. 1), 59A1. Seneca argues in favour of multiple orbital planes, Naturales quaestiones vii.24.

Oinopides was a little younger than Anaxagoras ( Diels Kranz , op. cit. (ref. 1), 41.1); for the belt of the zodiac, Diels and Kranz, op. cit. (ref. 1), 41.7.

He does not mention that the Sun also lags the isodromous planets in turn.

Philoponus is followed by Vicomercatus F. ( In quattuor libros Aristotelis Meteorologicorum commentarii (Paris, 1556, and Venice, 1565), 28e—g), who largely paraphrases Philoponus; so also Ideler J. L. , Aristotelis Meteorologicorum libri quattuor (Leipzig, 1834–36), i. 385–7 (who merely quotes Vicomercatus); Heath T. , Aristarchus of Samos: The ancient Copernicus (Oxford, 1913), 243, who simply states that the comet is “left behind by the Sun very slowly indeed, so that for a long time it remains so close to the Sun as not to be visible”; and Lee H. D. P. , Aristotle's Meteorologica (Cambridge, 1952), 41n.f.

He does not mention that the isodromous planets have two conjunctions every synodic period.

Philoponus is not arguing, as he might have, about the periods of the planets' invisibility due to the Sun's rays. Saturn's period of invisibility is about 29–49 days, Jupiter's about 28–38 days, and Mars about 94–244 days (at 36°; Neugebauer P. V. , “Tafeln zur Berechnung der jährlichen Auf- und Untergänge der Planeten”, Astronomische Nachrichten, cclxiv (1938), cols 313–22).

Aristotle makes clear (343a8–9 and a14–15) that the dry area is not just the band of the zodiac, but the entire inter-tropical zone.

For heavenly bodies drawing up moisture: Herodotos 2.25.2: Democritus in Diels and Kranz, op. cit. (ref. 1), 68B25.

There is little evidence for theories of reflection in the fifth century. The Pythagoreans say that mirroring occurs through the reflecting back of the visual ray: “For the visual ray is stretched out and carried as against a bronze object, and meeting and striking against a dense and smooth [surface] it turns back upon itself doing something like the stretching out of the hand and the turning back to the shoulder” ( Diels H. , Doxographi Graeci (Berlin, 1929), 405). Mugler C. (Dictionnaire historique de la terminologie optique des Grecs (Paris, 1964), v.s. 4) notes that Plato (Timaeus 45c; 46b) is the first evidence for the term in the sense of visual ray.

Aristotle describes the basic idea, “the only star that appears to possess this movement is the Sun, at sunrise or sunset, and this appearance is due not to the Sun itself but to the distance () of our visual ray. The visual ray being excessively prolonged becomes weak and wavering. The same reason probably accounts for the apparent twinkling of the fixed stars and the absence of twinkling in the planets. The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed star it is quivering because of the distance () and its excessive extension” (De caelo ii.8 290a13–22; modified Revised Oxford Translation ( Barnes J. (ed.), The complete works of Aristotle (Princeton, 1984)). So also Mete. i.5 342b5–7; iii.4; iii.6 378a9–11.

Plutarch , De facie in orbe lunae, 929e.

A Diodotus appears in a couple of lists of authors as having written commentaries on Aratus and treatises on the poles (Hermippus Grammaticus, frr. 96.6 and 97.5 ( Wehrli F. , Die Schule des Aristoteles, Supplementband 1: Hermippos der Kallimacheer (Basel and Stuttgart, 1974))). For a discussion of the lists see Maass E. , “Das Vaticanische Verzeichniss der Aratcommentatoren”, Hermes, xvi (1881), 1881–92, and Wehrli, op. cit., 98–99; Diodotus is otherwise unknown.

E.g. Alexander , op. cit. (ref. 4), 49.20–3.

Cf. Geminus iv.2.

Burkert , op. cit. (ref. 1), 314n78 notes the similarity of the segment of the circle to the quadrature of the lunule. Netz, Eudemus (ref. 1), 276–7 argues for the inclusion of geometrical and physical material in the same book, but does not comment on the stylistic similarities.

The literature on Hippocrates's quadratures is extensive: More recently Knorr W. , The ancient tradition of geometrical problems (Boston, 1986; reprinted New York, 1993), 25–41; Lloyd G. E. R. , “The alleged fallacy of Hippocrates of Chios”, Apeiron, xx (1987), 103–28; and Netz , Eudemus (ref. 1, 2004).

“But it would seem that in [Democritus's] time there was nothing yet clear about images and reflection.” Compare Meteorologica ii.9 370a16–19 on Cleidemus's theory of lightning as reflection.

My translation accepts Hayduck's deletion of [], and interchange of and .

The comet's orbit plane cannot intersect the solar plane at the equinoctial points, since then the comet would never be in the southern sky. In this case, it would indeed be invisible in the south, but not for the reasons attested.