The Material Culture of Greek Astronomy

For more details on some of the objects discussed here, see Evans James , The history and practice of ancient astronomy (New York, 1998). A useful discussion of the instruments of observation is Dicks D. R. , “Ancient astronomical instruments”, Journal of the British Astronomical Association , lxiv (1954), 77–85. See also Price Derek J. , “Precision instruments: To 1500”, in Singer Charles (eds), A history of technology , iii (New York and London, 1957), 582–619. A good general introduction to the images of ancient and medieval science is Murdoch John E. , Album of science , i: Antiquity and the Middle Ages (New York, 1984).

Aujac Germain (ed. and transl.), Géminos: Introduction aux phénomènes (Paris, 1975). Carolus Manitius (ed. and transl.), Gemini elementa astronomiae (Leipzig, 1898).

Morrow Glenn R. (transl.), Proclus: A commentary on the First Book of Euclid's Elements (Princeton, 1970).

Geminus is vague in distinguishing between dioptrics and meteoroscopy. According to Geminus the parts of astronomy are “gnomonics, which is engaged with the measurement of the hours through the placement of gnomons; meteoroscopy, which discovers the different altitudes [of the pole?] and the distances of the stars and teaches many other complex matters from astronomical theory; and dioptrics, which examines the positions of the Sun, Moon and the other stars by means of just such instruments [i.e., dipotras]”. (Aujac (ed.), op. cit. (ref. 2), 117. Morrow , op. cit. (ref. 3), 34–35.) We shall see below that there were many different kinds of dioptra. Ptolemy ( Geography I, 3) uses meteoroskopion for an instrument for taking celestial observations and says that he has given its description. Proclus ( Hypotyposis VI, 2) uses meteoroskopeion for a more complex version of the armillary astrolabe described in Almagest V, 1. So it is clear that both dioptrics and meteoroscopy dealt with taking astronomical observations with instruments, most probably with two different classes of instrument. Geminus's classification of the mathematial sciences is discussed by Tannery Paul , La géométrie grecque (Paris, 1887), 38–42, and by Heath Thomas L. , A history of Greek mathematics (Oxford, 1921), i, 10–18. See also Rome A. , “L'astrolabe et le météoroscope d'apres le commentaire de Pappus sur le 5e livre de l'Almageste”, Annales de la Société Scientifique de Bruxelles , série A, xlvii (1927), 2e partie, 77–102. According to Pappus of Alexandria (fourth century a.d.), “one also calls mechanics those who are skilled in sphairopoïa and construct a representation of the heavens with the aid of the uniform circular motion of water” ( Hultsch F. (ed.), Pappi Alexandrini Collectionis quae supersunt (Berlin, 1876–78), iii, 1026; Ver Eecke Paul (transl.), Pappus d'Alexandrie: La collection mathématique (Paris, 1933), ii, 813–14).

Cicero , De re publica I, 14.

The source for these titles of Eudoxus's works is Hipparchus's Commentary on Aratus and Eudoxus. Carolus Manitius (ed. and transl.), Hipparchi in Arati et Eudoxi Phaenomena commentariorum libri tres (Leipzig, 1894), i, 2.1–3.

Mair A. W. Mair G. R. (eds and transl.), Callimachus, Lycophron, Aratus (London and Cambridge, Mass., 1921).

For photographs of the Farnese Atlas see Harley J. B. Woodward David (eds), The history of cartography , i: Cartography in prehistoric, ancient and medieval Europe and the Mediterranean (Chicago, 1987), 142–3. For a study of medieval celestial globes see Savage-Smith Emilie , Islamicate celestial globes: Their history, construction and use (Smithsonian Studies in History and Technology, xlvi; Washington, D.C., 1985). See also Brendel Otto J. , Symbolism of the sphere: A contribution to the history of earlier Greek philosophy (Leiden, 1977).

Ptolemy , Almagest VII, 2. Heiberg J. L. (eds), Claudii Ptolemaei Opera quae exstant omnia (Leipzig, 1898–1954), i: Syntaxis mathematica [= the Almagest]. For an English translation see Toomer G. J. , Ptolemy's Almagest (London, 1984).

Ptolemy , Almagest VIII, 3.

For Ptolemy's Phaseis, see Opera (ref. 9), ii: Opera astronomica minora , 1–67.

Neugebauer Otto , A history of ancient mathematical astronomy (New York, 1975), 928–31. It has also been suggested that Hipparchus used a globe as a calculating device in compiling the “phenomena” section of his Commentary on Aratus and Eudoxus. See Nadal R. Brunet J.-P. , “Le ‘Commentaire’ d'Hipparque, I. La sphère mobile”, Archive for the history of exact sciences , xxix (1984), 201–36, and “Le ‘Commentaire’ d'Hipparque, II. Position de 78 étoiles”, ibid. , xl (1989), 305–54. See also Grasshoff Gerd , The history of Ptolemy's star catalogue (New York, 1990), 190–1.

Plato , Timaeus 36B–D.

Geminus , Introduction to the Phenomena XVI, 10–12. For the mural of an armillary sphere, see Arnaud Pascal , “L'image du globe dans le monde romain: Science, iconographie, symbolique”, Mélanges de l'École Française de Rome , xcvi (1984), 53–116, p. 73; as well as Camardo D. Ferrara A. , Stabiae: Le ville (Castellamare di Stabia, 1989), 67–68.

Plato , Republic X, 616B–617D.

Theon Smyrna , Mathematical knowledge useful for reading Plato III, 16. Dupuis J. (transl.), Théon de Smyrne, Philosophe platonicien. Exposition des connaissances mathématiques utiles pour la lecture de Platon (Paris, 1892; reprinted Brussels, 1966).

Plato , Timaeus 40B-D.

For mentions of Archimedes's models see Plutarch, Marcellus XVII, 3–5; Ovid , Fasti VI, 277–80; Cicero , De re publica I, 14; Tusculan disputations I, 25; On the nature of the gods II, 34–35. In the latter passage, Cicero also mentions a similar planetary mechanism constructed by Posidonius, who was his contemporary.

Eecke Ver (transl.), op. cit. (ref. 4), ii, 813–14.

The standard authority is Gibbs Sharon L. , Greek and Roman sundials (New Haven, 1976). See also: Price D. J. , “Portable sundials in Antiquity”, Centaurus , xiv (1969), 242–66. Arnaldi Mario Schaldach Karlheinz , “A Roman cylinder dial: Witness to a forgotten tradition”, Journal for the history of astronomy , xxviii (1997), 107–17.

Stuart James Revett Nicholas , The antiquities of Athens (London, 1762; reprinted New York, 1968).

For Ptolemy's On the analemma see Opera (ref. 9), ii, 186–223.

For a translation with an especially useful commentary, see Soubiran Jean , Vitruve: De l'architecture, Livre IX (Paris, 1969).

Drecker Joseph , Die Theorie der Sonnenuhren (Berlin, 1925). See also Soubiran , op. cit. (ref. 23).

For an introduction to to Hellenistic hydraulics, see Landels J. G. , Engineering in the ancient world (Berkeley, 1978).

Vitruvius , On architecture IX, 8.8–15.

For references to the literature on these two disks, see Neugebauer, History (ref. 12), 870, notes 5 and 6. For a sketch of the fragments of the second disk, found at Grand in the Vosges, see King Henry C. , Geared to the stars (Toronto, 1978), 12. The Vosges disk has no constellation figures but is engraved with month names.

For Ptolemy's Planisphere, see Opera (ref. 9), ii, 224–59. On the early history of stereographic projection see Neugebauer, History (ref. 12), 857–79.

For this interpretation of the channels in the floor of the Tower of the Winds, see: de Solla Price D. , “Piecing together an ancient puzzle: The Tower of the Winds”, National geographic , April 1967, 586–96, and Noble J. V. Price D. J. , “The water clock in the Tower of the Winds”, American journal of archaeology , lxxii (1968), 345–55.

There is an enormous modern literature on the astrolabe. For a good introduction see North John , “The astrolabe”, Scientific American , ccxxx, no. 1 (January 1974), 96–106. Among the published museum catalogues with useful general introductions are: Gibbs Sharon , Planispheric astrolabes from the National Museum of American History (Smithsonian Studies in History and Technology, xlv; Washington, D.C., 1984); Turner A. J. , The Time Museum: Catalogue of the collection , i, Part 1: Astrolabes and astrolabe related instruments (Rockford, Ill., 1985); d'Hollander Raymond , L'astrolabe: Les astrolabes du Musée Paul Dupuy (Toulouse, 1993).

Neugebauer O. , “The early history of the astrolabe”, Isis , xl (1949), 240–56. For the oldest extant Greek treatise on the astrolabe, and a French translation, see Segonds Alain , Jean Philopon: Traité de l'astrolabe (Paris, 1981).

The most important source for the early history of this genre among the Greeks is the parapegma appended to Geminus's Introduction to the phenomena (ref. 2). A useful survey of Greek and Roman parapegamata is available in the article “Parapegma” by Albert Rehm in Paulys Real-Encyclopädie der classischen Altertumswissenschaft, Neue Bearbeitung von Wissowa G. (Stuttgart, 1894–). See also Neugebauer , History (ref. 12), 587–9.

Translation adapted from Grenfell Bernard P. Hunt Arthur S. , The Hibeh papyri: Part I (London, 1906), 152.

Diels H. Rehm A. , “Parapegmenfragmente aus Milet”, Sitzungsberichte der königlich Preussischen Akademie der Wissenschaften , 1904, 92–111. Roman display calendars also used the hole-and-peg technology. The Roman examples were based on the Roman calendar year. Some Roman examples exhibited calendrical information only (day of the week and day of the month) and no astronomical information at all. Others included holes for indicating the current zodiac sign. An especially interesting example is the large bronze tablet known as the Calendar of Coligny, found north of Lyons and dated to the second century a.d. It is inscribed in Gallic and is the most extensive known sample of an early written Celtic language. The Calendar of Coligny covered a five-year lunisolar cycle. For discussion and an illustration see McCluskey Stephen C. , Astronomies and cultures in early medieval Europe (Cambridge, 1998), 54–60.

See Evans , History and practice (ref. 1), 337–42.

Our knowledge of Babylonian planetary theory is based on about 300 extant cuneiform tablets. These are collected with translations and commentaries in Otto Neugebauer, Astronomical cuneiform texts 2nd edn (New York, 1983), which provides the best introduction to Babylonian planetary theory. For a brief account, see Evans , History and practice , 312–15, 317–34.

Theon Smyrna , Mathematical knowledge useful for reading Plato III (ref. 16), 30.

For an overview of the transmission problem, see Alexander Jones, “The adaptation of Babylonian methods in Greek numerical astronomy”, Isis , lxxxii (1991), 441–53. For a useful description of the extant material, see his “A classification of astronomical tables on papyrus”, in Swerdlow N. M. (ed.), Ancient astronomy and celestial divination (forthcoming). For detailed studies of the Oxyrhynchus material, see Jones Alexander , “Studies in the astronomy of the Roman period, I: The standard lunar scheme”, Centaurus , xxxix (1997), 1–36; “Studies in the astronomy of the Roman period, II: Tables for solar longitude”, ibid. , 211–29; and “Studies in the astronomy of the Roman period, III: Planetary epoch tables”, Centaurus , xl (1998), 1–41.

Manitius C. , (ed.), Procli Diadochi Hypotyposis astronomicarum positionum (Leipzig, 1909). One may also add the influence of Pierre Duhem's account in To save the phenomena, which made the Greek astronomers out to be heroes of positivism. Pierre Duhem, ΣΩZEIN TA ϕAINOMENA: Essai sur la notion de théorie physique de Platon à Galilée (Paris, 1908); English transl. by Doland Edmund Maschler Chaninah , To save the phenomena (Chicago, 1969). For a detailed refutation of Duhem's instrumentalist interpretation of Greek planetary theory see Lloyd G. E. R. , “Saving the appearances”, Classical quarterly , xxviii (1978), 202–22.

This papyrus, probably of the third century a.d., is discussed in Jones Alexander , “Babylonian and Greek astronomy in a papyrus concerning Mars”, Centaurus , xxxiii (1990), 97–114.

Ptolemy , Almagest IX, 2. The situation was not so bad for the Sun and Moon, for Hipparchus's work had resulted in a perfectly satisfactory solar theory and in a reasonably good lunar theory.

For an introduction to Ptolemy's planetary tables see Evans , History and practice (ref. 1), 372–84.

Benjamin Francis S. Jr Toomer G. J. , Campanus of Novara and medieval planetary theory (Madison, 1971).

Proclus , Hypotyposis III, 66–72; Manitius , op. cit. (ref. 39), 72–77.

Ptolemy , Planetary hypotheses I, 2. Opera (ref. 9), ii, 72–73.

Ptolemy , Canons to the Handy Tables, Opera (ref. 9), ii, 165–9. [Nicolas] Halma (ed. and transl.), Commentaire de Théon d'Alexandrie sur les tables manuelles astronomiques de Ptolémée (3 vols, Paris, 1822–25), i, 7–11.

For an introduction to the history of the equatorium see North John , Richard of Wallingford (Oxford, 1976). A comprehensive study of the later period is provided by Poulle Emmanuel , Les instruments de la théorie des planètes selon Ptolémée: Equatories et horlogerie planétaire du XIIIe au XVIe siècle (Geneva and Paris, 1980). For a detailed study of a later Islamic instrument see Kennedy E. S. , “A fifteenth-century planetary computer: Al-Kashi's ‘Tabaq al-Manateq’”, Isis , xliii (1952), 42–50 and idem, The planetary equatorium of Jamshid Ghiyath al-Din al-Kashi (d. 1429) (Princeton, 1960). For the equatorium attributed to Chaucer see Derek J. de Solla Price, The equatorie of the planetis (Cambridge, 1955). For the sumptuous Renaissance equatoria of Petrus Apianus see Owen Gingerich, “Apianus's Astronomicum Caesareum and its Leipzig facsimile”, Journal for the history of astronomy , ii (1971), 168–77, and Ionides S. A. , “Caesar's Astronomy (Astronomicum Caesareum) by Peter Apian, Ingolstadt 1540”, Osiris , i (1936), 356–89.

Schöner Johann , Aequatorium astronomicum (Bamberg, 1521; reprinted, Nuremberg, 1534). For the use of these instruments see Evans, History and practice (ref. 1), 405–10.

de Solla Price D. , “Gears from the Greeks: The Antikythera mechanism — A calendar computer from ca. 80 BC”, Transactions of the American Philosophical Society , n.s., lxiv/7 (1974). For a revision of some details of Price's reconstruction, see Bromley Allan G. , “Notes on the Antikythera mechanism”, Centaurus , xxix (1986), 5–27.

Field J. V. Wright M. T. , “Gears from the Byzantines: A portable sundial with calendrical gearing”, Annals of science , xlii (1985), 87–138.

Sources for Meton's solstice include Ptolemy, Almagest III, 1 and Siculus Diodorus , Histories XII, 36.1–2. Of course, Meton did not express the date in terms of the Egyptian calendar; rather, this is the result of a conversion applied later by Hellenistic astronomers. The stated time of equinox is more than a day early.

Ptolemy , Almagest II, 6. Strabo , Geography II, 2.3–3.2.

Pliny , Natural history II, 182. See also Vitruvius , On architecture IX, 7.1.

Strabo , Geography I, 4.4, transl. by Jones H. L. . Pytheas of Massilia was a navigator, famous among the Greeks, who, around 285 b.c., explored the northwest coast of Europe. He recorded his exploits in a book, On the ocean, which has not survived.

Ptolemy , Almagest I, 12. This instrument is sometimes called the plinth. Ptolemy also describes a second form of meridian instrument, in which a complete graduated circle, engraved on a metal ring, replaces the quadrant. Proclus also gives a detailed discussion of the meridian ring in Hypotyposis III, 5–27. According to Proclus, this instrument should be not less than one half cubit in diameter. But a meridian ring of such small size would be so inadequate that we may well wonder how much experience Proclus had with real instruments. Both the quadrant and the meridian ring are discussed by Theon of Alexandria in his commentary on the Almagest. See Rome A. (ed.), Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste , ii: Théon d'Alexandrie, Commentaire sur les livres 1 et 2 de l'Almageste (Studi e Testi, lxxii; The Vatican, 1936), 513–26. For a still useful French translation see [Nicolas] Halma, Commentaire de Théon d'Alexandrie sur le premier livre de la Composition Mathématique de Ptolémée (Paris, 1821; reprinted Paris, 1993), 219–27. For valuable insights into the use of these instruments, see Britton John P. , Models and precision: The quality of Ptolemy's observations and parameters (New York, 1992).

Ptolemy , Almagest III, 1.

Theon Smyrna , Mathematical knowledge useful for reading Plato III (ref. 16), 12.

Ptolemy , Almagest I, 12.

Ptolemy , Almagest III, 4.

Ptolemy , Almagest III, 1. Theon of Alexandria makes a few remarks about observing with such rings and implies that their diameters are generally “not less than two cubits” ( Rome A. (ed.), Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste , iii: Théon d'Alexandrie, Commentaire sur les livres 3 et 4 de l'Almageste (Studi e testi, cvi; The Vatican, 1943), 817–18).

Bruin Frans Bruin Margaret , “The equatorial ring, equinoxes and atmospheric refraction”, Centaurus , xx (1976), 89–111. Rome A. , “Les observations d'équinoxes et de solstices dans le chapitre 1 du livre 3 du Commentaire sur l'Almageste par Théon d'Alexandrie”, Annales de la Société Scientifique de Bruxelles , lvii (1937), 213–36 and lviii (1938), 6–26. See also Britton , Models and precision (ref. 55).

In the Almagest, Ptolemy makes a few vague references to atmospheric refraction. For example ( Almagest I, 3) he mentions the familiar Moon illusion — the supposed fact that celestial bodies look bigger when they are near the horizon — and makes an analogy to the change in apparent size of objects immersed in water. But in his later Optics (V, 23–31) Ptolemy presents a very cogent discussion of atmospheric refraction. He notes that a celestial body when rising or setting appears to lie on a more northerly circle of declination and says that this is seen with the aid of an instrument for measuring stars. This could well refer to the use of an armillary sphere. Ptolemy also offers a psychological explanation of the Moon illusion ( Optics III, 59–61). Smith Mark A. , “Ptolemy's theory of visual perception: An English translation of the Optics with introduction and commentary”, Transactions of the American Philosophical Society , n.s., lxxxvi/2 (1996), 238–42 and 151–2. Cleomedes is the only other ancient writer who seems to be aware that refraction of the visual ray might have consequences for astronomy. Cleomedes mentions an eclipse of the Moon in which both the Sun and the Moon were seen above the horizon. Todd Robert (ed.), Cleomedis Caelestia (METEΩPA) (Leipzig, 1990), II, 6. For a French translation of Ziegler's 1891 edition of the Greek text see Goulet Richard , Cléomède. Théorie élémentaire (Paris, 1980), 171–4. The dates of Cleomedes are highly uncertain. Some writers have placed him in the first century a.d., others in the fourth.

On the use of the armillary sphere as instrument of observation see Evans James , “On the origin of the Ptolemaic star catalogue”, Journal for the history of astronomy , xviii (1987), 155–72 and 233–78. A number of details of practice that had not been noticed by bookish historians were discovered and elucidated by J. Włodarczyk, who actually made and used one of these instruments. See his “Examining the armillary sphere”, Journal for the history of astronomy , xviii (1987), 173–95. The debate over the origin of the star catalogue was reopened in the modern period by Robert R. Newton, The crime of Claudius Ptolemy (Baltimore, 1977). The most detailed study, with a history of the debate up to 1990, is Grasshoff , The history of Ptolemy's star catalogue (ref. 12). For a useful brief overview of the principal arguments, see Thurston Hugh , Early astronomy (New York, 1994), 150–5. For a recent development, favouring a Hipparchan date for the catalogue, see Dambis A. K. Efremov Yu. N. , “Dating Ptolemy's star catalogue with the proper motions: Hipparchan epoch”, Journal for the history of astronomy , forthcoming. According to Pappus, the diameter of the astrolabe is one cubit. The similar but more complex meteoroscope is half as large. Rome A. (ed.), Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste , i: Pappus d'Alexandrie, Commentaire sur les livres 5 et 6 de l'Almageste (Studi e Testi, liv; Rome, 1931), 6. See also Rome , op. cit. (ref. 4).

Evans , “On the origin of the Ptolemaic star catalogue” (ref. 63), 162–3.

Raeder H. Stromgren E. Stromgren B. , Tycho Brahe's description of his instruments and scientific work as given in Astronomiae instauratae mechanica (Copenhagen, 1946). See also Thoren Victor , The Lord of Uraniborg: A biography of Tycho Brahe (Cambridge, 1990).

Berggren J. L. Thomas R. S. D. , Euclid's Phaenomena: A translation and study of a Hellenistic treatise in spherical astronomy (New York, 1996), Proposition 1, 52–53.

Copernicus , On the revolutions of the heavely spheres I, 6.

Geminus , Introduction to the phenomena XII, 1–4.

Dicaearchus is mentioned as an authority on the heights of mountains by Theon of Smyrna, Mathematical knowledge useful for reading Plato III (ref. 16), 3.

For the text of Hero's Dioptra see Heronis Alexandrini Opera quae supersunt omnia , iii, ed. by Schone H. (Leipzig, 1903). See also Drachman A. G. , “Hero's dioptra and levelling instrument”, in Singer (ed.), A history of technology (ref. 1), iii, 609–12, and Drachman A. G. , “A detail of Hero's dioptra”, Centaurus , xiii (1950), 241–7.

Ptolemy , Almagest V, 14. Ptolemy says that Hipparchus used a dioptra four cubits long.

For a discussion of Archimedes's Sand reckoner see Dijksterhuis E. J. , Archimedes , transl. by Dikshoorn C. (Princeton, 1987). For the dioptra, see pp. 364–5.

Pappus gives a short description of the dioptra in his commentary on Book V of the Almagest. See Rome , Commentaires , i (ref. 63), 90–92. The most detailed ancient description is in Proclus, Hypotyposis (ref. 39) IV, 87–99.

Ptolemy , Almagest V, 12. For a Renaissance illustration of an astronomer using this instrument see Cuningham William , The cosmographicall glasse (London, 1559), figure reproduced in Olaf Pedersen, Early physics and astronomy (2nd edn, Cambridge, 1993), 80.

For the text of the Canobic inscription, see Ptolemy , Opera (ref. 9), ii, 149–55. For a discussion of the contents see Neugebauer , History (ref. 12), 913–17.

Hamilton N. T. Swerdlow N. M. Toomer G. J. , “The Canobic Inscription: Ptolemy's earliest work”, in Berggren J. L. Goldstein B. R. (eds), From ancient omens to statistical mechanics: Essays on the exact sciences presented to Asger Aaboe (Copenhagen, 1987), 55–73.

For a discussion of the Keskinto inscription see Neugebauer , History (ref. 12), 698–705. For a squeeze of the inscription see Tannery Paul , Mémoires scientifiques (17 vols, Paris, 1912–50), xv, 119. For the text, see de Gaertringen Hiller F. , Inscriptiones Graecae insularum Rhodi, Chalces, Carpathi cum Saro Cosi (Inscriptiones Graecae, xii/1; Berlin, 1895), inscription no. 913. For the mention of the boards of the astronomy of Eudoxus at Delos, see Vallois R. , “Le temple Délien d'Arsinoé Philadelphe ou d'Agathé Tyché”, Comptes rendues de l'Académie des Inscriptions et Belles Lettres , 1929, 32–40, p. 36; and Dürrbach F. Roussel P. (eds), Inscriptions de Délos , iii (Actes des fonctionnaires Athéniens préposés à l'administration des sanctuaires après 166 av. J.-C. (nos. 1400–1479); Paris, 1935), no. 1442B, lines 41–42. For the inscription of Diogenes of Oenoanda, see Smith Ferguson Martin , The Epicurean Inscription (Naples, 1993), and idem, The philosophical inscription of Diogenes of Oinoanda (Vienna, 1996).

Ptolemy , Almagest I, 1.

Strabo , Geography XVII, 1.17.

Geminus , Introduction to the phenomena II, 5. Strabo , Geography XVI, 1.6. Sextus Empiricus, Against the professors V, 2. Cicero , On divination II, 87–89. Vitruvius , On architecture IX, 6.2. The assertion of the Greek and Roman writers has been confirmed by the discovery of cuneiform horoscopes. For these, see Sachs A. , “Babylonian horoscopes”, Journal of cuneiform studies , vi (1952), 49–75.

Several good treatments of Greek and Roman astrology are available. A classic and still indispensible work is Bouché-Leclercq A. , L'astrologie grecque (Paris, 1899; reprinted Brussels , 1966). A good brief account of the basic principles is provided in the introduction to Goold G. P. , Manilius: Astronomica (Cambridge, Mass., 1977). For an accessible treatment that is up to date in terms of historical evidence, see Barton Tamsyn , Ancient astrology (London, 1994). For the place of astrology in the public life of Rome see Cramer Frederick H. , Astrology in Roman law and politics (Memoirs of the American Philosophical Society, xxxvii (1954)). Of vital importance for reconstructing the actual practice of ancient Greek astrology are the extant Greek horoscopes collected in Neugebauer O. van Hoesen H. B. , Greek horoscopes (Memoirs of the American Philosophical Society, xlvii (1959)). For entry to the enormous mass of late Greek astrological material, see Catalogus codicum astrologorum Graecorum (12 vols, Brussels, 1898–1953).

On the archaeology of Nemrut Dag see Akurgal K. , Ancient civilisations and ruins of Turkey 4th edn (Istanbul, 1978), 346–51.

The most important of these is the Anthology of Vettius Valens (late second century a.d). Pingree David (ed.), Vettii Valentis Antiocheni Anthologiarum libri novem (Leipzig, 1986). Also significant is the astrological poem of Dorotheus of Sidon, which however, survives only in an Arabic translation. Pingree David (ed. and transl.), Dorothei Sidonii Carmen astrologicum (Leipzig, 1976).

Betz Dieter Hans , The Greek magical papyri in translation , i (Chicago, 1986), 312; Betz's inventory number PGM (for Papyri Graecae Magicae) CX, lines 1–12.

For examples, see Barton , Ancient astrology (ref. 81), Plate 13.

Homer , Iliad XVIII, 478–89.

Earlier writers sometimes call this P. Parisinus 1. But it is now kept at the Musée du Louvre under the number N 2325. For the text see Blass F. , Eudoxi ars astronomica (Kiel, 1887). For a French translation see Tannery Paul , Recherches sur l'histoire de l'astronomie ancienne (Paris, 1893), 283–94.

Description de l'Égypte, ou, Recueil de observations et des recherches qui ont été faites en Égypte pendant l'éxpédition de l'armée française, publié par les ordres de Sa Majesté l'empereur Napoléon le Grand (Paris, 1809–28), iv, Plate 21. For another Greco-Egyptian zodiac (this one from Latopolis), see Plate 87 to vol. i in the same work. For a brief but interesting discussion of the Dendera zodiac, see Gingerich Owen , “Astronomical scrapbook: Ancient Egyptian sky magic”, Sky & telescope , May 1983, 418–20. For a discussion and illustrations of the Egyptian consellations, see Neugebauer Otto Parker Richard A. , Egyptian astronomical texts (London, 1969), iii.

The standard source for Babylonian constellations is Felix Gössmann, Planetarium Babylonicum oder Die Sumerisch-Babylonischen Stern-Namen , Deimel Anton (ed.), Sumerisches Lexikon , iv/2 (Rome, 1950). See also Hunger Hermann Pingree David , MUL.APIN: An astronomical compendium in cuneiform (Horn, Austria, 1989). For a photograph of a boundary stone in the British Museum decorated with astronomical images see Hoskin Michael (ed.), The Cambridge illustrated history of astronomy (Cambridge, 1997), 22.

Manilius , Astronomica II, 453–65. Sextus Empiricus, Against the professors V, 21–22.

The fundamental survey of Mithraic material is Maarten Vermaseren, Corpus inscriptionum et momumentorum religionis mithriacae (2 vols. The Hague, 1956–60). See also Campbell Leroy C. , Mithraic iconography and ideology (Leiden, 1968).

For a description of the other features of this relief and references to the vast literature concerning it, see Vermaseren , Corpus inscriptionum (ref. 91), ii, 64–66.

For two recent attempts at an astronomical interpretation see Ulansey David , The origins of the Mithraic mysteries: Cosmology and salvation in the ancient world (Oxford, 1989), and North J. D. , “Astronomical symbolism in the Mithraic religion”, Centaurus , xxxiii (1990), 115–48.

A useful tool is the table of astronomical motifs on Greek and Roman coins by Anson L. , Numismata Graeca , vi (1916), 1ff, reprinted in Cramer, Astrology in Roman law (ref. 81).

See A catalogue of the Greek coins in the British Museum: The Ptolemies, Kings of Egypt (London, 1883).

For the story see Callimachus , Aetia 110 and Catullus , poem 66.

For a detailed study see Ramsey John T. Licht Lewis A. , The comet of 44 BC and Caesar's funeral games (Atlanta, 1997). The earliest Roman accounts of this object described it as a star (sidus) and the earliest coins to depict it showed it without a tail. The images on coins acquired a tail in 17 b.c. See Weinstock Stefan , Divus Julius (Oxford, 1971), 379.

For many other examples see Mattingly Harold , Coins of the Roman Empire in the British Museum , i: Augustus to Vitellius (London, 1923; revised 1976). Augustus was born under Libra and therefore presumably conceived under Capricorn (Bouché-Leclerq, op. cit. (ref. 81), 369). The Capricorn also symbolized the ascent of the Sun after the solstice and, hence, the birth of a new age.