The Structure and Function of Ptolemy's Physical Hypotheses of Planetary Motion

British Museum , MS arab. 426 (Add. 7473), fol. 81b–102b (hereafter: BM), dated 1242, 81b, 1 – 88a, 3.

BM 88a, 4 — BM 92b, 14.

BM 93a, 1 — BM 95b, 27.

BM 96a, 1 — BM 102b, 21.

Neugebauer believed that Proclus (d. 485) did not have the complete text of Book I or any of Book II. His conclusion is based on the fact that Proclus failed to cite Ptolemy's placement of Venus and Mercury between the luminaries in the Hypotyposis and, in his commentary on the Timaeus, even claims that Ptolemy did not take up the question of planetary distances (cf. Neugebauer O. , History of ancient mathematical astronomy (New York, 1975; hereafter: HAMA), 918–19. Pingree and Ragep, however, have found a citation from Simplicius that corresponds to a passage at the beginning of Book II. Apparently, then, some part of this book survived in the West until at least the sixth century.

Bainbridge J. , (ed.), Prodi Sphaera, Ptolemaei de Hypothesibus Planetarium liber singularis, nunc primum in lucem editus (London, 1620).

Halma Abbé , Hypothèses des planètes ou movements des cercles célestespar C. Ptolémée (Paris, 1820).

Heiberg J. L. , Claudii Ptolemaei opera quae extant omnia, ii (Leipzig, 1907; hereafter: Heiberg), 69–145.

Leiden, MS arab. 115 (cod. 180 Gol.), fol. 1a — 44a (hereafter: L), 44a.

Pingree David , “The Greek influence on early Islamic mathematical astronomy”, Journal of the American Oriental Society, xciii (1973), 32–43, p. 42.

BM and L. Folios 23 and 24 of L are out of order.

Paris, MS hebr. 1028 (ancien fonds 470), fol. 54b — 87a.

Hartner Willy , “Mediaeval views on cosmic dimensions and Ptolemy's Kitāb al-Manshūrāt”, in Mélanges Alexandre Koyré, ed. by Cohen I. B. and Taton R. (Paris, 1964), i, 254–88.

Goldstein Bernard , “The Arabic version of Ptolemy's Planetary hypotheses”, Transactions of the American Philosophical Society, n.s., lvii, part 4 (Philadelphia, 1967).

HAMA, 900–26.

“La version Arabe du Livres des hypothèses de Ptolémée”, Mélanges Institut Dominicain d'Études Orientales du Cairo, xxi (1993), 7–85.

Heiberg, 70, 1. 1, and BM 81b, 5.

Heiberg, 70, 11. 6–8, and BM 81b, 20–21.

Heiberg, 70, 11. 8–10, and BM 81b, 21–22.

HAMA, 901–13.

If such a misreading did occur, both Arabic manuscripts descend from an incorrect text, as both read 22; 15.

HAMA, 908–9.

From the illustrations of the models in his 1620 Latin edition, it is clear that Bainbridge realized that Ptolemy's physical models, as seen in the Hypotheses, were descriptions of astronomical instruments. Among modern scholars, however, Sambursky S. , The physical world of late Antiquity (Princeton, 1962), 141–45, was the first of only a small number who have identified Ptolemy's objective in this text.

Heiberg, 70, 1. 20, and BM 81b, 14.

BM 95b, 20–23.

Heiberg, 70, 11. 15–18, and BM 81b, 11–13.

Van Helden Albert , Measuring the universe: Cosmic dimensions from Aristarchus to Halley (Chicago, 1985), esp. pp. 15–27.

Swerdlow Noel , “Ptolemy's theory of the distances and sizes of the planets”, Ph.D. dissertation, Yale University, 1968, esp. pp. 116–28 and 166–73.

Goldstein , op. cit. (ref. 14), 9–12.

BM 93a, 7.

BM 93a, 8–9.

Cf. Taub Chaia Liba , Ptolemy's universe (Chicago, 1993).

BM 93a, 14.

For instance, De caelo II, 292b: “We must, then, think of the action of the lower stars as similar to that of animals and plants.”

BM 94a, 3–5.

BM 93b, 20.

BM 93a, 25 — BM 93b, 4.

BM 94b, 4–9.

BM 95a, 5–8.

BM 95a, 12–14.

The nature of the prime mover is discussed in Metaphysics XII, vii, 1072a, 19 – 1072b, 31 and Physics VIII, vi, 258b, 10 – 260a, 19.

BM 95a, 15–16. Cf. Aristotle , Physics VII, i.

BM 94b, 3–4.

BM 94b, 7.

BM 95a, 23–26.

Cf. Metaphysics XII, viii, 1073b, 17 – 1074a, 18.

BM 93b, 25–27.

BM 94a, 8.

BM 94a, 23–25.

BM 94b, 3.

BM 94b, 24–25.

Since Ptolemy did not use this term in the extant section of Book I, the word he used to identify the sawn-off pieces is unknown. Hartner , “Mediaeval views” (ref. 13), 279, believes that Ptolemy would have chosen, and Toomer G. , Almagest (New York, 1984), 407, confirms this suggestion.

See also Hartner W. , “Falak”, in Encyclopedia of Islam, 2nd edn (Leipzig, 1960–), ii, 761.

BM 93b, 16. Cf. Plato , Republic X, 616b–617d.

HAMA, 922.

HAMA, 923.

BM 95b, 23.

BM 101a, 20–21.

BM 96a, 9–10.

BM 96a, 14.

BM 96a, 24 — BM 97a, 13.

This figure appears without error on BM 96b.

BM 98a, 3t.

BM 101b, 14–25.

BM 97a, 4.

BM 97a, 14 — BM 99a, 2.

A mislettered and misdrawn sketch of this figure occurs on BM 98b.

This term ‘parecliptic’ I have taken from J. Ragep's translation and commentary on Naṣīr al-Dīn al-Ṭūsī's Memoir on astronomy (al-Tadhkira fī 'ilm al-hay'a) (New York, 1993). Neugebauer (HAMA, 1079), however, notes that Nallino C. A. , Al-Battani sive Albatenii. Opus astronomicum, i (Milan, 1903), was the first to use this term. The parecliptic is a body that, as it revolves around its axis coinciding with that of the ecliptic, reproduces the motion of the ecliptic sphere, i.e. the slow progression of the apsides corresponding to the motion of the precession.

Heiberg, 102, 1. 16; 98, 1. 15; 94, 1. 14; and 90, 1. 15.

BM 98a, 22.

BM98a, 27.

BM98b, 1.

BM 98b, 20.

BM 98b, 22.

Neugebauer was the first to recognize the equant in this text: HAMA, 924.

BM 99a, 3–27.

A rough but essentially correct drawing of this figure appears on BM 99a.

BM99b, 1 — BM 100b, 16.

The figure for the Mercury model is entirely missing (BM 100b).

Heiberg, 86, 1. 27 and BM 84b, 11–12. Cf. Almagest IX, 9.

BM 99b, 19–20.

BM 100b, 17 — BM 101b, 13.

The figure for the lunar model is entirely missing (BM 101b).

Cf. Almagest V, 2.

Cf. Almagest V, 5.

BM 101b, 14–26.

Cf. HAMA, 926.

BM 93b, 16–17.

BM 102a, 4.

BM 101b, 19.

BM 101a, 20–21.

Cf. HAMA, 913.

BM 83a, 24 and BM 83b, 6; Heiberg, 80, ll. 11 and 24–25.

BM 94a, 10–17 and BM 102b, 309. Cf. HAMA, 904–5 and 913.

Both Arabic mss. list 230;19,13°, and Heiberg accepts the incorrect value 230;13° in his edition, 84, 1. 19.

This value is entirely missing from the Greek.

BM 102b, 9–17.

Heiberg accepts the following incorrect values: λ_A♂ = 110;44°, = 177;12°, = 52;16°, and =231;31°.

Cf. HAMA, 1005.

Ptolemy discusses a similar method of determining the true position in a section of the Handy tables entitled “”. Cf. abbé Halma , Tables manuelles astronomiques de Ptolemée et de Théon (Paris, 1823), 11.

Heiberg , 70, 11. 15–18 and BM 81b, 11–13.

Cf. Gingerich Owen , “The 1582 ‘Theorica Orbium’ of Hieronymus Vulparius”, Journal for the history of astronomy, viii (1977), 38–43.

Catalogued in Engelmann Max , Sammlung Mensing: Altwissenschafliche Instrumente Katalog (Amsterdam, 1924), 9 and the forthcoming Adler Planetarium catalogue (ed. by Chandler Bruce and Genuth Schechner Sara ).

This instrument is signed “HYRONIMVS VVLPARIA FLORENTINVS FA. A.D. M.D.L.XXV” on the lower face of the horizontal ring of the stand. See Levi Franco A. and Levi-Donati G. R. , “Due strumenti della scienza del Cinquecento custoditi a Perugia”, Bollettino della Deputazione di Storia Patria per l'Umbria, lxxxviii (1991), 119–29.

Catalogued in Horsky Zdeněk and Škopová Otilie , Astronomy gnomonics: A catalogue of instruments … in the collections of the National Technical Museum (Prague, 1968), 138–39 and Plate XXXIX.

See Turner A. , Early scientific instruments: Europe 1400–1800 (London, 1987), 34.