See NeugebauerO., “The equivalence of eccentric and epicyclic motion according to Apollonius”, Scripta mathematica, xxiv (1959), 5–21.
2.
See PingreeD., “Astronomy and astrology in India and Iran”, Isis, liv (1963), 229–246, and NeugebauerO.PingreeD., The Pañcasiddhântikâ of Varâhamihira (Copenhagen, 1971), passim.
3.
See PingreeD., The Yavanajâtaka of Sphujidhvaja, to appear shortly in the Harvard oriental series.
4.
PañcasiddhântikâVIII, 1–6.
5.
PañcasiddhânlikâIII, 1–3. The arguments against a Greek origin presented by ChatterjeeB., most recently in her edition of Brahmagupta's Khaṇḍakhâdyaka (2 vols., Calcutta1970: vol. i, pp. 264–295), are unconvincing if for no other reason because she assumes that Ptolemy is representative of all Greek astronomers.
6.
PingreeD., “The Paitâmahasiddhânta of the Viṣudharmottarapurâa”, Brahmavidyâ, xxxi-xxxii (1967–68), 472–510 (see III, 10–11 and IV, 7–12).
7.
SûryasiddhântaII, 2; Pingree, op. cit. (ref. 2), 242; and Bundahishn as translated by MacKenzieD. N., “Zoroastrian astrology in the Bundahišn”, Bulletin of the School of Oriental and African Studies, xxvii (1964), 511–529 (see especially 516–517).
8.
For a graphical representation of this model see PañcasiddhântikâII, 101, fig. 59.
9.
DasAagîtikâ, 8–9. The Daśagîtikâ was not always included in the Åryabhatîya; see, e.g., the recension of Nîlakantha.
10.
Kâlakriyâ, 17–20.
11.
E.g., Brahmagupta (628), BrâhmasphutasiddhântaXIV, 10–11 and XXI, 24; Bhâskara (ca629), MahâbhâskariyaIV, 19–23 and 48–54; and Lalla (ca750), Śiýdhîvrddhida, Golâdhyâya, Chedyakâdhikâra 8–12 and Grahagolabandha 3.
12.
De caeloI, 2–3 (268b–269b) and II, 5–8 (287b–290b).
13.
Eudemusvia Sosigenes quoted by Simplicius, In De caeloII, 12 (p. 488, Heiberg) = fr. 148 in WehrliF., Die Schule des Aristoteles, viii: Eudemos von Rhodes (Basel, 1955), 68. Cf. also Phaedrus246E–247C; Republic616B–617D; Timaeus34B; 36B–D; 38C–39D; and 40A–D; and Laws821B–822C.
14.
Metaphysics λ, 8 (1073a–1074b).
15.
Cf. ref. 27 below.
16.
The eccentric model of the Sun is described by Geminus, Posidonius's pupil, in IntroductioI, 31–41; see also CleomedesI, 6 (the Sun) and II, 5 (all the planets).
17.
Historia naturalisII, 59–73.
18.
SyntaxisI, 1.
19.
SyntaxisIII, 3.
20.
Hypotheses, p. 114, Heiberg.
21.
FreudenthalJ., Die durch Averroes erhaltenen Fragmente zur Metaphysik des Aristoteles (Berlin, 1885), 111; Simplicius, In De caeloI, 2 (pp. 31–32, Heiberg).
22.
Simplicius, In De caeloII, 12 (pp. 509–510, Heiberg).
23.
Theon of Smyrna, τà κατà τò μαθηματικòν χρηαμ is την, ed. HillerE. (Leipzig, 1878), 181–6. A contemporary qualitative epicyclic model is found in MichP.. 149; see AaboeA. in Centaurus, ix (1963), 1–10.
24.
Proclus, In Platonis Timaeum commentaria, iii, 56–57; 96; and 146–149, Diehl.
25.
Simplicius, In De caeloI, 2 (pp. 31–33, Heiberg) and II, 12 (pp. 504–7, Heiberg).
26.
Theon of Smyrna asserts (p. 188, Hiller) that Hipparchus (and Plato) preferred the epicycle over the eccentric because it is more natural. The authority of this assertion is questionable.
27.
Simplicius, In De caeloII, 12 (p. 505, Heiberg) = fr. 211 in RoseV., Aristotelis fragmenta (Leipzig, 1886).
28.
Simplicius, In De caeloII, 12 (p. 505, Heiberg).
29.
Plato, Timaeus38E–39B; Aristotle, De caeloII, 10 (291a–291b). The Indian ascending order before Greek influence was felt was apparently Sun, Moon, nakṣatras, and planets; see KirfelW., Das Purâna vom Weltgebäude (Bonn, 1954), 48–49 (where, however, the planets are listed in the order Mercury, Venus, Mars, Jupiter, and Saturn, indicating a conflation of the Greek tradition with the older Indian).
30.
GoldsteinB. R., The Arabic version of Ptolemy's “Planetary Hypotheses” (Philadelphia, 1967), 6–7; see also SwerdlowN., Ptolemy's theory of the distances and sizes of the planets, unpublished dissertation submitted to Yale University in 1968.
31.
See, e.g., PaitâmahasiddhântaIII, 6–7 and PingreeD., “The Later Pauliśasiddhânta”, Centaurus, xiv (1969), 172–241 (fr. P58–P61).
