On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle

See Neugebauer O. , “The equivalence of eccentric and epicyclic motion according to Apollonius”, Scripta mathematica , xxiv (1959), 5–21.

See Pingree D. , “Astronomy and astrology in India and Iran”, Isis , liv (1963), 229–246, and Neugebauer O. Pingree D. , The Pañcasiddhântikâ of Varâhamihira (Copenhagen, 1971), passim.

See Pingree D. , The Yavanajâtaka of Sphujidhvaja , to appear shortly in the Harvard oriental series.

Pañcasiddhântikâ VIII, 1–6.

Pañcasiddhânlikâ III, 1–3. The arguments against a Greek origin presented by Chatterjee B. , most recently in her edition of Brahmagupta's Khaṇḍakhâdyaka (2 vols., Calcutta 1970: vol. i, pp. 264–295), are unconvincing if for no other reason because she assumes that Ptolemy is representative of all Greek astronomers.

Pingree D. , “The Paitâmahasiddhânta of the Viṣudharmottarapurâa”, Brahmavidyâ , xxxi-xxxii (1967–68), 472–510 (see III, 10–11 and IV, 7–12).

Sûryasiddhânta II, 2; Pingree , op. cit. (ref. 2), 242; and Bundahishn as translated by MacKenzie D. N. , “Zoroastrian astrology in the Bundahišn”, Bulletin of the School of Oriental and African Studies , xxvii (1964), 511–529 (see especially 516–517).

For a graphical representation of this model see Pañcasiddhântikâ II, 101, fig. 59.

DasAagîtikâ, 8–9. The Daśagîtikâ was not always included in the Åryabhatîya ; see, e.g., the recension of Nîlakantha .

Kâlakriyâ, 17–20.

E.g., Brahmagupta (628), Brâhmasphutasiddhânta XIV, 10–11 and XXI, 24; Bhâskara (ca 629), Mahâbhâskariya IV, 19–23 and 48–54; and Lalla (ca 750), Śiýdhîvrddhida , Golâdhyâya, Chedyakâdhikâra 8–12 and Grahagolabandha 3.

De caelo I, 2–3 (268b–269b) and II, 5–8 (287b–290b).

Eudemus via Sosigenes quoted by Simplicius, In De caelo II, 12 (p. 488, Heiberg ) = fr. 148 in Wehrli F. , Die Schule des Aristoteles , viii: Eudemos von Rhodes (Basel, 1955), 68. Cf. also Phaedrus 246E–247C; Republic 616B–617D; Timaeus 34B; 36B–D; 38C–39D; and 40A–D; and Laws 821B–822C.

Metaphysics λ, 8 (1073a–1074b).

Cf. ref. 27 below.

The eccentric model of the Sun is described by Geminus, Posidonius's pupil, in Introductio I, 31–41; see also Cleomedes I , 6 (the Sun) and II, 5 (all the planets).

Historia naturalis II, 59–73.

Syntaxis I, 1.

Syntaxis III, 3.

Hypotheses , p. 114, Heiberg.

Freudenthal J. , Die durch Averroes erhaltenen Fragmente zur Metaphysik des Aristoteles (Berlin, 1885), 111; Simplicius, In De caelo I, 2 (pp. 31–32, Heiberg).

Simplicius , In De caelo II, 12 (pp. 509–510, Heiberg).

Theon of Smyrna, τà κατà τò μαθηματικòν χρηαμ is την, ed. Hiller E. (Leipzig, 1878), 181–6. A contemporary qualitative epicyclic model is found in Mich P. . 149; see Aaboe A. in Centaurus , ix (1963), 1–10.

Proclus , In Platonis Timaeum commentaria , iii, 56–57; 96; and 146–149, Diehl.

Simplicius , In De caelo I, 2 (pp. 31–33, Heiberg) and II, 12 (pp. 504–7, Heiberg).

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.

Simplicius , In De caelo II, 12 (p. 505, Heiberg) = fr. 211 in Rose V. , Aristotelis fragmenta (Leipzig, 1886).

Simplicius , In De caelo II, 12 (p. 505, Heiberg).

Plato , Timaeus 38E–39B; Aristotle , De caelo II, 10 (291a–291b). The Indian ascending order before Greek influence was felt was apparently Sun, Moon, nakṣatras, and planets; see Kirfel W. , 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).

Goldstein B. R. , The Arabic version of Ptolemy's “Planetary Hypotheses” (Philadelphia, 1967), 6–7; see also Swerdlow N. , Ptolemy's theory of the distances and sizes of the planets , unpublished dissertation submitted to Yale University in 1968.

See, e.g., Paitâmahasiddhânta III, 6–7 and Pingree D. , “The Later Pauliśasiddhânta”, Centaurus , xiv (1969), 172–241 (fr. P58–P61).

See e.g., Paltâmahasiddhânta V, 2–4.

Pañcasiddhântikâ VIII, 15.