NeugebauerO., “Planetary Motion in P. Mich. 149”, Bulletin of the American Society of Papyrologists, ix (1972), 19–22.
2.
Pliny, Natural history, II, 66–76 (Loeb Classical Library, 212–21).
3.
van der WaerdenB. L., “Die Astronomie der Pythagoreer”, Verhandelingen Kon. Akad. Amsterdam, 1st series, xx, no. 1 (1951).
4.
Ed. Manitius, 18; the translation of his and other Greek texts in this section is taken from Thomas Heath, Aristarchus of Samos (Oxford, 1913), 269–71.
5.
TanneryP., La géométrie grecque (Paris, 1887), ch. 1.
6.
Ibid, 18–19.
7.
Ed. Heiberg, 507.
8.
Geminus, Isagoge (Ed. Manitius), 11.
9.
See van der WaerdenB. L., Science awakening, ii (Leiden, 1974), 294.
10.
van der WaerdenB. L., “Die Erkenntnistheorie der Pythagoreer”, Rete, i (1972), 209.
11.
See ref. 4.
12.
See ref. 10, and the article “Pythagoreer 1 D” in Pauly-Wissowa, Real-Enzyklopaedie, xxiv, col. 227.
13.
Ed. Friedlein, 35. Translation by MorrowG. R. (Princeton, 1970), 29.
14.
Ed. Friedlein, 38. Transl. Morrow, 31.
15.
On the four sciences see also MerlanPh., From Platonism to neo-Platonism (The Hague, 1953).
16.
NeuenschwanderE., “Die ersten vier Bücher der Elemente Euklids”, Archive for history of exact sciences, ix (1973), 325–80.
17.
DielsH., Die Fragmente der Vorsokratiker (Berlin, 1903), Pythagoreische Schule B 18.
18.
Die Harmonielehre des Klaudios Ptolemaios, Ed. Düring (Göteborg, 1930).
19.
See my paper, “Die Harmonielehre der Pythagoreer”, Hermes, lxxviii (1943), 161–99, 168.
20.
Ed. Kroll, 24, 27.
21.
van der WaerdenB. L., “Die Arithmetik der Pythagoreer”, Mathematische Annalen, cxx (1947), 127–53.
22.
Cf. the article cited in ref. 12.
23.
Heath, Aristarchus of Samos, 50.
24.
Ed. Heiberg, 471.
25.
Cf.SchiaparelliL., “Die kozentrischen Sphären des Eudoxos…”, Abh.zur Geschichte der Math., i (1877), 101–98.
26.
Excerpta ex Nicomacho, iii (Musici scriptores Graeci, ed. JanC., 1895), 271.
27.
See van der WaerdenB. L., “Die Aegypter und die Chaldäer”, Sitzungsberichte der Heidelberger Akad., 5. Abhandlung (1972).
28.
See ref. 3.
29.
Op. cit. (ref. 23), 257, footnote.
30.
SmyrnaeusTheon, Expositio rerum mathematicarum … (Ed. Hiller), 200. Cf. the article cited in ref. 12.
31.
In the article cited in ref. 10.
32.
Op. cit. (ref. 30), 188–9.
33.
Commentatio in Timaeum (Ed. Wrobel), chs 81 and 109–11.
