The works of Archimedes, trans. and ed. HeathThomas (Cambridge, 1897, 1912; reprinted New York [n.d.]), 223. In Hypothesis 6 Aristarchus assumed “that the Moon subtends one fifteenth part of a sign of the zodiac”, i.e. 2° (Thomas Heath, Aristarchus of Samos (Oxford, 1913), 353), but in Prop. 8 he proves that the apparent diameters of the Sun and Moon are equal.
2.
Heath, Aristarchus, 348.
3.
Albert Lejeune has given a masterful analysis of Archimedes's observation and its sources of error, “La dioptre d'Archimède”, Annales de la société scientifique de Bruxelles, ser. I, lxi (1947), 27–47. See also DelambreJ. B., Histoire de l'astronomie ancienne (Paris, 1817; reprinted New York, 1965), i, 103–5; HultschFriedrich, “Winkelmessungen durch die Hipparchische Dioptra”, Abhandlung zur Geschichte der Mathematik, ix (1899), 193–209; CzwalinaArthur, “Eine physikalische Präzisionsmessung des Archimedes”, Archiv für Geschichte der Mathematik, der Naturwissenschaften und der Technik, x (1927–28), 464–6; and DelsidimePiero, “Uno strumento astronomico descritto nel corpus Archimedeo: La dioptra di Archimede”, Physis, xii (1970), 173–96.
4.
For a description and analysis of this experiment see Lejeune, 31–35.
5.
See ToomerG. J., “The chord table of Hipparchus and the early history of Greek trigonometry”, Centaurus, xviii (1974), 6–28.
6.
Delambre, i, 104–5; Hultsch, 197; Lejeune, 38.
7.
Arenarius, Archimedis opera omnia, ed. HeibergJ. L. (Leipzig, 1913; reprinted Stuttgart, 1972), ii, 226–30.
Lejeune, 36–37, points out that while elsewhere in the text , which literally means “the organ of vision”, may be translated as “eye”, here, and in the remainder of the experiment to find the small correcting cylinder or magnitude, should be translated as “pupil”. Archimedes is measuring the area from which the eye sees, the pupillary opening, and not the size of the entire eyeball.
10.
Arenarius, Archimedis opera omnia, ii, 222–6; this passage should replace Heath's paraphrase, Archimedes, 223–4. This translation was initially made from Heiberg's Latin translation and Paul Ver Eecke's French, Les oeuvres complètes d'Archimède (Paris, 1960), i, 356–8. The translation was then compared with the Greek text and revised with the aid of Asger Aaboe, Robert Bennett, and Gerald Toomer, all of whom I wish to thank for their generous help.
, which literally means “the organ of vision”, may be translated as “eye”, here, and in the remainder of the experiment to find the small correcting cylinder or magnitude, 
should be translated as “pupil”. Archimedes is measuring the area from which the eye sees, the pupillary opening, and not the size of the entire eyeball.