Four Lost Episodes in Ancient Solar Theory

Evans James Berggren J. Lennart , Geminos's Introduction to the Phenomena: A translation and study of a Hellenistic survey of astronomy (Princeton, 2006).

Dupuis J. , Théon de Smyrne philosophe platonicien: Exposition des connaissances mathématiques utiles pour la lecture de Platon (Paris, 1892); and Lawlor R. Lawlor D. , Theon of Smyrna: Mathematics Useful for Understanding Plato or, Pythagorean arithmetic, music, astronomy, spiritual disciplines (San Diego, 1979).

Toomer G. J. , Ptolemy's Almagest (Princeton, 1984), 153 ff.

Duke Dennis W. , “Hipparchus' eclipse trios and early trigonometry”, Centaurus, xlvii (2005), 163–177.

For the details of the geometrical analysis see ibid.; Toomer G. J. , “The chord table of Hipparchus and the early history of Greek trigonometry”, Centaurus , xviii (1973), 6–28 (although beware of several errors); Neugebauer O. , A history of ancient mathematical astronomy (Berlin, 1975), 75–76; and Neugebauer O. , The exact sciences in Antiquity, 3rd edn (New York, 1969), 211–14.

Britton John P. , Models and precision: The quality of Ptolemy's observations and parameters (New York, 1992), 14–24, is an excellent discussion of Hipparchus's observation errors.

Frans Bruin Margaret , “The equator ring, equinoxes and atmospheric refraction”, Centaurus, xx (1976), 89–111.

Britton , op. cit. (ref. 6), 24–37.

Toomer, op. cit. (ref. 3), 132–3. While Ptolemy records the results of many equinox determinations by Hipparchus, he reports only a single solstice determination. For a discussion and explanation of this see Jones Alexander , “In order that we should not ourselves appear to be adjusting our estimates to make them fit some predetermined amount”, in Buchwald J. Z. Franklin A. (eds), Wrong for the right reasons (= Archimedes, xi (2005)), 17–39. In addition, a recently discovered papyrus reveals an Hipparchan solstice determination for 26 June 158 b.c. not mentioned by Ptolemy: See Tihon Anne , “An unedited astronomical papyrus”, paper at the XXII International Congress of History of Science, Peking, 2005 (the abstract is at http://chama.fltr.ucl.ac.be/chama2/newsletter_5.htm).

Toomer , op. cit. (ref. 3), 137–8.

Ptolemy quotes a number of third century b.c. observations of Mercury from Babylon that he calls greatest elongations, but there is no evidence that the Babylonian observers made the series of measurements that is being discussed here. For a complete discussion see Jones Alexander , “Ptolemy's ancient planetary observations”, Annals of science, lxiii (2006), 255–90.

Toomer , op. cit. (ref. 3), 484.

Aaboe A. , “On the Babylonian origin of some Hipparchan parameters”, Centaurus, iv (1955), 122–5; Aaboe A. de Solla Price D. J. , “Qualitative measurement in Antiquity: The derivation of accurate parameters from crude but crucial observations”, Mélanges Alexandre Koyré, i (Paris, 1964), 1–20; and Britton J. P. , “Remarks on Almagest IV 2”, invited talk at ND VII, Notre Dame, 2005.

Toomer G. J. , “Hipparchus and Babylonian Astronomy,” in A scientific humanist: Studies in memory of Abraham Sachs, ed. by Leichty E. de J. Ellis M. Gerardi P. (Occasional Publications of the Samuel Noah Kramer Fund, 9; Philadelphia, 1988), 353–62.

Said S. S. Stephenson F. R. , “Precision of medieval Islamic measurements of solar altitudes and equinox times”, Journal for the history of astronomy, xxvi (1995), 117–32.

Duke Dennis W. , “Ancient declinations and precession”, DIO, xiii/3 (2006).

Sidoli Nathan , “Hipparchus and the ancient metrical methods on the sphere”, Journal for the history of astronomy, xxxv (2004), 73–86.

Pingree D. , “History of mathematical astronomy in India”, Dictionary of scientific biography, xv (1978), 533–633.

Duke Dennis W. , “Ptolemy's treatment of the outer planets”, Archive for history of exact sciences, lix (2005), 169–87.

Pingree D. , “The recovery of early Greek astronomy from India”, Journal for the history of astronomy, vii (1976), 109–23.

Duke Dennis W. , “The second lunar anomaly in ancient Indian astronomy”, Archive for history of exact sciences, lxi (2007), 147–57.

Duke , op. cit. (ref. 4), 176–7.

Jones Alexander , “Hipparchus's computations of solar longitudes”, Journal for the history of astronomy, xxii (1991), 101–25.

Thurston Hugh , “Three solar longitudes in the Almagest due to Hipparchus”, Journal for the history of astronomy, xxvi (1995), 164.

Jones Alexander , “Studies in the astronomy of the Roman period. IV: Solar tables based on a non-Hipparchian model”, Centaurus, xlii (2000), 77–88.

Jones Alexander , “Studies in the astronomy of the Roman period. II: Tables for solar longitude”, Centaurus, xxxix (1997), 211–29.

Ibid.

Jones Alexander , Astronomical Papyri from Oxyrhynchus (Memoirs of the American Philosophical Society, ccxxxiii), 119–21.

Neugebauer , op. cit. (ref. 5, 1975), 297–8.