Essay Review: Mathematical Astronomy in Antiquity,a History of Ancient Mathematical Astronomy

I am thinking of the late Islamic astronomers' successful attempts to approximate motions in algebraic curves (Moon, Mercury) resulting from the Ptolemaic theory by appropriately chosen superimposed circular motions.

Novum Organum, Book I, Aphorism 25, cited after The New Organon , ed. Anderson F. H. (The Liberal Art Press, New York, 1960), 44. First published 1620; Francis Bacon had doubtless no idea that Kepler had meantime dethroned the age-old axiom.

See my article on “The Young Avestan and the Babylonian Calendars and the Antecedents of Precession”, in the next issue of JHA.

See Sayili A. , The Observatory in Islam (Ankara, 1960), 72 et passim; and Hartner W. , “The Rôle of Observations in Ancient and Medieval Astronomy”, JHA, viii (1977), section 4, pp. 6f.

Fire conceived of as a terrestrial element seems no less mysterious a notion than ether. Both were never called into question seriously throughout the Middle Ages.

328 more figures accompany Books II and IV-VI (III, dealing with Egypt, comprises only 10 pages and has no figures), which makes in toto 619 figures, part of which are very complicated.

Almagest, III.1 (ed. Heiberg , i, 145).

A = 235/19 × 29;31,50,8,20^d = 365·2468223^d.

The first cycle starts with an Ululu₂ intercalary year in —502, and so do all later cycles except for the time of Artaxerxes; see Parker R. A. and Dubberstein W. H. , Babylonian chronology 626 B.C.–A.D. 75 (Providence, R.I., 1956), and Table 1 of my article cited in ref. 3. Each one of the 31 cycles down to s.e. 379 = a.d. 68, begins with the equinox (with a phase difference of 2 days at the most in the latest times) and no year starts before the equinox, except for —499, which due to an erroneous intercalation started on March 23, four days before vernal equinox.

The civil year has no intercalation.

The chronology of ancient nations (transl. Sachau E. , London, 1879), 12.

Nobody ever attempted to explain the reasons for choosing the year 375 of the Era Yazdagird. There can be no doubt that Bīrūnī himself was responsible for the reform.

In the equation (2c), p. 478, the denominations synodic and anomalistic have to change place.

Maeyama Y. , “On the Babylonian Lunar Theory”, Archives internationales d'histoire des sciences, xxviii, 21–35.

Gnomon, xliv (1972), 529–37; see pp. 534f. Note: Ibid., p. 534, n. 4, read S_A = 365·26063 instead of 365·26788.

See Tisserand F. , Traité de mécanique céleste, iii (Paris, 1894), section 74, pp. 152–5, and Strömgren E. and Strömgren B. , Lehrbuch der Astronomie (Berlin, 1933), 176.

Tisserand's approximate values are 206^d and 412^d, respectively (p. 154); a computation with the exact parameters yields 3232·582^d = 8·85017 sidereal years for one sidereal revolution of the line of apsides, and 411·7848^d for the Sun's return to the latter.

The book of instruction in the elements of the art of astrology, ed. and transl. Wright Ramsay R. (London, 1934), 104.

Opus astronomicum, ed. Nallino C. A. , i (Milan, 1903), 114.

Cf. my article on “The Rôle of Observations …” (see ref. 4), in which I show that the values obtained by the eastern Arabs are nearly perfect, while that of the westerner al-Zarqālī is wrong by 9;2°, and that of Copernicus by 2;3°. The first who reached again the high observational standard of the Islamic Middle Ages was Tycho Brahe (+1600). See also Hartner W. and Schramm M. , “Al-Bīrūnī and the Theory of the Solar Apogee: An Example of Originality in Arabic Science”, Scientific change, ed. Crombie A. C. (London, 1963), 206–18.

Almagest, ed. Heiberg , i, 207 (transl. Manitius , p. 145; see ref. 7).

See Neugebauer O. , Astronomical cuneiform texts, i (London, [1955]), No. 210 (pp. 271f.), Sect. 3, lines 11/12 and II B 8, p. 528.

The Uruk scheme (p. 359) and the GADEx texts (pp. 360ff.) of course make sense only if interpreted, as does Neugebauer without stressing it explicitly, as arranged in accordance with the tropical year.

See above, sub I B, and my article (see ref. 3).

The civil year has no intercalation (see ref. 10).

In the Table, short, “Neomenia”. Dates after Parker-Dubberstein (see ref. 9). In this context I refer to R. A. Parker's exhaustive analysis of the 25-year cycle in “The Calendars of Ancient Egypt”, Studies in ancient oriental civilization , no. 26 (Chicago, Ill., 1950), 13–23. Note: HAMA, p. 563, 1. 14, read invisibility instead of last visibility.

MS. Bodl. Or. 128, fol. 155r; see Hartner W. “Mediaeval Views on Cosmic Dimensions and Ptolemy's Kitāb al-Manshūrāt”, in Mélanges Alexandre Koyré, i: L'aventure de la science (Paris, 1964), 255–82, and “The Mercury Horoscope of Marcantonio Michiel of Venice”, in Vistas in astronomy, i (1955), 85–138; both also in Hartner W. , Oriens-Occidens (Hildesheim, 1968).

See ref. 27.

See Ginzel F. K. , Handbuch der mathematischen und technischen Chronologie, iii (Leipzig, 1914), 178ff.

See Hartner W. , “L'astronomia all'alba della civiltà cinese”, Accademia Nazionale dei Lincei: Problemi Attuali di Scienza e di Cultura, Quaderno No. 225 (Rome, 1977).