GoldsteinBernard, “Theory and observation in medieval astronomy”, Isis, lxiii (1972), 39–47.
2.
The present author has completed a working edition of this book based on all the manuscripts known to be extant, and is currently engaged in preparing a critical edition to be sent to the press soon.
3.
For a synopsis of the contents of this Zīj, and the parameters underlying its tables, refer to KennedyE. S., “A survey of Islamic astronomical tables”, Transactions of the American Philosophical Society, xlvi (1956), 162–4.
4.
The manuscript quoted here for reference is Arabic Marsh 139 of the Bodleian Library, Oxford. The author wishes to thank the Keeper of Oriental Books at this library, and all other librarians who have supplied the microfilms necessary for this study.
5.
For a discussion of this method, and its possible early use, see NeugebauerO., “Thabit ben Qurra ‘On the solar year’ and ‘On the motion of the eighth sphere’”, Proceedings of the American Philosophical Society, cvi (1962), 264–99.
6.
Medieval astronomers devised other methods as well, such as the one using only three solar observations, two of them in opposition, at points on the zodiac where the solar declination varies sensibly from one day to the next. See SalibaG., “Solar observations at the Maraghah Observatory before 1275: A new set of parameters”, Journal for the history of astronomy, xvi (1985), 113–22, and idem, “The determination of the solar eccentricity and apogee according to Mu'ayyad al-Dīn al- Urḍī (d. 1266)”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, ii (1986), 47–67.
7.
Sexagesimal fractions written in this form mean (here, for example) 2 + 2/60 + 6/602.
8.
Cf. fols 6r and 8v for precession value being l°/70 Persian years, where he says ḥaqqaqtu dhālika bi-l-raṣd, and fol. 10v for the motion of the apogee as being l°/60 Persian years.
9.
We cannot discuss this very complicated problem here, nor could we survey the medieval literature that this problem had given rise to. The reader should consult SwerdlowN., “Ptolemy's theory of the distances and sizes of the planets: A study of the scientific foundations of medieval cosmology” (unpublished Ph.D. diss., Yale University, 1968), and GoldsteinB. and SwerdlowN., “Planetary distances and sizes in an anonymous Arabic treatise preserved in Bodleian Ms Marsh 621”, Centaurus, xv (1970–71), 135–70.
10.
RobertsVictor, “The solar and lunar theory of Ibn al-Sh¯ṭir: A pre-Copernican Copernican model”, Isis, xlvii (1957), 428–32.
11.
For a brief description of the model, cf.NeugebauerO., The exact sciences in Antiquity (Providence, R.I., 1957), 193–7.
12.
Roberts, op. cit.
13.
This study will include an analysis of the numerical methods given in Ibn al-Shāṭir's astronomical handbook (Bodleian Seld., A. 30, fols 83r-84r), and their effect on the determination of planetary sizes and distances.
14.
In general terms, a paraphrase of cUrḍī's Lemma states: If two equal lines are erected on the same side of a straight line, such that they produce two equal angles with the straight line, be they corresponding or interior, then the line connecting the extremities of the two equal lines will be parallel to the first straight line (Kitāb al-Hay'a, Bodleian Library, Ms. Arabic Marsh 621, fol. 158r). In Figure 2 line GD is always parallel to AB, if AG and BD are equal and describe equal angles with respect to line AB. The proof is straightforward; both when the corresponding angles DBE and GAB, or the interior angles DBA and GAB are equal, since with the construction of line DZ parallel to AG, both cases become identical and require only Elements I, 27–33 to be proved.
15.
NeugebauerO., “On the planetary theory of Copernicus”, Vistas in astronomy, x (1968), 89–103, esp. pp. 95–96, and p. 96 n.l.
