Verification of Parallax in Ptolemy's Handy Tables

Tihon A. , “Les Tables faciles de Ptolémée dans les manuscrits en onciale (IX^e–X^c siècles)”, Revue d'histoire des textes, xxiii (1992), 47–87.

The use of the lower-case (v) to represent Vat. gr. 1291 may seem surprising; we have retained here the initials used in the edition of the Great commentary of Theon where V represents Vat. gr. 190 and v, Vat. gr. 1291: Tihon A. , Le “Grand commentaire” de Théon d'Alexandrie aux Tables Faciles de Ptolémée. Livres II et III (Studi e Testi, cccxl; Vatican, 1991).

Edited by Heiberg J. L. , Claudii Ptolemaei opera quae exstant omnia, ii: Opera astronomica minora (hereafter Op. min.) (Leipzig, 1907), 159–85. The text, as it appears in the manuscripts and in the edition of Heiberg, seems somewhat corrupt. An edition with a translation into French is to be found in Nicolas B. Halma, <image>. Commentaire de Théon d'Alexandrie sur le livre III de l'Almageste de Ptolémée. Tables manuelles des mouvemens des astres. Traduites pour la première fois du grec en française sur les manuscrits de la bibliothèque du Roi (3 parts, Paris, 1822–25), I, 1–26. The text and the translation are far from exact.

Books 1 to 4 have been edited by Rome A. , Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste , II and III (Studi e Testi, lxxii and cvi; Vatican, 1936, 1943). The remaining books are accessible only in the edition of Joachim Camerarius, produced in Basel in 1538: Claudii Ptolemaei Magnae constructionis, idest Perfectae caelestium motuum pertractationis lib. XIII. Theonis Alexandrini in eosdem commentariorum lib. XI.

Book I has been edited by Mogenet J. (Le “Grand commentaire” de Théon d'Alexandrie aux Tables Faciles de Ptolémée. Livre I, Histoire du texte, édition critique, traduction revues et complétées par A. Tihon; commentaire par A. Tihon (Studi e Testi, cccxv; Vatican, 1985)). Books II-III have been edited by Tihon A. (ref. 2). Book IV is in the process of being edited, and Book V is lost.

Edited by Tihon A. , Le “Petit commentaire” de Théon d'Alexandrie aux Tables Faciles de Ptolémée (Studi e Testi, ccvxxxii; Vatican, 1978).

Stahlman W. D. , The astronomical tables of Codex Vaticanus Graecus 1291 (University Microfilms no. 62–5761, 1960). Publication of this work is planned for 1993.

Delambre J. B. , Histoire de l'astronomie ancienne (2 vols, Paris, 1817; reprinted with preface by Neugebauer O. , New York and London, 1965), ii, 616–39; van der Waerden B. L. , “Die Handlichen Tafeln des Ptolemaios”, Osiris, xiii (1958), 54–78; Neugebauer O. , A history of ancient mathematical astronomy (3 vols, Berlin, Heidelberg and New York, 1975), ii, 969–1028.

The Almagest was edited by Heiberg J. L. , Claudii Ptolemaei opera quae exstant omnia, i: Syntaxis mathematica (2 vols, Leipzig, 1898, 1903); for the English translation, see Toomer G. J. , Ptolemy's Almagest (London, 1984).

For a discussion of this point, see Tihon , op. cit. (ref. 2), II, 111ff.

Ptolemy , Op. min. (ref. 3), 174, 25–175, 5; Theon , op. cit. (ref. 2), III, 262.

Neugebauer , op. cit. (ref. 8), ii, 993, n. 12, gives as the title <image>, “distance of the arc”, which does not agree with the manuscripts and which makes little sense. In v, the ends of the words <image> and <image> do not appear, so that they could, in fact, be read as <image>, “distance of the arc”, but this would not be consistent with the contents of col. 4.

Tihon , op. cit. (ref. 2), II, 61ff.

Heiberg , op. cit. (ref. 9), i, 174–87, 442–3, 48–63, respectively; Toomer , op. cit. (ref. 9), 123–9, 265, 57–60, respectively.

Tihon , op. cit. (ref. 2), III, 261ff.

Basel edition (ref. 4), 345–8. Commentary by Delambre , op. cit. (ref. 8), ii, 599ff.

Neugebauer , op. cit. (ref. 8), ii, 993.

Ibid.

The programme to compute parallaxes is explained in Chabás J. Roca A. , and Rodríguez X. , “Recalculació de taules de parai.laxi de finals de l'Edat Mitjana”, Actes de les III Trobades Cientifiques de la Mediterrània (Menorca, 1987), 237–48; for a summary in English, see Chabás J. , “The Astronomical Tables of Jacob ben David Bonjorn”, Archive for history of exact sciences, xlii (1991), 279–314. For the mathematical treatment of parallax, see especially Kennedy E. S. , “Parallax theory in Islamic astronomy”, Isis, xlvii (1956), 33–53 (reprinted in Studies in the Islamic exact sciences (Beirut, 1983), 164–84); Goldstein B. R. , The Astronomical Tables of Levi ben Gerson (New Haven, Conn., 1974), 116–22; Pedersen O. , A survey of the Almagest (Odense, 1974), 213–19; Neugebauer , op. cit. (ref. 8), i, 112–17.

Neugebauer , op. cit. (ref. 8), ii, 992, Table 33.

Ptolemy , Op. min. (ref. 3), 174–6. The relevant passage is found in the chapter concerning the parallax of the Moon: “… in the last columns are shown the sections of the horizon which are to be taken for the prosneusis. Thus, the degrees to be found there represent the arcs of the horizon delimited by the points of intersection on the latter of the point of the ecliptic which is setting and the meridional arc of the great circle perpendicular to the zodiac for the beginning of the dodecatemory”.