From Toledo to Venice: The Alfonsine Tables of Prosdocimo De' Beldomandi of Padua (1424)

For a transcription of the text, an analysis of its astronomical content, and an overview of its diffusion, see Chabás José Goldstein Bernard R. , The Alfonsine Tables of Toledo (Dordrecht and Boston, 2003).

Besides the works mentioned in Chabás Goldstein , The Alfonsine Tables of Toledo, 243–306, the reader may refer to North John D. , “The Alfonsine Tables in England”, in Maeyama Y. Salzer W. G. (eds), Prismata: Festschrift für Willy Hartner (Wiesbaden, 1977), 269–301; Chabás José Goldstein Bernard R. , “John Vimond and the Alfonsine trepidation model”, Journal for the history of astronomy, xxxiv (2003), 2003–70; de Mateo Beatriz Porres , Les tables astronomiques de Jean de Gmunden: Édition et étude comparative (Thèse de doctorat, École Pratique des Hautes Études; Paris, 2003); Chabás José , “Were the Alfonsine Tables of Toledo first used by their authors?”, Centaurus, xlv (2004), 2004–50; and Chabás José Goldstein Bernard R. , “Early Alfonsine astronomy in Paris: The tables of John Vimond (1320)”, Suhayl, iv (2004), 2004–94.

Descriptions of some of the manuscripts are found in Favaro A. , “Intorno alla vita ed alle opere di Prosdocimo de' Beldomandi matematico padovano del secolo XV”, Bulletino di bibliografia e storia delle scienze matematiche, xii (1879), 171–251, and xviii (1885), 405–23. See also Thorndike Lynn Kibre Paul , A catalogue of incipits of mediaeval scientific writings in Latin (London, 1963), cols 28 and 549.

Note that MSS B and V have Facta and MS S has Acta, beginning with a capital ‘A’.

MS S has aggregando.

Jacopo de Dondi was the father of Giovanni (c. 1328–89), the inventor of an ingenious astronomical instrument called astrarium and professor of astronomy at Padua, and Gabriele, who apparently was also acquainted with the Parisian Alfonsine Tables. For the biographies and activities of these three members of the Dondi family, see Pesenti T. , Dizionario biografico degli Italiani (Rome, 1992), xli, 95–111.

The term “signa phisica” appears in the heading of the table for the planetary stations in MS B, f. 21r and “signa physica” in that of MS V, f. 19v. For the meaning of this expression, see John of Saxony's canons to the Parisian Alfonsine Tables, in Poulle Emmanuel , Les tables alphonsines avec les canons de Jean de Saxe (Paris, 1984), 30.

For the Parisian Alfonsine Tables, see the editio princeps (Venice, 1483), ed. by Ratdolt Erhardt : Tabule astronomice illustrissimi Alfontij regis castelle. For a partial version of them, see Poulle , Les tables alphonsines (ref. 7). The Tables of Novara unfortunately have not been edited, but see Pedersen Fritz S. , The Toledan Tables: A review of the manuscripts and the textual versions with an edition (Copenhagen, 2002), 1205–7. For this work I have consulted Vatican, MS Vat. lat. 3118.

See Pedersen , Toledan Tables (ref. 8), 1259–308.

See Toomer Gerald J. , Ptolemy's Almagest (New York, 1984).

For an explanation of these values, see Neugebauer Otto , A history of ancient mathematical astronomy (Berlin, 1975), 208.

See Chabás Goldstein , “The tables of John Vimond” (ref. 2).

Lisbon , Biblioteca de Ajuda, MS 52-XII-35, ff. 63r–64r.

See Goldstein Bernard R. Chabás José , “Ptolemy, Bianchini, and Copernicus: Tables for planetary latitudes”, Archive for history of exact sciences, lviii (2004), 453–73.

We note, however, that Bianchini's extremal value for the deviation of Mercury is −0;45°, as in the Almagest.

However, the same value is found in various manuscripts of the Alfonsine corpus; see, e.g., Lisbon, Biblioteca de Ajuda, MS 52-XII-35, and Oxford, Bodleian Library, MS Can. Misc. 27, as well as in the Oxford Tables (e.g., Vienna, Nationalbibliothek, MS Vin. 2440).

See Goldstein Chabás , “Planetary latitudes” (ref. 14), 462.

Pedersen , Toledan Tables (ref. 8), 972–5 and 1037–71.

See Stahlman W. D. , The astronomical tables of Codex Vaticanus Graecus 1291 (Ph.D. diss., Brown University; University Microfilms, no. 62–5761 (1959)), 255–7.

For a justification of these formulas, see Neugebauer , op. cit. (ref. 11), 994–5.

See Pedersen , Toledan Tables (ref. 8), 1347.

If we assume, as the Parisian Alfonsine Tables do, that the apogees of the planets are at fixed distances from the solar apogee and, thus, that they all progress at the same rate, then the value called aux communis in the text should result from adding two components (one is a linear term and the other a sinusoidal term): The difference between solar apogee at epoch Alfonso and at epoch Incarnation (9;11,37° = 80;37,0° — 71; 25,23°), and the arc travelled by the solar apogee between these two epochs (8;11,26° = 8;4,1° + 0;7,25°). The result is 17;23,3° when using the Alfonsine values in the list of radices in the editio princeps (Ratdolt, 1483), c8r.

As indicated by Kunitzsch, Ptolemy actually catalogued 1025 stars, of which 3 stars in the constellation of Leo were counted separately from the current counting of 1022 stars: See also Kunitzsch Paul , “Albumasariana”, Annali, lxii (2002), 19–28.

See Kunitzsch Paul , Der Sternkatalog des Almagest: Die Arabisch-mittelalterliche Tradition, ii: Die lateinische Übersetzung Gerhards von Cremona (Wiesbaden1990).

The Libro de las estrellas de la ochaua espera, also known as Libro de las XLVIII figuras de la VIII spera and Libro de las estrellas fixas, was edited by Sinobas Manuel Rico , Libros del saber de astronomía del Rey D. Alfonso X de Castilla (Madrid, 1863–67), i, 5–145.

For an explanation of this value and the various approaches on its derivation, see Chabás Goldstein , The Alfonsine Tables of Toledo (ref. 1), 234–5 and 247–8.

Kunitzsch Paul , “The star catalogue commonly appended to the Alfonsine Tables”, Journal for the history of astronomy, xvii (1986), 90–92.

Vienna, Nationalbibliothek, MSS Vin. 5208 and 5415; Munich , Bayerische Staatsbibliothek, MSS Cgm 595, Clm 10662, and Clm 24103.