Alfonsine Meridians: Tradition versus Experience in Astronomical Practice c. 1500

Aurifaber Stanislaus , Ephemerides anni Christi MDCII (Cracow, 1512), sig. ai^v; Angelus Joannes , Almanach novum atque correctum … calculatum super anno domini 1512 (Vienna, 1512), sig. ii^v, transl. in Dobrzycki Jerzy Kremer Richard L. , “Peurbach and Marāgha astronomy? The ephemerides of Johannes Angelus and their implications”, Journal for the history of astronomy , xxvii (1996), 187–237, p. 222.

Dobrzycki Kremer , op. cit. .

Aurifaber , op. cit. (ref. 1), sig. ai^v.

See Kennedy Edward S. Kennedy Helen Mary , Geographical coordinates of localities from Islamic sources (Frankfurt, 1987). The Toledan Tables generally did not include tables for converting solar and lunar radices to non-Toledan meridians. The Canones Azarchelis, which often accompany the Toledan Tables in manuscript, do briefly describe how such conversions might be made, given knowledge of a local meridian; however, they offer no instructions for determining local meridians. See Toomer G. J. , “A survey of the Toledan Tables”, Osiris , xv (1968), 5–174, pp. 9, 134–5; Pedersen Fritz S. , “Canones Azarchelis: Some versions and a text”, Cahiers de l'Institut du Moyen Âge Grec et Latin , liv (1987), 129–218, pp. 172–3.

Strabo , Geography 1.1.12, quoted in Germaine Aujac, “Greek cartography in the early Roman world”, in Harley J. B. Woodward David (eds), The history of cartography (Chicago, 1987), i, 166–76, p. 166. For reviews of the development of knowledge of longitudes in medieval cartographic and astronomical traditions, see Schoy C. , “Längenbestimmungen und Zentralmeridian bei den älteren Völkern”, Mitteilungen der k.k. geographischen Gesellschaft in Wien , lviii (1915), 27–62; Wright Kirtland John , “Notes on the knowledge of latitudes and longitudes in the Middle Ages”, Isis , v (1922), 75–98; Mercier Raymond P. , “Meridians of reference in pre-Copernican tables”, Vistas in astronomy , xxviii (1985), 23–27; idem, “Geodesy”, in Harley Woodward (eds), op. cit. , ii/1 (1992), 175–88; Tibbetts Gerald R. , “The beginnings of a cartographic tradition”, ibid. , 90–107; and especially Durand Bennett Dana , The Vienna-Klosterneuburg map corpus of the fifteenth century: A study in the transition from medieval to modern science (Leiden, 1952).

See Wright , op. cit. (ref. 5), 85; Mercier Raymond , “Astronomical tables in the twelfth century”, in Adelard of Bath , ed. by Burnett Charles (London, 1987), 87–118, p. 108.

Wright , op. cit. (ref. 5), 94–95.

Durand , op. cit. (ref. 5), 132–44.

Schoener Johannes , (ed.), Scripta clarissimi mathematici M. Ioannis Regiomontani (Nuremberg, 1544), republished in facsimile by Schmeidler Felix (ed.), Joannis Regiomontani opera collectanea (Osnabrück, 1972), 645–51. See Durand , op. cit. (ref. 5), 102–13, 335–6.

Durand , op. cit. (ref. 5), 102–13, 335–6, p. 105. See Dobrzycki Jerzy , “Astronomy versus cartography: Late medieval longitudes”, Vistas in astronomy , xxviii (1985), 187. For sixteenth-century examples of computing meridians from eclipse observations, in both astronomical and navigational contexts, see Zinner Ernst , Leben und Wirken des Joh. Müller von Königsberg genannt Regiomontanus 2nd edn (Osnabrück, 1968), 188–9; Randles W. G. L. , “Portuguese and Spanish attempts to measure longitude in the 16th century”, Vistas in astronomy , xxviii (1985), 235–41.

Durand , op. cit. (ref. 5), 107, mentions finding some lists, which added several European cities to the Islamic places of the tabula regionum accompanying the Toledan Tables, in (unspecified) manuscripts of the Alfonsine Tables. The editio princeps of the Alfonsine Tables, published in 1483 by Erhard Ratdolt in Venice, did include a tabula regionum, listing latitudes and longitudes for 146 places. The origins of this tabula, which combines Islamic and European places, remains unstudied. See Wagner Hermann , “Ueber das von S. Günther 1888 herausgegebene spätmittelalterliche Verzeichnis geographischer Koordinatenwerte”, Nachrichten von der königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen , 1891, 256–78.

See Gingerich Owen , “Erasmus Reinhold and the dissemination of Copernican theory”, Studia Copernicana , vi (1973), 43–62, 123–25.

Despite the prevailing uniformity, a significant portion of the manuscripts in our sample contain glossed radices that yield divergent meridians for the same place, as indicated in the first column of Appendix 1. Apparently, Alfonsine users circulated local radices without always confirming their internal consistency.

Poulle Emmanuel , “John of Saxony”, Dictionary of scientific biography , vii, 139–41. Lacking a university, Magdeburg was not known especially as a centre of astronomical activity in the fourteenth and fifteenth centuries.

The following represents a rank ordering of the frequency in appearance of given cities, considered singly, in the Alfonsine glosses: Paris, Magdeburg, Prague, Cracow, Erfurt, Vienna, Wroclaw, Toruń. For an earlier analysis of similar data, see Dobrzycki Jerzy , “Reference meridian of the Copernican astronomy”, in From stars to quasars , ed. by Grudziński Stefan Krygier Bernard (Toruń, 1989), 12–15.

As noted by Durand , op. cit. (ref. 5), 143, the Klosterneuburg longitudes often followed Ptolemaic values for places distant from central Europe; for regions northeast of old Rhine-Danube frontier, they provided new coordinates.

The meridians in Schoener's 1515 geographical text, however, differ significantly from those published in his astronomical ephemerides of 1532.

Clm 4988, which contains one of the Toledan Table-related tabula regionum, was purchased by Schoener in Bamberg in 1509, according to his own gloss on f. 189^s. See Zinner , op. cit. (ref. 10), 297.

See Peschel Ferdinand Oskar , Geschichte der Erdkunde (Munich, 1865), 575–6.

See Peterson Viggio , “The three lunar models of Ptolemy”, Centaurus , xiv (1969), 142–71. For the procedures employed in our evaluation of Alfonsine lunar theory at selected dates in 1320, 1420 and 1510, see Dobrzycki Kremer , op. cit. (ref. 1), Appendix 4 and n. 17. According to Peschel, op. cit. (ref. 19), 376, the errors of geographical longitudes in Kepler's Rudolphine Tables ranged from 0;30° to 0;48°.

Wright , op. cit. (ref. 5), 91–93, and Mercier , “Meridians” (ref. 5), 26–27, also noted this pattern.

Wagner Hermann , “Die Rekonstruktion der Toscanelli-Karte vom Jahre 1474 und die Pesudo-Facsimilia des Behaim-Globus vom J. 1492”, Nachrichten von der k. Gesellschaft der Wissenschaften zu Göttingen, phil.-hist. Kl. , 1894, 208–312, p. 304, suggests that Gerard of Cremona may have measured the meridian of his hometown relative to Toledo.

Cracow , BJ 579, f. 1^v: “Radix Christi in sole verior pro meridiano Cracoviensi … supputata longitude Cracoviae 44;20 [or 33;20 E. of Toledo, assuming the latter is 11° E. of a prime meridian set at the Fortunate Isles], prout per eclipses cognovi potest.” See Appendix 1, Cracow, BJ 576.

This glossator was specifying the traditional Alfonsine meridian as the “tabular” value for Cracow (see ref. 23). Uppsala Un. Inc. 35:229, p. 31: “In Cracovia longitudo est 44 gradum, licet habetur 32 in tabulis.” See Czartoryski Pawel , “The library of Copernicus”, Studia Copernicana , xvi (1978), 355–96, p. 378.

See Werner's commentary on Ptolemy's Geography, in idem, In hoc opere haec continentur … (Nuremberg, 1514); Folkerts Menso , “Werner, Johann”, Dictionary of scientific biography , xiv, 272–7.

Quoted in Gallois L. , Les géographes allemands de la Renaissance (Amsterdam, 1963; first pub. 1890), 107–9, 114–15.

Double entries indicate different values derived from the glossed solar and lunar radices, respectively, in a given MS.

Shelfmarks : BJ = Jagellonian Library, Cracow; BN = Bibliothèque Nationale, Paris; Clm, Cgm = Bayerische Staatsbibliothek, Munich; HAB = Herzog-August-Bibliothek, Wolfenbüttel; ÖNB = Österreichische Nationalbibliothek, Vienna; PRC = Clementinum, Prague; PRA = National Archive, Prague; UFF = University Library, Frankfurt a.M.; ULP = University Library, Leipzig; UPR = University Library, Princeton; UTO = Univerity Library, Toruń; UWR = University Library, Wroclaw. An apostrophe following a shelfmark indicates a second set of glossed radices in that manuscript.

Sources: Alfonsine glossae = Appendix 1 (value appearing most frequently in the glossae for a given place); TolTa = ÖNB 4988, f. 317v, tabula regionum expanded from list of Islamic places frequently appended to the Toledan Tables (cf. Toomer , op. cit. (ref. 4), 134–5), supplemented with five additional MSS edited by Wagner , op. cit. (ref. 22), 304–7, and with four Parisian MSS edited by Wright , op. cit. (ref. 5), 93; Ptolemy Ptol , Cosmographia (Vicenza, 1475), an asterisk indicates that the Ulm (1484) and Strassburg (1513) editions contain variant readings (never diverging, however, by more than 1;20°); UT2 = Vienna School, c. 1420s, University table of latitudes and longitudes, Version 2, ed. from 16 MSS by Durand, op. cit. (ref. 5), Appendix 4; RheB = Reinhard (Vienna-Klosterneuburg School), 1430s, Coordinate table B, ed. from 6 MSS by Durand , op. cit. (ref. 5), Appendix 7; Regio = Regiomontanus, Vsum ephemeridis cuiuslibet breuiter exponemus (Nuremberg, 1474); AlfTa = Tabulae astronomicae (Venice, 1483); S&P = Johann Stöffler and Jacob Pflaum, Almanach nova (Ulm, 1499); Scho1 = Schoener Johann , Luculentissima quaeda terrae totius descriptio (Nuremberg, 1515), nearly identical coordinates, with additions for Landsberg (19;26°) and Poznań (26;14°) are found in Peter Apian, Cosmographicus liber (Landshut, 1524); Scho2 = Schoener Johann , Ephemeris (Nuremberg, 1532); Apian = Apian Peter , Astronomicum caesareum (Ingolstadt, 1540); Vird = Virdung Johannes , Tabulae resolutae (Nuremberg, 1542); Carelli = Carelli Battista Giovanni , Ephemerides (Venice, 1558); Eisen = Eisenmerger Samuel (Siderocrates), Libellus geographicus (Tübingen, 1562). The ephemerides of Regiomontanus, Stöffler and Pflaum, Schoener, and Carelli, like the tables of Virdung, all are computed from the Alfonsine Tables.