Calculating with Andreas Aurifaber: A New Source for Copernican Astronomy in 1540

Aurifaber Andreas , Practica auff das Jar M.D.XLI (Danzig: Franz Rhode, 1540). Loosely bound in the sixteenth-century with 26 other practica and cometary tracts from the 1520/40s, this copy has been held since 1971 by the Landesbibliothek Coburg, shelfmark Mo A 12, for its owner, the church library of St Moriz, also in Coburg. The codex probably once belonged to Georg Caupert (d. 1640), an obscure Coburg government official whose personal library was acquired by St Moriz in 1677. The title page of the Coburg copy is inscribed “Sum Andreae Aurifabrj A. 1541” (see Appendix); a digital scan is available at http://bvbm1.bib-bvb.de/view/custom/DisplayPersistentURL.jsp?pid=172587 (accessed 1 August 2010). Another copy of Aurifaber's practica, also bound with other sixteenth-century practica, appears in a nineteenth-century inventory of the Staats- und Universitätsbibliothek Königsberg. See Isolde Kalter, personal communication to the author, 30 July 2010; Erdmann Jürgen , Die Bibliothek zu St. Moriz als Zeugnis coburger protestantischer Tradition (Coburg, 1983), 7, 20; Päsler Ralf G. , “Die Handschriftensammlungen der Staats- und Universitätsbibliothek der Stadtbibliothek und des Staatsarchivs Königsberg”, in Königsberger Buch- und Bibliotheksgeschichte , ed. by Walter Alex (Cologne, 2004), 189–249, p. 225.

“Further study is warranted to determine to what extent these and other astronomical forecasts in Aurifaber's practica actually made use of Copernican theory, in whatever form Aurifaber could have accessed it in 1540, and also to what extent someone with Aurifaber's education and experience could have made use of Copernican tables at that time.” See Green Jonathan , “The first Copernican astrologer: Andreas Aurifaber's Practica for 1541”, Journal for the history of astronomy , xli (2010), 157–65, p. 161; Schnaase Eduard David , “Andreas Aurifaber und seine Schola Dantiscana: Ein Beitrag zur Geschichte der Schulen in Danzig”, Altpreußische Monatsschrift , n.s., xi (1874), 304–25, 456–80, p. 308. For previous studies of what had been considered the earliest printed Copernican practica, see Karl Heinz Burmeister, “‘mit subtilen fündlein und sinnreichen speculierungen …’, die ‘Practica auff das M.C.XLvj. Jar’ des Achilles Pirmin Gasser im Umfeld zeitgenössischer Astrologen”, Vierteljahresschrift für Geschichte und Gegenwart Vorarlbergs, lv (2003), 107–20; Danielson Dennis , “Achilles Gasser and the birth of Copernicanism”, Journal for the history of astronomy , xxxv (2004), 457–74; Kremer Richard L. , “Copernicus among the astrologers: A preliminary study”, in Astronomy as a model for the sciences in early modern times , ed. by Folkerts Menso Kühne Andreas (Augsburg, 2006), 225–52.

More than 70 titles appeared in Rhode's Danzig printshop between 1538 and his death in 1559. In addition to official materials for Danzig's schools and City Council, Rhode printed songs and polemical and satirical texts against the Church and other authorities. As far as I know, the Narratio prima and Aurifaber's practica were the only two astronomical texts he printed. See Kawecka-Gryczowa Alodia Korotajowa Krystyna (eds), Drukarze dawnej polski od XV do XVIII wieku, iv: Pomorze (Wrocław, 1962), 366–78; Reske Christoph , Die Buchdrucker des 16. und 17. Jahrhunderts im deutschen Sprachgebiet (Wiesbaden, 2007), 146.

Reske , Buchdrucker (ref. 3), 145–6; Misocacus Wilhelm , Prognosticum oder Practica auffs Jar … 1580 (Danzig: Jakob Rhode, 1579).

Green , “Aurifaber's practica” (ref. 2), 158–9; Copernicus Nicolaus , Gesamtausgabe (Hildesheim, 1974–), vi/1, 290–1; Hugonnard-Roche Henri Verdet Jean-Pierre (eds), Georgii Joachimi Rhetici Narratio prima: Édition critique, traduction française et commentaire (Wrocław, 1982), 192. For his exuberant description of the new school and an early textbook, see Aurifaber Andreas , Schola Dantiscana ad literas bonas (Danzig: Franz Rhode, 1539), reprinted in Schnaase , “Andreas Aurifaber” (ref. 2), 456–80; Aurifaber Andreas , Methodus grammatices donati plurimis variorum grammaticorum succinctis definitionibus & tabellis (Danzig: Franz Rhode, 1540). Might Aurifaber have arranged for Rhode to print the Narratio?.

In 1542, the Duke gave Aurifaber a stipend of 500 Mark to support three years of study. Note that Rheticus served as dean in the winter of 1541 as did Erasmus Reinhold in the winter of 1540 and summer of 1549. Cf. Kuhnert Ernst , Geschichte der Staats- und Universitäts-Bibliothek zu Königsberg, von ihrer Begründung bis zum Jahre 1810 (Leipzig, 1926), 41; Sennert Andreas , Athenae: Intemque inscriptiones wittebergensis (Wittenberg, 1655).

Möller Wilhelm , Andreas Osiander: Leben und ausgewählte Schriften [1870], facs. reprint (Nieuwkoop, 1965), 340–4; “Aurifaber (Goldschmid), Andreas”, Biographisch-bibliographisches Kirchenlexikon, ed. by Bautz Friedrich Wilhelm (Hamm, 1970–2009), i, 302–3; Stupperich Martin , Osiander in Preussen, 1549–1552 (Berlin, 1973); Burmeister Karl Heinz , Georg Joachim Rhetikus, 1514–1574: Eine Bio-Bibliographie (Wiesbaden, 1967–68), ii, 43; Arp Ingrid , “Hans Daubmann und der königsberger Buchdruck im 16. Jahrhundert: Eine Profilskizze”, in Königsberger Buch- und Bibliotheksgeschichte , ed. by Walter Alex (Cologne, 2004), 87–126; Gingerich Owen , An annotated census of Copernicus' De revolutionibus (Nuremberg, 1543 and Basel, 1566) (Leiden, 2002), 135, 209. According to Gingerich, Aurifaber's copy of De revolutionibus (now in private hands in Vicenza) is not interestingly annotated, but its front quire does contain a Greek elegaic poem in the hand of the Leipzig humanist Joachimus Camerarius, a text also copied by Camerarius into a front fly leaf of the De revolutionibus now in the Biblioteca Palatina in Parma.

Aurifaber , Practica 1541 (ref. 1), sig. a2v, as translated by Green , “Aurifaber's practica” (ref. 2), 162. It would be interesting to know to whom Aurifaber was referring as he mentioned “others who in this city or land are knowledgeable in this art”. As noted above, no other practica would be printed in Danzig until 1580, and no other practica would be printed in the Duchy of Prussia until Titius Simon , Practica teutsch auff das MDLV Jar (Königsberg: Johann Daubmann, 1554). Titius, who claimed to base his practica on the Copernican Prutenic Tables, had been called in 1553 to Königsberg as professor of medicine by Aurifaber, then rector of the university, according to Schnaase, “Andreas Aurifaber” (ref. 2), 322.

Green , “Aurifaber's practica” (ref. 2), 160. Cf. Westman Robert S. , “The Melanchthon circle, Rheticus and the Wittenberg interpretation of the Copernican theory”, Isis , lxvi (1975), 165–93.

Gingerich Owen , “Early Copernican ephemerides”, in Science and history: Studies in honor of Edward Rosen , ed. by Hilfstein Erna Czartoryski Paweł Grande Frank D. (Wrocław, 1978), 403–17. Hilary took the syzygy times from Stoeffler's Alfonsine-based ephemerides, but converted them to Italian hours (numbered starting from sunset), the common time-keeping system in many sixteenth-century Eastern European cities. My least-squares analysis suggests that Hilary adjusted the times for a geographical latitude of 51° and a longitude 25 time minutes east of Stoeffler's meridian of Tübingen. Cf. Birkenmajer Aleksander , “Hilary de Wislica, était-il un zelateur du système heliocentrique de Copernic a Cracovie?”, Studia Copernicana , iv (1972), 721–60.

Hugonnard-Roche Verdet (eds), Narratio prima (ref. 5), 84–5.

Wapowski to Sigismund von Herberstein, 15 October 1535, in Copernicus, Gesamtausgabe (ref. 5), vi/1, 186–8. This letter, first discovered in 1933 in the Budapest National Museum, was published by Brachvogel Eugen , “Zur Koppernikusforschung [publ. 1933]”, Zeitschrift für die Geschichte und Altertumskunde Ermlands , xxv (1935), 237–45. For a fascimile, see Biskup Marian , Regesta Copernicana (Wrocław, 1973), figs 16–17. Cf. Swerdlow N. M. Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (New York, 1984; hereafter MACR), 17–18.

Wapowski added a postscript to his letter: “At certain places I found an error in the [almanac's] aspects that must be ascribed to the rushing scribe and not the author. But anyone could easily improve and add where the aspects are lacking, since the planetary motions are true and certain. In February, the scribe erred in the conjunctions and oppositions of the Sun and Moon.”

Apian Peter , Practica auff das M.D.XXXXI Jar (Nuremberg: Hieronymus Andreae, 1540); Eißlinger Balthasar , Practica vff das MDXLI Jar (Speyer: Anastasius Nolt, 1540); Wolmar Johann , Vier wunderliche jar, 1541, 1542, 1543, 1544, Practica oder pronostication auff die vier nechstvolgenden Jar (Nuremberg: Johann Petreius, 1540); von Roermond Salomon , Ein newe prognostication mit wunderlichen propheceyen von dem jahr XLI biß zum ende des L. Jars (Nuremberg: Georg Wachter, 1540).

Imser Philipp , Ephemeridium opus Ioannis Stoefleri Iustingensis … a … MCXXXII in alios XX proxime subsequentes, ad veterum imitationem accuratissimo calculo, elaboratum (Tübingen: Ulrich Mohart, 1531). Interestingly, slavishly copying from ephemerides can propagate errors. For example, Eißlinger listed an opposition of Jupiter and Mercury for 7 March 1541 (sig. B2v), following Imser's aspects page (sig. T5r); however, the opposition on that date was Jupiter and Venus, as is clear from Imser's page of the planetary longitudes. Eißlinger blindly followed Imser's typographical error.

Aurifaber , Practica 1541 (ref. 1), sig. B2r, vaguely (i.e., non-quantitatively) described two horoscopes for the last new moon before the Sun's entry into Aries (i.e., 25 February) and for that cardinal point (11 March), noting that Venus ruled both charts and that Mercury was at the ascendant in one of them. At these times, however, the Alfonsine and Prutenic predictions for Mercury differ by only 1–3°, and I cannot determine which source Aurifaber may have used to specify the longitude of Mercury.

Aurifaber , Practica 1541 (ref. 1), sig. B1v. For comparison and to spare me the labour of using De revolutionibus, I have computed the aspect times from Reinhold Erasmus , Prutenicae tabulae coelestium motuum (Tübingen: Ulrich Mohard, 1551).

Aurifaber , Practica 1541 (ref. 1), sig. B1v.

Alphonso X , Tabulae astronomicae (Venice: Ratdolt, 1483). The meridian of the Alfonsine Tables is Toledo. Eißlinger's meridians from the cardinal time are 47 time minutes east of Toledo for Aries and Libra, and 49 minutes east for Cancer. I have found that early sixteenth-century practica makers commonly achieved a computational precision of ± several minutes in using the Alfonsine Tables, i.e., that my computer algorithms to look up tabular values and compute positions from the 1483 editio princeps of the Alfonsine Tables usually match their pencil-and-paper results to at least ±3 minutes of time or arc. Later editions of the Alfonsine Tables (Venice 1492, 1503, 1518, 1524) may include additional auxilliary tables, but the basic tables for mean motions, radices and equations remain unchanged.

Aurifaber , Practica 1541 (ref. 1), sig. B1v. For the time in December, I correct Aurifaber's 11 Dec p.m. (“nach”) to 12 Dec a.m. (“vor”). I have rewritten Aurifaber's times to count hours from midnight, marking hours as does Copernicus.

For Copernicus's treatment of precession in De revolutionibus, see Swerdlow Neugebauer , MACR (ref. 12), 129–48.

322/10,000 = 0.0322 versus 2,16/60 = 0.0378. See North J. D. (ed.), Richard of Wallingford: An edition of his writings, with introductions, English translation and commentary (Oxford, 1976), iii, 197.

Swerdlow N. M. , “On establishing the text of ‘De revolutionibus’”, Journal for the history of astronomy, xii (1981), 35–46.

Copernicus Nicolaus , Opera omnia (Warsaw, 1973–92), i, 1–49; Swerdlow N. M. , “The holograph of ‘De revolutionibus’ and the chronology of its composition”, Journal for the history of astronomy , v (1974), 186–98.

Swerdlow Neugebauer , MACR (ref. 12), 165.

Swerdlow Neugebauer , MACR (ref. 12), 155.

Swerdlow Neugebauer , MACR (ref. 12), 164.

Swerdlow Neugebauer , MACR (ref. 12), 168. Note that in the Narratio prima, Rheticus specified the minimal solar eccentricity as 321 parts, the value ostensibly used to compute the solar correction in M. See Hugonnard-Roche Verdet (eds), Narratio prima (ref. 5), 47, 97–8, 153. As is well known, Copernicus's tables often were inconsistently calculated. A least squares analysis of Copernicus's table for c₅ indicates a best fit for e = 322 parts, but 24 of the 60 values still deviate by ± 0;01° from my computed values. The maximal value in M for c₅ (1;50°) requires e = 321 parts; the maximal value for N of 1:51° requires e = 322 to 324 parts. Only three c₅ values differ between M and N, for arguments of 84, 90 and 93°. In the Prutenic Tables, Reinhold computed c₅ for intervals of 1° rather than 3° and to arcsecs rather than arcmins. A least squares analysis indicates that Reinhold also used e = 322 parts; his values invariably match my recomputation to ± 0; 00, 02°, a precision an order of magnitude better than Copernicus's. See M, f. 103r–v; N, ff. 94v–95r; Reinhold, Prutenicae tabulae (ref. 17), ff. 41v–44r. For the geometry of this computation, see Swerdlow and Neugebauer, MACR (ref. 12), 154.

Chabás José Goldstein Bernard R. , “Nicholaus de Heybech and his table for finding true syzygy”, Historia mathematica , xix (1992), 265–89; Chabás José Goldstein Bernard R. , “Computational astronomy: Five centuries of finding true syzygy”, Journal for the history of astronomy , xxviii (1997), 93–105; Kremer Richard L. , “Wenzel Faber's table for finding true syzygy”, Centaurus , xlv (2003), 305–29; Kremer Richard L. , “John of Murs, Wenzel Faber and the computation of true syzygy in the fourteenth and fifteenth centuries”, in Mathematics celestial and terrestrial: Festschrift für Menso Folkerts zum 65. Geburtstag , ed. by Dauben Joseph W. (Stuttgart, 2008), 147–60; Swerdlow Neugebauer , MACR (ref. 12), 276.

Eißlinger , Practica 1541 (ref. 14), sig. B2v–B4v; Apian , Practica 1541 (ref. 14), sig. A4v–B4r.

Aurifaber , Practica 1541 (ref. 1), sig. B4v–C4v. For 27 January, I read “vor” for “nach”; for 11 Feb, read “nach” for “vor”; for 11 March, read “4:31 vor” (from Aurifaber's lunar eclipse prediction, sig. B1v) for “8;56 vor” (mistakenly repeated from Aurifaber's first cardinal point); for 8 June, read 1 for 2 hours; for 8 July, read “vor” for unspecified; for 19 October, read 19 for 9 days; for 17 Nov, read “nach” for unspecified and read 9 for 10 hours. Although this number of typographical or computational errors is not unusual for mid-sixteenth-century practica, the quantitative data in Aurifaber's imprint are less precisely specified than are those in our comparative practica for 1541. I list Aurifaber's times, counting hours from midnight, although his “vor” and “nach” are usually from noon.

Swerdlow Neugebauer , MACR (ref. 12), 272–73.

Since Copernicus presumably borrowed col. 5 of his lunar corrections directly from the 1483 Alfonsine Tables, it would be surprising to find Aurifaber employing a different set of lunar corrections. See Swerdlow Neugebauer , MACR (ref. 12), 226–7.

Swerdlow Neugebauer , MACR (ref. 12), 166–71.

Hugonnard-Roche Verdet (eds), Narratio prima (ref. 5), 46–7, 97–8. In their forthcoming study of medieval astronomical tables, Goldstein B. R. Chabás J. review solar parameters used by dozens of table-makers. The lowest value for the maximal solar correction they find is 1;50°. Chabás, personal communication to the author, 6 August 2010.

Apian calculated both the “minutes of imersion”, i.e., time from first contact to the beginning of totality, and “minutes of delay”, i.e., time from beginning of totality to mid-eclipse; and he offers the magnitude to two significant digits, unlike Imser.

Aurifaber , Practica 1541 (ref. 1), sig. B1v. For the lunar eclipse, Aurifaber specified only the duration of totality, from which I have computed his times for the beginning and end of totality. Likewise, I compute his duration by doubling his time from the beginning to mid-eclipse. Wolmar mentioned the lunar eclipse, but provided no quantitative detail; he did not list the solar eclipse in his practica. In this table, I render times as hours as do most of the practica, where “vor” is ante meridiem and “nach” is post meridiem. All times in square brackets I have computed from other data available in the respective practica. Both the 1483 Alfonsine Tables, sig. b6v, and De revolutionibus IV, 32, state that the time of apparent conjunction (i.e. the time of maximal magnitude) in solar eclipses occurs midway between the apparent beginning and apparent end of the eclipse. Yet because of changing lunar parallax over the duration of the eclipse, this generally is not true. Eißlinger accepted the Alfonsine approximation; Apian did not, presumably recalculating the lunar parallax at the beginning and end of the eclipse. Aurifaber did not include times for the beginning or end of the solar eclipse, thereby not taking a position on the question.

Swerdlow Neugebauer , MACR (ref. 12), 271.

Alphonso X, Tabulae astronomicae (ref. 19); Collimitius Georg Tanstetter (ed.), Tabulae eclypsium magistri georgij peurbachij, Tabula primi mobilis joannis de monte regio (Vienna: Johann Winterburger, 1514).

Swerdlow Neugebauer , MACR (ref. 12), 255–6.

Copernicus's table for lunar latitudes, N, f. 113v–14r, identical to M, ff. 121v–22r, is extracted from the Alfonsine Tables and was not recomputed by him, according to Swerdlow Neugebauer , MACR (ref. 12), 229.

Perhaps Aurifaber misrepresented this computational result? If 3;29 were to refer not to the time of first contact (note that Aurifaber did not specify “vor” or “nach” for this time) but to the phases, it would yield a duration of 1;45h from first contact to mid-eclipse, much closer to Imser's and my results.

Swerdlow Neugebauer , MACR (ref. 12), 117, 279. Cf. Neugebauer O. , “Three Copernican tables”, Centaurus , xii (1968), 97–9. Note, however, that Copernicus's parallax table is independent of geographical latitude; the user-friendly parallax tables entered with solar longitudes and time require separate tables for each “climate” of geographical latitude.

Swerdlow Neugebauer , MACR (ref. 12), 262–3. Indeed, given the small values of parallax and the rather crude 6° intervals of interpolation in Copernicus's table for parallax in IV, 24, errors of ±1° in zenith distance (due to the Moon's latitude at solar eclipses) barely affect the parallax computation, especially in northern regions like Danzig where the Moon never gets close to the zenith.

I find a solar parallax of 0; 02, 10° and a lunar parallax of 0; 45, 48°. For a cogent explanation of Copernicus's method of dealing with parallax in solar eclipses, see Swerdlow Neugebauer , MACR (ref. 12), 278–85.

For a modern map of the 1541 partial solar eclipse, whose track of greatest magnitude passed through central Siberia and western limit of semi-totality (magnitude of 0.5 or 6 digits) passed roughly from Königsberg down through the eastern Black Sea, see Espenak Fred Meeus Jean , Five millennium canon of solar eclipses, −1999 to +3000 (Washington, DC, 2005), A-421.

Copernicus copied a fragment of a parallax table for a geographical latitude of 51° (Cracow), of the Handy Tables format, into one of his books. Presumably manuscript copies of such tables were available to Cracow astronomers. Cf. Swerdlow Neugebauer , MACR (ref. 12), 279–80, 554.

Cf. Kremer Richard L. , The Copernican revolution from below: Computational astronomy from 1540 to 1640 (forthcoming).

Hugonnard-Roche Verdet (eds), Narratio prima (ref. 5), 43, 93.

Kuhnert , Staats- und Universitäts-Bibliothek zu Königsberg (ref. 6), 51–2. In 1552, Aurifaber as first professor of medicine and rector of the University of Königsberg received an annual salary of 200 Mark. A library worth more than twice the annual salary of a valued civil servant must have been impressive. Cf. Schnaase , “Andreas Aurifaber”, 320.

For a colour reproduction of the front binding of Aurifaber's copy of De revolutionibus, now in Vicenza , see The collection of the Garden Ltd. magnificent books and manuscripts (New York, 1989), no. 51.

Cf. Kuhnert , Staats- und Universitäts-Bibliothek zu Königsberg (ref. 6), 42, 59, 256; Tondel Janusz , Eruditio et prudentia: Die Schloßbibliothek Herzog Albrechts von Preußen, Bestandskatalog 1540–1548 (Wiesbaden, 1998), 28–9. Particular codices are identified in the following sources: Deckert Helmut , Katalog der Inkunabeln der sächsischen Landesbibliothek zu Dresden: Ein Bestandsverzeichnis nach den Kriegsverlusten des Jahres 1945 (Leipzig, 1957); Gingerich , Census (ref. 7); Hipler Franz , Spicilegium copernicanum: Festschrift des historischen Vereins für Ermland zum vierhundertsten Geburtstage des ermländischen Domherrn Nicolaus Kopernikus (Braunsberg, 1873); Ozóg Jan , Katalog poloników XVI w. biblioteki uniwersyteckiej we wrocławiu (Wrocław, 1991); Sokól Stanisław Pelczarowa Maria , Ksieͅgozbiór gdańskich lekarzy krzysztofa i Henryka Heyllów (Gdańsk, 1963); Walde O. , “Neue bücher- und bibliotheksgeschichtliche Forschungen in deutschen Bibliotheken”, Nordisk tidskrift för bok- och biblioteksväsen , xxix (1942), 165–262; Zdanevich Boris , Katalog inkunabul (Kiev, 1974); Zinner Ernst , Entstehung und Ausbreitung der copernicanischen Lehre [1943], ed. by Nobis Heribert M. Schmeidler Felix , 2nd edn (Munich, 1988). Since some of these sources appeared before the Second World War, not all of these volumes may still be extant. To identify the texts, see Gesamtkatalog der Wiegendrucke (GW) and Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des XVI. Jahrhunderts (entries beginning with letters in col. 4), both best consulted on-line.