Marcus Schinnagel's Winged Polyptych of 1489: Astronomical Computation in a Liturgical Format

In 1492, Schinnagel signed his Prognostikon auf das Jahr 1493 [Latin] (Leipzig, 1492), f. 1r, as “Magister Marcus Schinagel de Choschovia Alme vniuersitatis Cracoviensis Astrologus”. His Cracow matriculation is less firmly documented; the name “Schinnagel” does not appear in the published university records. However in 1466, a “Marcus Nicolai de Cassowia” did matriculate, perhaps the son of one “Nicolaus Schynagel de Waidlinga” who in 1430 had matriculated at the Vienna University. See Zathey Jerzy Reichan Jerzy , Indeks studentów Uniwersytetu krakowskiegowlatach 1400–1500 (Wrocļaw, 1974), 175; Gall Franz , Die Matrikel der Universität Wien, 1377–1450 (Graz, 1956), 172. Franz Heidi , personal communication, April 2012, speculates that “Marcus Nicolai” was the son of “Nicholaus Schynagel”. She guesses that the latter came from Waiblingen near Stuttgart to study in Vienna and then moved to Cassowia (Košice) where other Schinnagels were living. In any case, the standard biographical source, dating Schinnagel's birth to 1464, is untenable. Die deutsche Literatur des Mittelalters, Verfasserlexikon, 2nd rev. edn (Berlin, 1978–2008), s.v. “Schinnagel”, justifies that birthdate by referring to Vienna, Österreichische Nationalbibliothek (hereafter ÖNB) Cod. 10534, a manuscript collection of astrological and astronomical texts and notes that contains “Cracow lectures from 1483–86” and was attributed by Ernst Zinner, Verzeichnis der astronomischen Handschriften des deutschen Kulturgebietes (Munich, 1925), #9410, to Schinnagel. The 1664 birthdate was worked back from the date of the codex. More recently, however, Monika Maruska, “Johannes Schöner — ‘Homo est nescio qualis’: Leben und Werk eines fränkischen Wissenschaftlers an der Wende vom 15. zum 16. Jahrhundert”, Ph.D. dissertation, Universität Wien, 2008, 108, identified this manuscript as having belonged to Johannes Schöner (acquired in 1542) and Johannes Werner (d. 1522), both of Nuremberg. She found no evidence of Schinnagel provenance, a conclusion confirmed by my own examination of the codex in June 2011. Franz's suggested identification of the matriculation record and the earlier birthdate thus seem quite plausible.

Schinnagel Marcus , Prognostikon auf das Jahr 1491 (Basel, 1490), f. 1v.

Reproduced in Goff Frederick R. , “Some undescribed ephemera of the 15th century in the Library of Congress”, Beiträge zur Inkunabelkunde, 3rd ser., i (1965), 100–2, Abb. 20. “For who made the text / prognosticated and thoroughly conceived? / Master Marx Schinnagel he is named, / well known in Swabia. / He calls himself an astronomer, / he is well recognized as an astrologer, / he is also a mathematician. / With his arts he is free.”

London, British Library Add MS 34603, ff. 21v–22r.

Eisermann Falk , Verzeichnis der typographischen Einblattdrucke des 15. Jahrhunderts im Heiligen Römischen Reich Deutscher Nation (Wiesbaden, 2004), S7–S10; Gesamtkatalog der Wiegendrucke, M40839, M4084320, M40846–50, M4085020, M4085030. Interestingly, for his extant imprints through 1489, printed in Augsburg and Ulm, Schinnagel simply copied Regiomontanus's syzygy times, computed for the meridian of Nuremberg, 65 time minutes east of Toledo. For his 1490 and 1491 practica printed in Basel, he shifted Regiomontanus's meridian 10 time minutes west; his 1491 practica printed in Ulm shifts the meridian 5 time minutes west. The post-1491 practica printed in Leipzig, Vienna and Ulm again copy Regiomontanus's meridian. From this evidence, we might speculate that Schinnagel in 1490–91 had moved to Basel, or at least had considered his readers to be located significantly west of Nuremberg. Basel is not listed in the table of places included in Regiomontanus, Beham, or the Stuttgart polyptych.

Add MS 34603 (ref. 4), paper, Latin, 306 folios, a large miscellany of astronomical tables, astrological and medical texts, apparently in one hand, probably Schinnagel's. On ff. 21v, 140r, 141r and 303v, he signed himself “… per me magistrum Marcum Schynagel/Schinagel”. For contents, see the British Library's on-line “Search our Catalogue Archives and Manuscripts” (accessed March 2012); Zinner , op. cit. (ref. 1), #9406. Wolfenbüttel, Herzog August Bibliothek Cod. Guelf. 22.1. Aug.4°, paper, 197 folios, a miscellany of astronomical tables, horoscopes (including one for Duke Albrecht of Bavaria “calculate per accutissimum astronomum magistrum Marcum Schinagel”, f. 57r) and astrological texts, Schinnagel autograph. For contents, see von Heinemann Otto , Die Augusteischen Handschriften [1900], facs. reprint edn (Frankfurt aM, 1966), #3255; Zinner , op. cit. (ref. 1), #9407, 9408, 9409. A third manuscript, Cracow, Biblioteka Jagiellońska (henceforth BJ), Cod. 8, parchment, Latin, 50 folios, containing astronomical and astrological tables and a prognostication for 1501, has been attributed to Schinnagel on the basis of an abbreviation on f. 1r: M[arcus] N[icolai] C[assoviensis] b[accalarius] C[racoviensis] A[strologus]. See Catalogus codicum manuscriptorum medii aevi Latinorum qui in Bibliotheca Jagellonica Cracoviae asservantur (Wrocļaw, 1980–2008), i, 3–5. I have not seen this latter manuscript and thus cannot comment on its attribution. Although many of the tables on Schinnagel's polyptych can be found in Add MS 34603, I shall reserve my analysis of the latter for a separate publication.

Pflaum Jacob , Kalendarium (Ulm, 1478), ff. 19r–v, 20v–22r, 25v–26v; Regiomontanus, Almanach … ad annos xviij acuratissime calculata (Augsburg, 1488), ff. 13v–18r.

Chabás José Goldstein Bernard R. , The Alfonsine Tables of Toledo (Dordrecht, 2003).

The Parisian Alfonsines provide tables for this multiplication that still require adding six or seven six- or seven-place numbers to determine a total mean motion. See Alphonso X. , Tabulae astronomicae (Venice, 1483).

Kremer Richard L. , “‘Abbreviating’ the Alfonsine Tables in Cracow: The Tabulae aureae of Petrus Gaszowiec (1448)”, Journal for the history of astronomy, xxxviii (2007), 283–304. It is conceivable that Schinnagel studied with Gaszowiec.

Interestingly, the lines for laying out the calendar were designed to start with January, as did Regiomontanus and Pflaum, at the top left (with 31 lines), followed by February (with 28 lines), and the remaining months each of which was given 31 lines. Schinnagel's calendar for April is thus placed into 28 lines with data for 29–30 April not included; and his material for February is placed into a space with 31 lines, with the final three lines empty.

For this calendar, the lines allotted correspond to the number of days in each successive month, so presumably that central panel was lined first and then altered to match the layout of the right outer wing after Schinnagel had decided to start the mean motions with 1 March.

[Lazarus Beham], Notamdum quod in isto libello habentur duo kalendarij [Cologne, c. 1476], f. 13v.

This format for tabulating mean motions (rather than computing them from the number of days since epoch as per the Parisian Alfonsine Tables) had appeared in the Oxford Tables of 1348 and in John of Gmunden's tables of the 1430s.

Kremer , op. cit. (ref. 10), 288–90.

[Beham], op. cit. (ref. 13), f. 16r. An unremarkable astrological text, “Von den wurkungen der 7 planeten vnd der 12 zaichen”, attributed to “Lazarus Bechem von Sulczbach practicus in quadrivio” (138r), appears in Munich, Bayerische Staatsbibliothek Cgm 328, ff. 122r–38r. See Schneider Karin , Die deutschen Handschriften der Bayerischen Staatsbibliothek München, Cgm 201–350 (Wiesbaden, 1970), 335–42.

The Parisian Alfonsine Tables, like most medieval tables, generally list equations for arguments from 0 to 180 degrees, since the values are symmetrical around 180 degrees albeit with opposite signs. Schinnagel thus included redundant values for the arguments from 180 to 360 degrees, but by prominently labelling the columns “Subtractio” and “Addictio” [sic] he presumably made it easier for users to apply the signs correctly.

For example, the two columns on the central panel for the solar longitudes are consistently labelled signs and degrees, when they present (as had Regiomontanus) data in degrees and minutes of longitude. The mean lunar motions on that panel do provide data in signs and degrees; the painter erroneously gave the same headings to both sets of columns.

Kremer , op. cit. (ref. 10), 291–2. Note, however, that Gaszowiec followed the Parisian Alfonsines in giving the equations to minutes but shortened the tables by including arguments at only five-degree intervals. Schinnagel and Gaszowiec thus differently abbreviated the Alfonsine equations.

See Pedersen Olaf , A survey of the Almagest (Odense, 1974), 184–5.

Cf. Regiomontanus , Kalendarium [Latin] (Nuremberg, 1474).

Pflaum , op. cit. (ref. 7), ff. 17r–18v. Regiomontanus's and Pflaum's eclipse times vary by up to ±0;15h.

[Beham], op. cit. (ref. 13), ff. 39v–40r, with instructions for using the columns on ff. 40v–41r. Schinnagel (inadvertently?) omitted two (Oxford, Córdoba) of Beham's 62 locations, although spaces for these entries were prepared in the table. The number, order of places and most of the geographical coordinates in Beham's handbook are identical to those appearing in the similar table in Regiomontanus's 1474 calendars. Schinnagel's autograph set of tables, Add MS 34603 (ref. 4), ff. 227v–28r, also omits Oxford and Córdoba.

Cf. Bouché-Leclercq Auguste , L'astrologie grecque (Paris, 1899), 328–47; Abenragel Haly , De iudiciis astrorum (Venice, 1485), VIII, 36–7.

Angelus Joannes , Astrolabium in planum tabulis (Augsburg, 1488), ff. 31v–34r.

This circular table is incomplete. A ring, labelled for embolism, has no data entered.

Pflaum , op. cit. (ref. 7), 16v.

For a concise summary of the dignities, concepts that circulated widely in medieval Arabic and Latin astrology, see Alchabitius , Libellus isagogicus (Venice, 1482), ff. a2v–a4v; Burnett Charles Yamamoto Keiji Yano Michio , Al-Qabī⋅ī (Alcabitius): The introduction to astrology, editions of the Arabic and Latin texts and an English translation (London, 2004), 230–7.

Usually medium caeli is not included in these terms. See Alcabitius , op. cit. (ref. 28), ff. c5v–c7v; Burnett , op. cit. (ref. 28), 316–26.

The artist has (inadvertently?) divided March into 32 days, despite the text's assertion that “Martius hat xxxi tag”.

That is, the unnecessary eccentricity of the zodiacal circle does not markedly distort the results when working at a precision of degrees.

Cf. North J. D. (ed.), Richard of Wallingford: An edition of his writings, with introductions, English translation and commentary (Oxford, 1976). Poulle Emmanuel , Les instruments de la théorie des planètes selon Ptolémée: Équatoires et horlogerie planétaire du XIIIe au XVIe siècle (Geneva, 1980), 279–94, 455–7, Pl. XXIV–XXV, located only one equatoria constructed of wood, consisting of vovelles on three panels each measuring about 1 × 1 m, designed to rest horizontally on a table. Constructed in Augsburg in 1428, this large instrument is presumed to have made its way by 1438 to the Cistercian monastery in Stams (Tirol), where it remains today. No texts or tables accompany the Stams equatoria.

The compendium was acquired before 1856 by the local antiquarian and founder of the museum, Hans Philipp Werner Freiherr von und zu Aufseß (1801–72). Nothing further is known concerning its provenance. Bott Gerhard Willers Johannes , Focus Behaim-Globus (Nuremberg, 1992), 511–14; see 511 for a colour illustration of the crudely painted diagram of the Aristotelian cosmos of concentric spheres, visible on the outer surfaces of the wings when closed. At the upper corners of this surface are painted a “Theorica Solis” and “theorica lune”, identical in form (if not quite in scale) to those diagrams in Peurbach, Theoricae novae planetarum (Nuremberg, 1473), ff. 1r, 3r. The earliest known manuscript of this text and diagrams, an autograph by Regiomontanus dated 1454, ÖNB Cod. 5203, ff. 1r, 2v, shows similar diagrams.

One pointer is broken and apparently originally had a groove cut through its surface to allow an attached component to move radially along its axis. Otherwise, the artifact appears intact.

Grotefend Hermann , Zeitrechnung des deutschen Mittelalters und der Neuzeit [1891–98] (Aalen, 1970), i, 24–5 (Glossar). A cisiojanus is a medieval poem with one syllable for each day of the year, used to memorize important feast days.

The “Secundus canon de gradus solis inventione”, nicely legible on the central panel above the dial, describes how to subtract 14, 29 and 43 minutes from the tabular values for the next three years, respectively, thereby enabling the device to yield Alfonsine true solar longitudes for the years 1461–64.

Gmunden's calendar provides true solar longitudes to degrees, true lunar longitudes to signs, and day lengths for a geographical latitude of 49;48 degrees. Clearly, the maker of the Nuremberg triptych did not rely exclusively on Gmunden's calendar, which I have consulted in ÖNB Cod. 2440.

Interestingly, the mean lunar arguments are listed for midnight (rather than the usual noon) on 1 January, for a meridian 80 minutes east of Toledo. The mean motions are listed for noon on 26 December, for a meridian only 26 minutes east of Toledo. I have extracted these parameters by least squares, using the parameters of the Parisian Alfonsine Tables and all the values I can read on the right wing (8 motions, 16 arguments). Like Schinnagel's polyptych, the Nuremberg compendium combines inconsistently computed Alfonsine materials.

Golden numbers, Sunday letters, weeks to Lent, weeks from Whitsunday to John the Baptist's day and from Whitsunday to Advent.

King David A. , Astrolabes and angels, epigrams and enigmas: From Regiomontanus' acrostic for Cardinal Bessarion to Piero della Francesca's Flagellation of Christ (Stuttgart, 2007), 34–5.

He began this practice in his earliest extant autograph manuscript, ÖNB Cod. 4988, which contains his syzygy times for nearly every year from 1448 to 1462.

A fragment of a similarly formatted circular calendrical compendium, a manuscript written in red and brown ink on parchment, is bound among the flyleaves of BJ Cod. 1356. Roughly half of the original circle, which measures about 45 cm in diameter, is extant. The circle is crudely divided into 365 days, into which are written the Roman kalends, Sunday letters, the same cisiojanus found on the Nuremberg compendium, and sets of three numbers for every second or third day whose significance I do not understand. The codex contains a miscellany of 41 texts, mostly sermons and other theological treatises, some copied as early as 1395. Its catalogers did not date the binding but remarked on the “similarity in forms and sizes” between the Cracow sheet and Schinnagel's compendium in Stuttgart. Catalogus, op. cit. (ref. 6), ix, 46–62, p. 57. I find the Cracow sheet much closer in format and content to the Nuremberg compendium than to Schinnagel's.

Museum records indicate that the triptych (Inv. 5563) was donated to the museum by Robert Harder, a local antiquarian active early in the twentieth century; nothing is known of its earlier provenance. Briefly mentioned by Zinner Ernst , Deutsche und niederländische astronomische Instrumente des 11.–18. Jahrhunderts (Munich, 1956), 36–7, this compendium and its accompanying treatises have never been analysed.

Erlinger Georg , Argumentum canonis super instrumentum planeticum (Augsburg, 1516); Erlinger Georg , Inhalt des planetischen Wercks, das auffsteigend zaichen all zeit und stund (Cologne, 1517). Erlinger had studied at the university in Ingolstadt (1502) without taking a degree. From 1521 until his death in 1541, he operated a print shop in Bamberg and Wertheim, issuing nearly 90 titles. Most of his imprints are official documents or Reformation pamphlets; except for the two manuals noted above and a 1525 treatise on the astrolabe by Johannes Copp (VD16 C5030), none treats astronomical or mathematical topics. Schottenloher Karl , Die Buchdruckertätigkeit Georg Erlingers in Bamberg von 1522 bis 1541 (1543) (Leipzig, 1907); Reske Christoph , Die Buchdrucker des 16. und 17. Jahrhunderts im deutschen Sprachgebiet (Wiesbaden, 2007), 57.

Cf. Erlinger , op. cit. (ref. 44, 1517), f. A2v; Regiomontus , op. cit. (ref. 21), f. 29v. Erlinger's lunar radices are close (±1–2 degrees) but not identical to Regiomontanus's.

Pilz Wolfgang , Das Triptychon als Kompositions- und Erzählform in der deutschen Tafelmalerei von den Anfängen bis zur Dürerzeit (Munich, 1970); cf. Lankheit Klaus , Das Triptychon als Pathosformel, Abhandlungen der Heidelberger Akademie der Wissenschaften, phil.-hist. Kl., iv (Heidelberg, 1959).

Pilz , op. cit. (ref. 46), 16, 228. Cf. Elsner Jakob , Portrait of Imhoff , 1486, 36.5 × 22.5 cm (opened), Munich, Bayerisches Nationalmuseum, MA 310; Albrecht Dürer, Portrait of Krel, 1499, 88 × 50 cm (opened), Munich, Alte Pinakothek, WAF 230 (arms of Krel and of his wife); Master of Mühldorf, Pfeffinger family tree, 1516, 323 × 83 cm (opened), Munich, Bayerisches Nationalmuseum, R 584; Cranach Lucas Sr , Three Saxon electors , 1532, 131× 68 cm (opened), Hamburg, Kunsthalle, 606. For reproductions, see Lankheit , op. cit. (ref. 46), Tafel 11–13, 16. Cf. Schilling Edmund , “Dürer und der Illuminist Jacob Elsner”, Phoebus , i (1946), 135–44; Dülberg Angelica , Privatporträts: Geschichte und Ikonologie einer Gatung im 15. und 16. Jahrhundert (Berlin, 1990), 86–7, 191–2, 214, 268–9, and Abb. 606–7; Goldbert Gisela Heimberg Bruno Schawe Martin , Albrecht Dürer, Die Gemälde der Alten Pinakothek (Heidelberg, 1998), 236–59.

The art historian Angelica Dülberg , op. cit. (ref. 47), 107–8, has found that arms are most frequent on portraits of families from the free or imperial cities of Frankfurt aM, Nuremberg, Ulm, Augsburg and Munich.

Appuhn-Radtke Sibylle Schwarzmann Annelis (eds), 1000 Jahre Petershausen: Beiträge zur Kunst und Geschichte der Benediktinerabtei Petershausen in Konstanz (Konstanz, 1983), 113–16; Staiger Franz Xaver , Salem oder Salmansweiler ehemaliges Reichskloster Cisterzienser-Ordens jezt Großh. Markgräfl. Bad. Schloß und Hauptort der Standesherrschaft Salem … topographisch-historisch ausführlich beschrieben (Konstanz, 1863), 4; Durm Josef Kraus Franz Xaver , Die Kunstdenkmäler des Grossherzogthums Baden , i: Kreis Konstanz (Freiburg i.Br., 1887), 555–7.

Runkel Sebastian , Die Freiherren von Reischach (Munich, 2009), 7; Franz Heidi , personal communication, June 2011.