The Geometrical Diagrams in Regiomontanus's Edition of His Own Disputationes ( c . 1475): Background,Production,and Diffusion

Zinner Ernst , Leben und Wirken des Joh. Müller von Königsberg, genannt Regiomontanus , 2nd edn (Osnabrück, 1968), 13–15, 19; Geldner Ferdinand , “Das Helmaspergersche Notariatsinstrument in seiner Bedeutung für die Geschichte des ältesten Mainzer Buchdrucks”, and Geldner , “Die ersten typographischen Drucke”, in Widmann Hans (ed.), Der gegenwärtige Stand der Gutenberg-Forschung (Stuttgart, 1972), 91–121, esp. p. 107; and 148–74, esp. pp. 156, 160–1, 166–7. In his Ein neu entdeckter astronomischer Kalender für das Jahr 1448 (Mainz, 1902), Gottfried Zedler originally proposed a printing date of 1447 (for issue in 1448). A generation later, he was criticized by Wehmer and Stegeman in Carl Wehmer, Mainzer Probedrucke in der Type des sogenannten astronomischen Kalenders für 1448 (Munich, 1948), which seems to have persuaded many historians of the book that the work was printed in 1457/1458. The issue remains perplexing for I am aware of no historian of astronomy who considers it sensible to hypothesize that an almanac with 1448 planetary positions would have been issued a decade later because it was addressed to laymen; see Wehmer, Mainzer Probedrucke, 32f, 45–52.

Zinner , Regiomontanus (ref. 1), 186–8.

In addition to Zinner's work, see Wingen-Trennhaus Angelika , “Regiomontanus als Frühdrucker in Nürnberg”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg , lxxviii (1991), 17–87; and the 2007 Columbia University Ph.D. dissertation of Renzo Baldasso, “Illustrating the Book of Nature in the Renaissance: Drawing, painting, and printing geometric diagrams” (Ann Arbor: Proquest Information and Learning Company, 2007; UMI 3285042), chap. 6. On early self-printers in science, see Lowood Henry E. Rider Robin E. , “Literary technology and typographic culture: The instrument of print in early modern science”, Perspectives on science , ii (1994), 1–37, esp. pp. 4–8.

For an excellent, mostly post-Regiomontanus introduction to astronomical illustration, see Pantin Isabelle , “L'illustration des livres d'astronomie à la Renaissance: L'évolution d'une discipline à travers ses images”, in Meroi Fabrizio Pogliano Claudio (eds), Immagini per conoscere: Dal rinascimento alla rivoluzione scientifica (Florence, 2001), 3–41, esp. pp. 18–22 (on the Regiomontanus edition of Peuerbach).

Regiomontanus's editio princeps of what we now call the Disputationes left the work untitled. It is to Erhard Ratdolt's first edition of the work, in the compendium that also includes Sacrobosco's Sphere and Peuerbach's Theoricae novae planetarum (Venice, 1482; Goff J-405) that we owe this descriptive title, printed in red at the beginning of the book: “… contraque cremonensia in planetarum theoricas delyramenta Joannis de monte regio disputationes tam acuratissimas quam utilissimas” would become the Disputationes contra deliramenta cremonensia (Hain 13805).

A partial list of these editions appears in Zinner Ernst , “Johannes Müller von Königsberg (Regiomontanus)”, Philobiblon , ix (1936), 89–97; and in Aiton E. J. , “Peurbach's Theoricae novae planetarum: A translation with commentary”, Osiris , 2nd ser., iii (1987), 4–43, esp. p. 7.

Inc.: Circulus eccentricus vel egresse cuspidis. For an introduction to the Theorica planetarum communis and the responses to it by Peuerbach and Regiomontanus, see Pedersen Olaf , “The decline and fall of the Theorica planetarum literature: Renaissance astronomy and the art of printing”, in Studia Copernicana , xvi (Wrocław, etc., 1971), 157–85, esp. pp. 171–82 [Pedersen's translation of the work appears in Grant Edward (ed.), A sourcebook in mediaeval science (Cambridge, MA, 1974), 451–65]; Grössing Helmuth , Humanistische Naturwissenschaft: Zur Geschichte der Wiener mathematischen Schulen des 15. und 16. Jahrhunderts (Saecula spiritalia, viii; Baden-Baden, 1983), 121, 222–9; Byrne James , “The stars, the Moon, and the shadowed Earth: Viennese astronomy in the fifteenth century”, Ph.D. dissertation, Princeton University (Ann Arbor, 2007).

The two manuscripts with early versions of the text are Florence, Biblioteca Nazionale Centrale, Magl. XI 144, 18r–24r; and Trier, Stadtbibliothek, ms 8^o cod. 1924/1471, 232r–43r. Curiously, neither has diagrams.

Vienna, Österreichische Nationalbibliothek, cod. 5203, 100r–117r. Also from the Viennese sphere of influence is a partial copy from 1393 in the library of the Benedictine abbey of Melk (Stiftsbibliothek 601); see Kren Claudia , “A medieval objection to Ptolemy”, The British journal for the history of science , iv (1969), 378–93, esp. p. 378. James Byne has recently found another version of these proofs in a 15th-century commentary on the Theorica planetarum in Vienna, Österreichische Nationalbibliothek, cod. 5182; see his “The stars, the Moon, and the shadowed Earth” (ref. 7), 173–5. In my opinion, this commentary was written by yet another Viennese reader of Langenstein's De reprobatione.

See Zinner Ernst , “Die wissenschaftlichen Bestrebungen Regiomontans”, Beiträge zur Inkunabelkunde, NF, ii (1938), 89–103; and Zinner , Regiomontanus (ref. 1), chap. 7. The book list is now edited from three of the surviving copies and commented in Michela Malpangotto, Regiomontano e il rinnovamento del sapere matematico e astronomico nel Quattrocento (Bari, 2008), 149–54, 184–209.

Possible signs of haste appear in the book itself, from the initial setting of a page with two extra lines (corrected during the press run), through the last folio (left entirely blank), to the diagrams themselves, which are fully adequate to their purpose, but scarcely perfect.

These editions are the Ferrara 1472 Sacrobosco (Hain 14100), which includes the Theorica planetarum communis and the Venice edition of the same pairing (not after 8 May 1472; Goff J-400). As my monograph on the Disputationes will show in detail, the preface resonates with themes articulated by another member of the Bessarion circle, Niccolò Perotti in his letter on press censorship; see Monfasani John , “The first call for press censorship: Niccolò Perotti, Giovanni Andrea Bussi, Antonio Moreto, and the editing of Pliny's Natural history”, Renaissance quarterly , xli (1988), 1–31. On the preface (including translations), see Pedersen , “Decline and fall of the Theorica planetarum” (ref. 7), 171–82; and Malpangotto, Regiomontano (ref. 10), 155–62.

The edition survives in 25 exemplars, of which I have seen all but the Moscow copy (in Dresden before the Second World War): London, British Library, IB 7885; Oxford, Bodl., Auct. 0.4.19(2); Cambridge, Trinity Coll., Grylls 3.478; Cambridge, Trinity Coll., VI.15.80; Paris, Bibliothèque Nationale, Rés. V. 298; Augsburg, Stadt- und Staatsbibliothek, 2^o Ink 411; Göttingen, Universitätsbibliothek HS Di4 Astr I, 971 Inc.; Munich, Staatsbibliothek, Clm 27 [= ms]; Munich, Staatsbibliothek, 2^o Inc. s.a. 1021^o; Munich, Staatsbibliothek, 2^o Inc. s.a. 1010; Leipzig, Universitätsbibliothek, Libri sep. 962; Nuremberg, Germanisches Nationalmuseum 4^o 33887a; Nuremberg, Stadtbibliothek, Math 3 2^o; Nuremberg, Stadtbibliothek, Will III 882; Würzburg, Universitätsbibliothek, I.t.f.XL; Parma, Biblioteca Palatina, Parm. 421; Vienna, Österreichische Nationalbibliothek, II.D.6; Poznań, Archiwum Archidiecezjalne, Inc 104; Stockholm, Kungl. Biblioteket, Ink. 839 [Collijn 607]; Boston, Public Library, Q.403.74; Cambridge, MA, Houghton Library (Harvard), Inc. 2214; New Haven (Yale), Beinecke Library, Taylor 19 (Johannes Serlinger copy); New Haven (Yale), Beinecke Library, Zi +4383 copy 2 (copy inscribed by Bernard Walther); New Haven, Yale Medical Historical Library, old call number X.vi.20 [Harvey Cushing Collection, Incunabula +E-113].

I have found no evidence of a shift in the position of the initials in any of the copies I have seen. Some contemporary printers experimented with printing woodblocks simultaneously with text. At least two South-German printers who first printed their illustrations after the text (notably Albert Pfister in Bamberg in the 1460s and Günther Zainer in Augsburg in 1471) began to print the two with one pull of the press (undated and 1472, respectively), but their techniques did not immediately supplant the old practices; see Vincent Auguste , “La technique de certains incunables illustrés. Tirage séparé des gravures et du texte. Figures en lamelle métalliques”, Gutenberg-Jahrbuch , n.v. (1929), 101–8, esp. p. 101; and Needham Paul , “Prints in the early printing shops”, in Parshall Peter (ed.), The woodcut in fifteenth-century Europe (Washington, DC, 2009), 39–91.

Donati Lamberto , “Studi sul passagio dal manoscritto allo stampato: La decorazione degli incunaboli”, Studi di paleografia … in onore di Cesare Manarese (Milan, 1953), 331–41; and Donati Lamberto , “I fregi xilografici stampati a mano negl' incunabuli italiani”, La bibliofilia , lxxiv (1972), 157–64, 303–27; and lxxv (1973), 125–74. Zainer in Augsburg seems to have preceded Regiomontanus in printing decorative initials with the text. I am preparing detailed studies of Regiomontanus's initials and their history.

See the illustrations described in Benjamin Francis S. Jr Toomer G. J. (eds), Campanus of Novara and medieval planetary theory (Madison, 1971), 26–7 and 59–125 (passim); Grant , Sourcebook (ref. 7), 453–60.

Redgrave called Ratdolt's 1482 edition of Euclid, “the first attempt to illustrate the work of this author with woodcuts of the problems”; see Redgrave Gilbert R. , Erhard Ratdolt and his work at Venice (London, 1893), 16. This qualified statement has sometimes been misinterpreted to give Ratdolt credit for the first geometrical illustrations. Redgrave's still valuable work is clearly wrong to credit Ratdolt with the first coloured astronomical diagrams (p. 17).

I have not yet seen evidence of casting-off marks linked to Regiomontanus's press, but his autograph manuscript of the De triangulis omnimodis (St Petersburg, Archive of the Russian Academy of Sciences, IV-1-936) preserves the ‘casting off’ marks of Johannes Petreius. He both indicates the breaks and includes folio numbers, sometimes visibly (in lead?), sometimes by mere indentation that is much harder to see (dry point?), sometimes at mid-word. The marks are consistently off by one page. Thus, at 25r and 26r, the breaks for D8 and E1 in the ms correspond respectively to D4r and D4v in the 1533 edition from the Nuremberg printing shop that, a decade later, would publish Copernicus's De revolutionibus (1543).

According to Pollard, Schoeffer after 1462 rubricated his books before selling them; Pollard Alfred W. , Early illustrated books (London, 1893), 7.

Such eclipse diagrams also appear in some fifteenth-century manuscripts.

His vocabulary runs from “figuratio” (3v, 6r, 7r) through “figuratio linearis” (5v) to “figura” (9r — Also the terminology of the Theorica planetarum communis that Cracoviensis quotes at 5r).

The words “Omitte figurationem; perspicua enim tua est argumentatio” (7v) also appear in the manuscripts with early versions of the text, even though the latter have no diagrams at all.

On the background of this issue, see Byrne James , “The mean distances of the Sun and commentaries on the Theorica planetarum”, Journal for the history of astronomy, xlii (2011), 205–21.

Grant , Sourcebook (ref. 7), 459.

This criticism is of considerable significance. It shows that the Theorica planetarum communis (and the many readers trained by it) considered the behaviour of the eccentric deferent with respect to the equant point to be completely uniform about the equant point and in effect to be consistent with the behaviour of a rigid ring or sphere. Following Henry of Langenstein, however, Regiomontanus's proof showed that the circumference of the eccentric as a whole did not move uniformly about the equant. The wide diffusion of Regiomontanus's criticism in multiple editions of the Disputationes in the late fifteenth and early sixteenth centuries brought to his readers' attention a serious geometrical, and implicitly physical, objection to the equant, an issue that famously motivated Copernicus to seek alternative planetary models, as he noted in the Commentariolus; see Swerdlow Noel , “The derivation and first draft of Copernicus's planetary theory: A translation of the Commentariolus with commentary”, Proceedings of the American Philosophical Society, cxvii (1973), 423–512, esp. pp. 434–5.

A similar criticism and an analogous proof already appear in Langenstein's De reprobatione; see Kren , “Medieval objection” (ref. 9), 383–5. My forthcoming analysis of the Disputationes will detail this relationship, discussed briefly in my “Regiomontanus and homocentric astronomy”, Journal for the history of astronomy, xxvii (1998), 157–66, esp. p. 161.

See, e.g., Defensio Theonis contra Georgium Trapezuntium , Book 9, 184v–185r (from the digital facsimile of St Petersburg, Archive of the Russian Academy of Sciences, St Petersburg Branch, IV-1-935, available at http://regio.dartmouth.edu/). In contrast, the two manuscripts of the Epitome of the Almagest that Regiomontanus prepared for Cardinal Bessarion (Venice, Biblioteca Nazionale Marciana, fondo antico 328 [1760] and fondo antico 329 [1843]) present the text as a block, leaving very wide margins into which he drew the diagrams, a layout replicated in Johannes Hamann's editio princeps (Venice, 1496).

This order is very clear in the three Yale copies (Beinecke, Zi +4383 and Taylor 19; Yale Medical History Library +E-113), which I saw soon after I began asking myself these detailed questions.

Needham , “Prints in the early printing shops” (ref. 14), 48; Parshall Peter Schoch Rainer , “Early woodcuts and the reception of the primitive”, in Peter Parshall and Rainer Schoch, The origins of European printmaking: Fifteenth-century woodcuts and their public (Washington, DC and New Haven, 2005), 1–17.

In addition to Gutenberg himself, note that the legal documents that Anna Modigliani recently discovered about printing societies in Rome of the 1460s feature a goldsmith; Modigliani Anna , Tipografi a Roma prima della stampa: Due società per fare libri con le forme (1466–1470) (Rome, 1989), 59, 63–5, 81–6. For goldsmiths and engraving, see Hayter S. W. , New ways of gravure: A practical guide (New York, 1949), 170; and Hind Arthur , Andrea Mantegna and the Italian pre-Raphaelite engravers (London, 1911), 6–7.

The research of Blaise Agüera y Arcas and Paul Needham has raised serious doubts about Gutenberg's use of the standard punch-and-matrix method when casting his early fonts; see Needham Paul , “Johann Gutenberg and the Catholicon Press”, Papers of the Bibliographical Society of America , lxxvi (1982), 395–456; and Blaise Agüera y Arcas “Temporary matrices and elemental punches in Gutenberg's DK type”, in Jensen Kristian (ed.), Incunabula and their readers: Printing, selling, and using books in the fifteenth century (London, 2003), 1–12. Without taking the so-called standard method for granted, my naked-eye sampling of Regiomontanus's roman font — Almost a generation after Gutenberg's — Nevertheless suggests that he probably was using such a method (his letters appear to fall into a very small number of types of ‘identical’ imprints, a distribution consistent with several castings using slightly different matrices, the likely result of striking the same punch with minute variations in the strength of the hammer blow and the orientations of the punch).

Corsten Severin , “Die Erfindung des Buchdrucks im 15. Jahrhundert”, in Die Buchkultur im 15. und 16. Jahrhundert (Hamburg, 1995), 125–202, esp. pp. 139–40; Vincent , “La technique de certains incunables illustrés” (ref. 14); Baldasso , “Illustrating the Book of Nature” (ref. 3), especially chaps. 5–7.

Needham , “Prints in the early printing shops” (ref. 14), 55–8.

Needham , “Prints in early printing shops” (ref. 14), 55–71, passim. Copper engraving in printed books evidently dates to Brugge/Bruges in 1473 (Caxton) and 1476 (Mansion); see Hind A. M. , A short history of engraving and etching (London, 1908), 32–3; Landau David Parschal Peter (eds), The Renaissance print, 1470–1550 (New Haven, 1994), 35; Vandamme Ludo , “Colard Mansion et le monde du livre à Bruges”, in Aquilon Pierre Claerr Thierry (eds), Le berceau du livre imprimé: Autour des incunables (Turnhout, 2010), 177–86.

For the literature, see Turner Gerard L'E. King David A. , “The astrolabe presented by Regiomontanus to Cardinal Bessarion”, Nuncius , ix (1994), 65–206; with additional material in the appendices to David King, Angels and astrolabes, epigrams and enigmas: From Regiomontanus's acrostic for Cardinal Bessarion to Piero della Francesca's Flagellation of Christ (Boethius, lvi; Stuttgart, 2007). For attention to manufacturing techniques, including the use of punches, see Lamprey John , “An examination of two groups of Georg Hartmann astrolabes and the tables used in their manufacture”, Annals of science , liv (1997), 111–42, esp. pp. 136–8, 140–1.

A possible illustration of this process appears in Baccio Baldini's woodcut of the planet Mercury (c. 1468), which shows the shop of a silversmith (as indicated by the nearby plates, the belt buckles, and the pitcher, along with metal working tools); the foreground figure in the shop appears to be engraving a human form on a flat surface, presumably of silver as well. Lippmann claims that Baldini is responsible for three copper engravings in Bettini's Monte Santo di Dio (Florence, 1477), and that the 1481 Divina commedia has copper engravings partly attributable to Baldini; he also ascribes the first Florentine illustrated book (a geography of Berlighieri) to engravings on copper plates, a parallel to Ptolemy's Geography of Rome 1478, by Sweynheym and Buckink; Lippmann Friedrich , The art of wood-engraving in Italy in the fifteenth century (London, 1888), 19–21.

Art. “Nuremberg”, in Campbell Gordon (ed.), The Grove encyclopedia of the decorative arts, ii (Oxford, 2006), 162–74.

Zinner , Regiomontanus (ref. 1), 157–60, 164–5.

von Stromer Wolfgang , “Meister Konrad Scherp, Regiomontans Experte für Feinmechanik in der Nürnberger Officina Febrilis [sic!] und für den wissenschaftlichen Buchdruck”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, lxxix (1992), 123–32.

Eirich Raimund , “Bernard Walther (1430–1504) und seine Familie”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, lxxiv (1987), 77–128, esp. p. 106.

Needham , “Prints in the early printing shops” (ref. 14), 51 (with many illustrations, passim).

Montucla Jean-Etienne , Histoire des mathématiques (Paris, An VII), i, 555 [for the online STC, see http://istc.bl.uk/search/search.html?operation=record&rsid=1173940&q=6 (access 8 July 2011)]; Zinner , Regiomontanus (ref. 1), 175–7; Wingen-Trennhaus , “Regiomontanus als Frühdrucker in Nürnberg” (ref. 3), 52–4; Baldasso , “Illustrating the Book of Nature” (ref. 3), 206 (Baldasso believes, correctly in my view, that Regiomontanus's tables and the paper instruments at the back of the Calendars were printed from metal plates). Leading dissenters are discussed below.

For a thorough description of the process and its pitfalls, see Corsten , “Die Erfindung des Buchdrucks im 15. Jahrhundert” (ref. 32), 139–43.

Hayter , New ways of gravure (ref. 30), 52–3.

The circle seems to have been engraved first, for the execution of the rectilinear segments betrays caution as the straight lines approach the intersection with the circle. The line AC seems to have been constructed from the E towards A, from E towards G, from G towards N, from N towards C.

Hind , Mantegna (ref. 30), 6–10.

Ratdolt's own chronicle of his life mentions that he went to Venice (from Augsburg) for the last time on 15 September 1474; Schwarz Ignaz , “Die Memorabilien des Augsburger Buchdruckers Erhard Ratdolt (1462–1523)”, in Breslauer Martin Koehler Kurt (eds), Werden und Wirken: Ein Festgruss Karl Hiersemann gesandt… (Leipzig, 1924), 399–406, p. 404. Since this date occurs late in the year in which Regiomontanus issued his printing advertisement, his Ephemerides, and the German and Latin Calendars, one cannot help wondering if, before crossing the Alps, Ratdolt already had access to copies of these Regiomontanus editions.

In the Renner edition, the diagram of the “Theorica solis” (f. e2r) in the old Theorica is much more complicated than the one Regiomontanus included in his edition of Peuerbach: It shows 8 different positions of the Sun and has lines from the centre of the eccentric and from the centre of the Earth. Even more intriguingly, this very plate was reused in Ottaviano Scoto's 1490 Venice joint edition of Sacrobosco, Regiomontanus, and Peuerbach, where it appeared as a supplement to diagrams in the Theoricae novae — now labelled “Theorica alia linearum et motuum solis sequitur” (1490, d8r). The two impressions have similar nicks and idiosyncrasies: For example, three of the most misshapen solar disks are misshapen in exactly the same way (checked at the Observatoire de Paris, 21286 and 21391). The 1490 edition also shows traces of additional wear: A deformation of the outer circle at the top and two portions of line segment on the outer rim have broken or been depressed.

Redgrave gives good reasons for thinking that some of Renner's editions were imitating Ratdolt's, but dates and content show that he is wrong to extend the case to their Spheres; see Redgrave , Erhard Ratdolt (ref. 17), 14.

Malpangotto , Regiomontano (ref. 10), 149–51, 184–209.

“ut qua facilitate litterarum elementa imprimuntur, ea etiam geometrice figure conficerentur.” See Baldasso Renzo , “La stampa dell' editio princeps degli Elementi di Euclide (Venezia, Erhard Ratdolt, 1482)”, in Pon Lisa Kallendorf Craig (eds), The Books of Venice – Il libro veneziano, Miscellanea Marciana, xx (2005–7) (New Castle, DE, 2008), 61–100, esp p. 63.

Redgrave , Erhard Ratdolt (ref. 17), 16; Thomas-Stanford Charles , Early editions of Euclid's Elements (London, 1926), 4; Lippmann , The art of wood-engraving in Italy (ref. 36), 66–7; Rider Robin , “Early modern mathematics in print”, in Mazzolini Renato G. (ed.), Non-verbal communication in science prior to 1900 (Florence, 1993), 91–113, esp. p. 96.

See most recently Baldasso, “Illustrating the Book of Nature” (ref. 3), chap. 7; and Baldasso , “La stampa” (ref. 51), 72–9. I am, however, not fully convinced that Ratdolt used metallic strips, as Baldasso maintains.

De Morgan Augustus , “Eucleides”, Dictionary of Greek and Roman biography and mythology (3 vols, Boston, 1849), ii, 63–74, esp. pp. 70–1. Butsch believed that the famous title-page decoration for Ratdolt's 1476 edition Regiomontanus's Calendar was also printed from three metal elements (“drei Metallschnittleisten”); see Butsch Albert Fidelis , Bücher-Ornamentik der Renaissance, historisch-kritisch dargestellt (2 vols, Leipzig, 1878–81; repr. in 2 vol. in 1 portfolio, Munich, 1922), 4.

Thomas-Stanford , Early editions of Euclid's Elements (ref. 52), 3–4.

Illustrations in Ferino-Pagden Sylvia Scirè Giovanna Nepi (eds), Giorgione: Myth and enigma (Milan, 2004), 124, 127.

Although familiar with Ratdolt, recent work on the subject seems unaware of the connection to Regiomontanus; see Gentili Augusto , “The Castelfranco frieze: The Great Conjunction of 1503/04 and the decline of the arts”, in Ferino-Pagden Scirè Nepi (eds), Giorgione (ref. 56), 124–31.