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The original motivation for Copernicus’s research: Albert of Brudzewo’s Commentariolum super Theoricas novas Georgii Purbachii

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Abstract

In 1454 Georg Peurbach taught astronomy at the Collegium Civium in Vienna by reading a work of his own: the Theoricae novae planetarum. In 1483 Albert of Brudzewo, teaching astronomy at Cracow University, adopted Peurbach’s text together with a commentariolum of his own. Among the numerous commentaries preserved both in manuscript and in printed form, Brudzewo’s stands out because it submits Peurbach’s work to a subtle analysis that, while recognising the merits for which it was widely accepted, also focuses on the limitations of the celestial spheres described in it. Budzewo’s commentary is of interest, in itself both for its criticism of Peurbach’s descriptions of solar, lunar and planetary theory and also for its importance to Copernicus’s own planetary theory. For Copernicus makes clear in the Commentariolus that his concern was the very same issue, violation of uniform circular motion by the rotation of spheres, that Brudzewo criticises in detail. In this way, Brudzewo’s commentary stands as the original motivation for the investigation of the motion of the planets that was eventually to lead Copernicus to a planetary theory based strictly upon uniform rotation of spheres, and through that investigation to the motion of the Earth and the heliocentric theory.

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Notes

  1. Cod. 5203, Österreichische Nationalbibliothek, Wien, f. [24r]; Codex Sancrucensis 302, Stiftbibliothek, Heiligenkreuz , f.[60v]; Cod. 5245, Österreichische Nationalbibliothek, Wien, f.[26v] (om. “Wienne in Collegio Civium penultima mensis Augusti”). For a description of these manuscripts and of the other manuscripts which transmit Peurbach’s Theoricae novae during the life of its author, see (Malpangotto 2012).

  2. This results from the analysis of the extant manuscripts and printed editions spreading Peurbach’s Theoricae novae, alone or with commentary, from fifteenth to seventeenth century. Cf. (Malpangotto 2016 à paraître).

  3. For a description of the way in which Peurbach, in his Theoricae novae planetarum, presents the structure of the planetary spheres, see (Malpangotto 2013b). For an analysis of what distinguishes Peurbach’s Theoricae novae from the previous tradition, see (Malpangotto 2016 à paraître). To insert Peurbach’s contribution in the previous tradition, (Duhem 1913–1915, vol. III), (Grant in Lindberg 1978), (Lerner 2008), (Barker 2011) remain the reference works and the following question in (Lerner 2008, I, 120–121) is still opened: «  Faut-il voir dans cette incorporation des cercles abstraits de l’Almageste dans des orbes solides, le résultat de la diffusion progressive d’un modèle de machinerie céleste dont les origines lointaines remontent à Ptolémée lui-même? On peut le penser. En tout cas, tout se passe comme si ce processus de diffusion, qui mériterait de faire l’objet d’une étude particulière, avait trouvé chez Peurbach son aboutissement   » .

  4. Cod. 5203, Österreichische Nationalbibliothek, Wien, f. [2r]; Codex Sancrucensis 302, Stiftbibliothek, Heiligenkreuz , f.[40r]; Cod. 5245, Österreichische Nationalbibliothek, Wien, f.[1r].

  5. (Duhem 2003), (Jardine 1984), (Lerner 2008), (Barker 2011) considers, for exemple, the real or “fictionalist” interpretation of the celestial orbs adopted by different authors.

  6. Only the better known printed versions of the Theoricae novae are evoked here: (Capuano 1495), (Mazzolini de Prierio 1514), (Reinhold 1542), (Schreckenfuchs 1556), (Nunes 1566), (Wursteisen 1568). For a complete description of the spreading of Peurbach’s work and a catalogue describing both manuscripts and printed editions transmitting the Theoricae novae from 1454 to 1653, see (Malpangotto 2016 a paraître).

  7. L, f. 69r; R, f. 79r; D, f. 149v; K, 189r. For a Latin transcription, see the “Appendix”. In 2013, in the same month of May, two studies on Brudzewo’s Commentariolum appeared: (Barker 2013) and (Malpangotto 2013a). Barker considers the vexed question of the reality of the celestial orbs to suggest that the common view of modern commentators, who usually depict Brudzewo as a fictionalist denying the physical reality of the orbs described by Peurbach in his Theoricae novae planetarum, “is an error based on selective reading and ignoring the context in which Brudzewo was writing”. (Malpangotto 2013a) presented the first French version of our analysis of Brudzewo’s text, which we here develop in more detail.

  8. L: f. 69r; R: 79r; D: 149v; K: 189r. For a Latin transcription see the “Appendix”.

  9. The explicit of L confirms that Brudzewo’s teaching dates back to the year 1483: “Dictum est anno domini Millesimo quadringentesimo octogesimo tertio”. The Liber diligentiarum of the Arts Faculty starts with year 1487 and does not enable to know the teachers for the previous period. According to Birkenmajer in (Brudzewo 1900: XXVII), the manuscript annotation saying “1483 Brudzew legit”, in the margin of f. sign. a3 v of the 1495 printed version Inc. 2705 of the Jagiellonian Library, confirms that in 1483 Brudzewo read his Commentariolum.

    The same explicit in L also says that the text of the Commentariolum was made public to students in 1488: “Scriptum vero et in publicum editum anno domini Millesimo quadringentesimo octogesimo octavo”. This same course should be the one written in manuscripts, R, D, K (see “Appendix”).

    The Liber diligentiarum of the Arts Faculty of Cracow (Wisłocki 1886: 5) reveals that Brudzewo gave a course on the Theorica planetarum in 1488. So he taught the commentary copied in these manuscripts. Manuscript C confirms that the Commentariolum is still read at Cracow University in 1493: “finitum in vigilia Circumcisionis domini a. d. 1493 Finis”. For this semester, the Liber diligentiarum says that the Theorica planetarum was taught by Simon Sierpc (Wisłocki 1886: 23).

  10. The Commentariolum was first printed in Milan in 1494 by the printer Uldericus Scinzenzeler (M in the “Appendix”; unknown to Birkenmajer). All the extant copies of this edition M lack any f. ai and Brudzewo’s name does not appear anywhere in the volume. In 1495, the same printer published a second edition of the Commentariolum (E in the “Appendix” and in Brudzewo 1900). The titlepage on f. [ai]r does not mention Brudzewo’s name. In the dedication letter, at f. [ai]v, Johannes Otto de Valle Uracense says that this is Brudzewo’s work and states that Brudzewo was his praeceptor and the printer’s colophon at f. sign. [g viii]v explicitly attributes the work to Brudzewo.

  11. (Brudzewo 1900: 23): “Littera autem taliter probatur”. With “littera” Brudzewo always refers to the text of Peurbach’s Theoricae novae.

  12. (Brudzewo 1900: 47): “probatur in littera”. As usual, with “littera” Brudzewo always refers to the text of Peurbach’s Theoricae novae.

  13. (Brudzewo 1900: 84): “Sequens etiam littera Magistri satis plana est et evidens in figura”. Usually with “Magister” Brudzewo is referring to Georg Peurbach.

  14. Brudzewo’s Commentariolum is divided into three parts: the Tractatus primus has no title in the manuscripts, but it concerns the texts about the Sun, the Moon and the planets (Brudzewo 1900: 22–127), while the titles of Tractatus secundus: De passionibus planetarum (Brudzewo 1900: 128–145) and De motu octavae sphaerae tractatus (Brudzewo 1900: 146–151) appear in the extant manuscripts.

  15. (Brudzewo 1900: 22–44).

  16. (Brudzewo 1900: 44–78).

  17. (Brudzewo 1900: 78–107).

  18. (Brudzewo 1900: 107–110).

  19. (Brudzewo 1900: 110–127).

  20. At the beginning of each section of his commentary, Brudzewo presents this structure which is common to each section of Peurbach’s text. See (Brudzewo 1900: 22, 44, 78, 107, 110).

  21. This conviction is regularly repeated and becomes particularly evident each time Brudzewo has to present the astronomical terms and the lines determining them in geometrical terms. In these passages he notices that Peurbach transforms the arrangement of the real orb carrying the celestial body into an imaginary circle represented on a plane: “In fact, the Theoristae, who know the real orbs’ arrangement, habitually subordinate to these real orbs some imaginary circles which resemble them and which are arranged in the same way that finally each one, which imitates such an arrangement, be exposed to sight in a plane, for, as Ptolemy says, sense perception frequently aids the intellect to investigate. Sensus enim saepius adiuvat intellectum ipsum speculari inquit Ptolemaeus.  » (Brudzewo 1900: 34); cf. also 57, the commentary to “Vocatur autem superficies”.

  22. (Brudzewo 1900: 57): “Iam Magister, posita declaratione ecentrici, qui est orbis realis, [...]”.

  23. (Brudzewo 1900: 22): “In prima parte ponit Magister divisionem totius sphaerae solaris in orbes reales partiales [...]”.

  24. (Brudzewo 1900: 79–80): “[...] in revolutionibus, quae esset absque diversitate qualibet. Talis enim motus est quasi proprietas conveniens corporibus coelestibus, alienatis a natura istorum inferiorum, quorum motus [est] absque similitudine et ordine [...]”.

  25. Cf. (Brudzewo 1900: 23): “Omnem motum coelestis corporis simplicem et verum aequalem esse, hoc est, super aequos angulos in centro motus consistentes et in arcus cadentes aequales, aequalibus fieri temporibus”. This passage faithfully recalls the same words taken from the third book of the Abbreviatio Almagesti that Brudzewo ascribes to Albertus Magnus. Cf. manuscript Wien, Österreichische Nationalbibliothek, Cod. 5266, f. 186r.

  26. (Brudzewo 1900: 23).

  27. (Peurbach [1472]: ff. [1v–2r]): “Sed orbis solare corpus deferens motu proprio super suo centro scilicet eccentrici regulariter secundum successionem signorum, quotidie. lix. minutis et octo secundis fere de partibus circumferentiae per centrum corporis solaris una revolutione completa descriptae, movetur. [...] Cum autem centrum solare ad motum orbis ipsum deferentis regulariter super centro eccentrici moveatur; necesse erit ut super quocumque puncto alio irregulariter moveatur. Quare Sol super centro mundi in temporibus aequalibus inaequales angulos, et de circumferentia zodiaci inaequales arcus describit.” Here and in what follows, we have preferred to refer to Peurbach’s editio princeps and directly translate its text instead of using Aiton’s translation of the third edition of the Theoricae novae.

  28. Cf. (Brudzewo 1900: 30–31): “Etsi Solem in suo ecentrico regulariter moveri sit primum principium in Astronomia (ideo cum negante illud, non est amplius in Astronomia disputandum), tamen tale principium potest per scientiam subalternantem, scilicet mathematice demonstrari sic. Sol in temporibus aequalibus, aequales super centrum suum describit angulos et aequales resecat arcus, ergo aequaliter movetur.”

  29. Cf. (Brudzewo 1900: 27–28).

  30. (Brudzewo 1900: 23): “concluserunt Solem in zodiaco inaequaliter moveri.”

  31. (Brudzewo 1900: 23): “Et cum ipse Sol diverso motu et inaequali moveatur in zodiaco, senserunt ipsum—ex principiis philosophiae—debere moveri in suo orbe, aequali motu et simplici.”

  32. (Brudzewo 1900: 23–24): “Haec itaque duo prae oculis pensantes, diversum scilicet motum Solis in zodiaco, uniformem vero et aequalem in suo orbe, arguebant: Si ipse Sol haberet suum orbem zodiaco concentricum, de facto etiam moveretur in zodiaco aequaliter [...] Cum itaque Sol in zodiaco moveatur irregulariter, causam non invenientes magis consonam, ecentricitatem orbis solaris assignaverunt, qui quidem ecentricus in una parte elevabitur a centro mundi ad zodiacum accedendo, in altera vero ad centrum mundi appropinquabit, removendo se a zodiaco. Hoc namque pacto Sol videbitur in zodiaco irregulariter moveri et in una medietate morari diutius quam in altera.”

  33. Cf. (Brudzewo 1900: 25): “Amplius imaginati scrutatique sunt, an foret conveniens ipsi Soli hunc unicum habere orbem ecentricum et quaerebant, si omnes sphaerae essent ecentricae: invenerunt quidem, quod sphaera stellata est mundo concenrica. Istud enim probaverunt per Pleiades et alias stellas Pleiadibus diametraliter oppositas, videlicet, quod quando Pleiades oriebantur, illae occidebant, et e converso. Viderunt insuper motum septem planetarum, diversum et varium inter se. Si ergo octava sphaera est concentrica et planetae inter se moventur motibus diversis, positis eorum orbibus totaliter ecentricis, profecto inter sphaeram octavam et inter sibi immediate inferiorem, ratione motus diversi accideret scissio sphaerarum et commixtio vacui; et sic in aliis sphaeris inferioribus. Quod eis videbatur absurdum sentire, alias enim coelum esset corruptibile. [...] Movebant ergo eos duae causae contrariae: una propter quam coacti sunt ponere ecentricum orbem Solis cum ceteris planetarum sphaeris, altera quia si totae ecentricae fuissent, scissio sphaerarum committeretur. Hinc inde revolventes, non invenerunt aliquid magis consonum, nisi quod in unaquaque sphaera essent tres orbes ad minus taliter dispositi, ut inquit littera.”

  34. (Peurbach [1472]: f. [1v]): “Moventur autem orbes deferentes augem Solis propriis motibus proporcionalibus ita quod semper strictior pars superioris sit supra latiore inferioris.” (Brudzewo 1900: 29) criticise the improper character of the adjective “propriis” that Peurbach attributes to the motion of these orbs.

  35. Cf. (Brudzewo 1900: 29–30): “Ex hoc enim, quod horum orbium principale centrum sit centrum mundi [...] ideo habent motum proportionalem, sic quod moles unius crassitudinem alterius non derelinquit, nec e converso. Cuiuslibet etiam corporis coelestis circa centrum suum motus est aequalis, ut dictum est, nec procedit instantia quorumdam, videlicet quod isti duo orbes quoad unam superficiem habent centrum mundi, quoad alteram vero centrum ecentrici; ergo si movebuntur super centro mundi, simili ratione super centro ecentrici. Dicunt ergo: esse inimaginabile,eumdem orbem eodem motu super diversis centris moveri. Sed revera non est inconveniens. Ex hoc enim quod habeant diversa centra respectu diversarum suarum superficierum, motus ipsorum orbium secundum diversas eorum superficies ad diversa centra referri possunt. Orbem tamen, in utraque superficie similis dispositionis, eodem motu super diversis centris moveri, sine inconvenienti non esset.”

  36. (Peurbach [1472]: f. [6v]): “Haec tamen difformitas hanc regularitatis habet normam [...]”.

  37. For a description of these influences in the case of the sphere of Mercury, see (Malpangotto 2013b: 278–294).

  38. Cf. (Brudzewo 1900: 85–86): “inquit Ptolemaeus dictione \(\hbox {IX}^{\mathrm{na}}\) capitulo \(5^{\mathrm{to}}\): Et centra orbium revolutionis neque revolvuntur super hos orbes centrorum egredientium, quorum centra per motus suos revolvuntur in revolutione aequali et perambulant in temporibus aequalibus angulos aequales. Haec ille.”

    Brudzewo transcribes this passage of the Almagest which, as mentioned above, he knows from Gerard of Cremona’s Arabo-Latin version (cf. Ptolemy 1515: f. 103r). It should be noted that Brudzewo remains faithful to this Arabo-Latin version in which the circles of the Almagest are systematically called “orbs”.

  39. (Peurbach [1472]: f. [6v]): “Motus autem epicyclum deferentis super centro et polis suis difformis est. Haec tamen difformitas hanc regularitatis habet normam ut centrum epicycli super quodam puncto in linea augis tantum a centro huius orbis quantum hoc centrum a centro mundi distat elongato: regulariter moveatur. Unde et punctus ille centrum aequantis dicitur et circulus super eo ad quantitatem deferentis secum in eadem superficie imaginatus eccentricus aequans appellatur.”

  40. (Brudzewo 1900: 86): “Quantum est in se, ad motum orbium non est opus aequante. Nihil enim aequans facit ad motum orbis realis, cum sit circulus imaginarius, sed quantum ad opus astronomicum, seu ad calculationem Tabularum, quae calculantur iuxta principia et conclusiones mathematicas, quae quidem conclusiones, quia saepius non possunt accomodari et applicari motibus, ut sunt in sua natura, seu ut apparent.”

  41. Cf. (Brudzewo 1900: 86): “Ideo ipsi Mathematici quandoque capiunt alio modo motus corporum coelestium, quam sunt in sua natura, vel aliter quam apparent, et considerant eos tali modo, qualiter serviunt eorum arti et operationi, cum alio modo nullatenus eos ad opus rectum et praecisum possent ponere.”

  42. (Brudzewo 1900: 87): “Et sic per motum aequalem iterum cognoscunt, quantum motus diversus maioritate aut minoritate planorum angulorum et arcuum addat aut diminuat supra motum aequalem: propter hoc ergo ponuntur aequantes.”

  43. (Brudzewo 1900: 86): “Imaginantur ergo aequalem esse motum, qui non aequalis videtur in se, propter opus ut rectius ponant. Et ex hoc convicti sunt et coacti ponere aequantes, circulos imaginatos, super quibus motus orbium diversos et inaequales, aequales esse considerant, reducuntque illos motus diversos primum ad aequalitatem in aequantibus, tamquam in id, ex quo iudicium diversi motus sumpturi sunt.”

  44. (Peurbach [1472]: ff. [4r–4v]): “Circumvoluitur tamen epicyclus taliter ut super centro proprio atque axe irregulariter moveatur. Sed haec irregularitas ad uniformitatem reducitur istam ut a puncto augis epicycli mediae, quicunque sit ille, quolibet die naturali tredecim gradus et quatuor minuta fere recedendo regulariter elongetur. Aux autem media epicycli est punctus circumferentiae epicycli quem ostendit linea a puncto diametraliter opposito centro eccentrici in circulo parvo per centrum epicycli ducta.”

    The “small circle” to which Peurbach refers, is determined by the motions of the secundum quid orbs and from the repositioning of their mass. Even if the sphere of the Moon has a different structure, it is the same mechanism which makes the centre of the eccentric carrying Mercury’s epicycle describe a “small circle” too. For an explanation of this, see (Malpangotto 2013b: 279–292).

  45. Cf. (Brudzewo 1900: 62–66).

  46. Cf. (Brudzewo 1900: 66): “Sic enim operati sunt antiqui, videlicet quod primo invenerunt revolutiones epicycli aequales et motum Lunae in epicyclo aequalem per considerationes eclipsium lunarium.” See also (Brudzewo 1900: 46–47).

  47. (Brudzewo 1900: 66): “Tandem demonstrationibus experti sunt arcum epicycli, inter lineam medii motus centri epicycli et inter centrum Lunae interceptum, esse maiorem aut minorem arcu medii motus Lunae in epicyclo.”

  48. See (Brudzewo 1900: 62–65).

  49. (Peurbach [1472]: f. [4v]): “Aux autem media epicycli est punctus circumferentiae epicycli quem ostendit linea a puncto diametraliter opposito centro eccentrici in circulo parvo per centrum epicycli ducta.” For the “small circle”, see supra, n. 44.

  50. (Brudzewo 1900: 65): “Unde est manifestum, quod—procedente centro epicycli a longitudine longiore ecentrici ad longitudinem propiorem—longitudo longior epicycli vera praecedit longitudinem longiorem aequalem, et—procedente centro epicycli a longitudine propiore ecentrici ad longitudinem longiorem— longitudo longior vera subsequitur longitudinem longiorem aequalem.”

  51. Cf. (Brudzewo 1900: 67): “Videtur [Ptolemaeus] in istis verbis innuere, quod declinatio et reclinatio non ex sola computatione proveniat, sed ex motu realiter apparenti in Luna. Luna enim ratione istius declinationis et reflexionis consequitur quasdam figuras post elongationem eius a Sole, videlicet quod apparet concava, seu excisa, et hoc circa quintum diem fere post coniunctionem. Apparet etiam tumida vel gibbosa, et hoc circa decimum diem fere post coniunctionem.”

  52. Cf. (Brudzewo 1900: 67–68): “Propter ergo salvare istum motum apparentem in Luna, quidam imaginantur epicyclum talem in Luna, quod habeat alium intra se inclusum, qui movet epicyclum deferentem Lunam motu declinationis et reflexionis, quod non videtur esse inconveniens.” The two figures drawn by Birkenmajer from C, L and E, although they differ in detail, show two concentric epicycles, one inside the other. There are also figures of lunar phases, including concave and gibbous.

  53. Thanks to Noel Swerdlow we could formulate this model and give a graphical representation.

  54. (Brudzewo 1900: 68, n.1): “Lunam quidam imaginantur habere duos epicyclos, unum maiorem, alterum minorem, in quo est eius corpus situatum, et ita epicyclus superior tantum, motu declinationis et reflexionis movetur. Et pro tanto illa macula, quae in Luna aspicitur, semper una et eadem apparet propter istum epicyclum: quod non esset, si talis epicyclus non esset.” This passage is found in the margin of f. 51r in L in the hand of the scribe and a similar annotation, literally different but on the same subject, is in the margin of f. 61v in R.

  55. Grazyna Rosinska’s research on the astronomy teachers at Cracow University in the first half of the fifteenth century enabled her to find a double epicycle for the Moon, in Sandivogius de Czechel’s commentary on the Theorica planetarum Gerardi written in about 1430, which appears to be for this purpose. See (Rosinska 1974, 1973).  The description appears to be of a second small epicycle surrounding the Moon itself that causes its body to rotate, not the two concentric epicycles described in Brudzewo’s text. Brudzewo’s text and the marginal annotation have also been considered by (Barker 2013: pp. 137–139), who reaches the same conclusion, that Brudzewo describes two concentric epicycles for the motion of the mean apogee of the epicycle and that these cannot cause the same side of the Moon to face the Earth.

  56. (Schreckenfuchs, 1556, pp. 120–121) says this for the superior planets referring to the more explicit explanation given for the Moon at pp. 58–61.

  57. (Brudzewo 1900: 94): “Ideo planeta in epicyclo iam habebit motum regularem et uniformem super centro aequantis, de quo linea ducta per centrum epicycli ostendit punctum, a quo computandus est aequalis motus planetae in epicyclo, qui Aux media appellatur. Quae quidem Aux media variabilis est quoad concavitatem illam, in qua situatur epicyclus, sic videlicet, quod continue sub alio et alio puncto sit concavitatis, vel etiam variabilis est in superficie convexa reali ipsius epicycli, ideo, quod continue alius et alius punctus superficiei realis epicycli succedit propter motum epicycli; non autem variabilis est quoad circumferentiam imaginatam in epicyclo, in qua motus planetae et revolutio computantur.”

  58. See supra the analysis of Mathematical artifices in Peurbach’s universe.

  59. (Peurbach [1472]: f. [3r]).

  60. (Peurbach [1472]: f. [6v]).

  61. (Peurbach [1472]: f. [4r]).

  62. (Peurbach [1472]: f. [7r]).

  63. (Brudzewo 1900: 55).

  64. (Brudzewo 1900: 85).

  65. (Brudzewo 1900: 65).

  66. (Peurbach [1472]: f. [3r]): “quamvis eccentricus epicyclum deferens super axe atque polis suis moveatur, non tamen super eisdem regulariter movetur.”

  67. (Peurbach [1472]: f. [2v]): “Orbis vero epicyclum deferens movetur secundum successionem signorum regulariter super centro mundi ita quod omni die naturali tali motu centrum epicycli XIII gradus et XI minuta fere perambulet.”

  68. (Brudzewo 1900: 30): “[...] Solem in suo ecentrico regulariter moveri sit primum principium in Astronomia (ideo cum negante illud, non est amplius in Astronomia disputandum), [...]”.

  69. Cf. (Peurbach [1472]: f. [9v]): “Ex his igitur et dictis superius manifestum est singulos sex planetas in motibus eorum aliquid cum Sole communicare: motumque illius quasi quoddam commune speculum et mensurae regulam esse motibus illorum.” Peurbach only introduces this concept in the section devoted to the sphere of Mercury, while Brudzewo brings it forward in the De Luna section. (Brudzewo 1900: 57): “Hic iam [Magister] determinat de motu eorumdem [Augem deferentium et epicyclum deferentis] per comparationem ad Solem, cum quo Luna et ceteri planetae in motibus suis naturalem habent connexionem, [...]”. He then notices that this idea had already been expressed by Haly in his commentary on the first book of Ptolemy’s Quadripartitum.

  70. (Brudzewo 1900: 54): “[...] et tu etiam poteris reperire sic. Motum Solis, quem habet Sol in uno die per tempus unius mensis multiplica et producto 360 gradus adde: sic enim provenient gradus, quos centrum epicycli percurrit in uno mense. Hoc itaque aggregatum per tempus unius lunationis divide, et in quotiente habebis, quantum centrum epicycli, seu deferens epicyclum, movetur quolibet die naturali motu aequali in Zodiaco.”

  71. (Brudzewo 1900: 54): “Ex his etiam, centrum epicycli moveri aequaliter super centro mundi, mathematice ostendi potest, scilicet per respectum ad lineam medii motus Solis, respectu cuius circa centrum mundi aequales constituit angulos, et aequales in temporibus aequalibus de Zodiaco resecat arcus. Ergo movetur aequaliter, sicut dicit littera, scilicet 13 gradibus 10 minutis etc.”. It is useful to note that Peurbach gives “about 13 degrees and 11 minutes.”

  72. The line of the Sun’s mean motion is the line drawn from the centre of the world to the zodiac, parallel to the line of the Sun’s motion in its eccentric. The line of the mean motion of the Moon’s epicycle is the line passing through the centre of the epicycle, drawn from the centre of the world to the zodiac.

  73. (Peurbach [1472]: f. [3r]): “Ex istis sequitur primo quod quamvis eccentricus epyciclum (sic) deferens super axe atque polis suis moveatur, non tamen super eisdem regulariter movetur.”

  74. (Peurbach [1472]: f. [3r]): “Signatis enim aliquibus angulis aequalibus super centro mundi versus augem et oppositum: qui versus augem est maiorem arcum eccentrici quam alter versus oppositum complectitur.”

  75. (Brudzewo 1900: 55): “Corellarium primum habet veritatem, scilicet quod ecentricus super axe suo et polis et circa centrum suum movetur irregulariter, motum ipsius in Zodiaco computando respectu centri ecentrici et non respectu centri mundi.”

  76. (Peurbach [1472]: f. [3r]): “Secundo quanto epicyclus lunae augi deferentis eum vicinior fuerit tanto velocius centrum eius movetur et quanto vicinior augis eiusdem opposito tanto tardius.”

  77. (Brudzewo 1900: 55).

  78. (Brudzewo 1900: 79): “Et hoc patet per Ptolemaeum dictione IX capitulo \(2^{\mathrm{do}}\), ubi inquit: In inquisitione vero diversitatum ingreditur ex dubitatione non parum propterea, quod videntur cuiusque stellarum duae diversitates, quae non sunt aequales, neque in magnitudine, neque in temporibus reditionum, quarum una videtur propter Solem et altera propter partes orbis signorum. Et cum coniunxerimus eas ambas, erit semper proprietas cuiuscumque earum propter illud difficilis cognitionis. Haec ille. In istis verbis Ptolemaeus vult quomodo quinque stellae erraticae, seu planetae habent diversum motum in Zodiaco, quia moventur aliquando versus septemtrionem, aliquando versus meridiem ab ecliptica et interdum vero sub ecliptica, aliquando motu tardo, aliquando veloci. Respectu etiam Solis habent diversum motum. Cum enim videbantur prope Solem, eorum motus [...] apparebat velox, cum circa quadras a Sole non moveri quidem sed stare videbantur, [...] et cum in diametro fuerunt cum Sole, contra signa tendebant.”

  79. (Peurbach [1472]: f. [6v]): “Motus autem epicyclum deferentis super centro et polis suis difformis est”.

  80. (Brudzewo 1900: 85): “Quod Magister dicat: centrum epicycli super centro ecentrici irregulariter moveri, non est verum intelligendo simpliciter.” Simpliciter is used here in the same sense as absolute, taken by itself, and is translated in the same way.

  81. (Brudzewo 1900: 85): “Hoc enim esset contra illam maximam, qua dictum est, omnem motum corporis coelestis simplicem et aequalem esse, et contra philosophiam, quae corporis simplicis et regularis motum ponit simplicem ac regularem. Et sic motus deferentis epicyclum, in se et absolute consideratus, de facto uniformis est [...]”.

  82. Cf. (Brudzewo 1900: 85): “Et hoc quidem esse verum, videlicet quod centrum epicycli habeat diversum motum in suo ecentrico [...]”.

  83. (Peurbach [1472]: ff. [6r-6v]): “Sed orbis epicyclum deferens super axe suo axem zodiaci secante secundum successionem signorum movetur [...] Motus autem epicyclum deferentis super centro et polis suis difformis est.”

  84. (Peurbach [1472]: f. [4r]): “Circumvoluitur tamen epicyclus taliter ut super centro proprio atque axe irregulariter moveatur.”

  85. (Brudzewo 1900: 65): “Secundum Campanum Luna in epicyclo movetur uniformiter et sic [movetur] et epicyclus circa centrum suum quod quidem verum est considerando motum epicycli simpliciter in se et absolute, sine relatione ad aliquem punctum. Cuilibet enim orbi coelesti motus uniformis convenit ratione suae naturae”.

  86. The statement “without reference to any point” excludes any point other than the centre, for the epicycle must turn uniformly about its centre.

  87. (Brudzewo 1900: 65): “Cuilibet enim orbi coelesti motus uniformis convenit ratione suae naturae”.

  88. (Brudzewo 1900: 65): “Quod autem Magister dicit in littera, epicyclum circumvolvi irregulariter, etiam verum est in ordine ad aspectum in centro mundi constitutum.”

  89. (Brudzewo 1900: 65): “Si enim epicyclus moveretur regulariter in ordine ad centrum mundi, extunc arcum epicycli medii motus semper staret esse tantum, quantum inter centrum Lunae et inter lineam medii motus centri epicycli, seu Augem veram epicycli (quod idem est) compraehenderetur, quod non fit. Dumtaxat, centro epicycli in Auge ecentrici vel in opposito eiusdem constituto, dicti arcus aequantur; centro autem epicycli a longitudine longiore ecentrici progrediente usque ad propiorem, semper minor est arcus medii motus Lunae in epicyclo arcu, inter centrum Lunae et lineam medii motus epicycli intercepto. In reliqua vero medietate ecentrici fit e converso [...]”.

  90. (Peurbach [1472]: f. [7r]): “[Motus huius] est super centro epicycli irregularis

  91. (Brudzewo 1900: 93–94): “Quod etiam Magister dicit, illum motum epicycli esse irregularem super centro suo, intelligit non simpliciter et secundum se considerando motum epicycli, sed in ordine ad oculum, qui de centro orbis signorum illum spectaret motum; si ibi (L) enim motus epicycli irregularis cadit tali modo, quod—centro epicycli discurrente ab auge ecentrici usque ad oppositum—semper minor est arcus medii motus planetae in epicyclo, quam arcus epicycli interceptus inter augem veram epicycli et inter centrum planetae, et in tantum minor, quantum correspondet distantiae inter centrum orbis signorum et inter centrum aequantis. In reliqua vero medietate iterum sit maior: sic ergo fit irregularis in ordine ad centrum mundi.” The variant “si ibi” appears only in manuscript L; all the other manuscripts and the printed editions write “sibi”.

  92. (Brudzewo 1900: 34): “Notandum. Mathematici seu doctrinales determinant de locis astrorum modo visuali ac si uterque oculus in centro mundi esset constitutus loca astrorum prospiciens secundum lineas ab ipso per astra ducibiles; hoc faciunt iudicio sensus nostri satisfacientes. [...] Determinant etiam de locis astrorum in ordine ad centrum mundi, quoniam illud uno et eodem modo se habeat respectu omnium corporum coelestium et est immobile.”

  93. L: f. 69r; R: 79r; D: 149v; K: 189r. For a Latin transcription see the “Appendix”.

  94. (C: f. 154r and f. 169v). The explicit at f. 169r says that at the end of the year 1493 Michael de Ruszoczjcze copied this text which was probably adopted for a course given by one of the Faculty teachers. The student says that he finished the copy in “vigilia Circumcisionis domini”, the evening of 31 December 1493: he could have followed the course in the summer semester of 1493 (cf. “Appendix”). For this semester, the Liber diligentiarum says that the Theorica planetarum was taught by Simon Sierpc (Wisłocki 1886: 23).

  95. In M, the editio princeps of the Commentariolum, Brudzewo’s name appears nowhere in the volume, but it is worthy to notice that all the extant copies lacks of f. ai, so it is impossible to know what appeared on the title page. The second edition (E: f. [a i]) presents a dedication letter of Johannes Otto de Valle Uracense. Here Johannes Otto says that he is a student of Brudzewo and expresses his appreciation of his master’s work: “In Theoricas planetarum Georgii Purbachii viri sane in astronomia disertissimi, interpretationem Alberti Prosevi praeceptoris mei [...] Non enim ingrato commentarium hoc iudicatum iri existimo: ubi motuum superiorum corporum diversitates reciprocationesque dispares contemplari ceperint.”

  96. For the Cracovian milieu see (Birkenmajer 1972). More recently A. Goddu devoted an important work to the influence of the aristotelian tradition on “Copernicus’ path to heliocentrism”.

  97. (Swerdlow 1973: 433–434). Copernicus, Commentariolus, (Prowe 1884: II, 184–202): “Multitudinem orbium caelestium maiores nostros eam maxime ob causam posuisse video, ut apparentem in sideribus motum sub regularitate salvarent. Valde enim absurdum videbatur caeleste corpus in absolutissima rotunditate non semper aeque moveri. Fieri autem posse animadverterant, ut etiam compositione atque concursu motuum regularium diversimodo ad aliquem situm moveri quippiam videretur.

    Id quidem Callippus et Eudoxus per concentricos circulos deducere laborantes non potuerunt et his omnium in motu sidereo reddere rationem, non solum eorum, quae circa revolutiones siderum videntur, verum etiam, quod sidera modo scandere in sublime, modo descendere nobis videntur, quod concentricitas minime sustinet. Itaque potior sententia visa est per eccentricos et epicyclos id agi, in qua demum maxima pars sapientium convenit.

    Attamen quae a Ptolemaeo et plerisque aliis passim de his prodita fuerunt, quamquam ad numerum responderent, non parvam quoque habere dubitationem. Non enim sufficiebant, nisi etiam aequantes quosdam circulos imaginarentur, quibus apparebat neque in orbe suo deferente, neque in centro proprio aequali semper velocitate sidus moveri. Quapropter non satis absoluta videbatur huiusmodi speculatio, neque rationi satis concinna.”

  98. (Swerdlow 1973: 435). Copernicus, Commentariolus, (Prowe 1884: II, 184–202): “Igitur cum haec animadvertissem ego, saepe cogitabam, si forte rationabilior modus circulorum inveniri possit, e quibus omnis apparens diversitas dependeret, omnibus in seipsis aequaliter motis, quemadmodum ratio absoluti motus poscit.”

  99. To be correct, one should say around the centre of the Earth’s sphere, which is “near the Sun”: cf. infra, third postulate.

  100. (Swerdlow 1973: 436). Copernicus, Commentariolus, (Prowe 1884: II, 184–202): “Prima petitio: Omnium orbium caelestium sive sphaerarum unum centrum non esse. Secunda petitio: Centrum terrae non esse centrum mundi, sed tantum gravitatis et orbis Lunaris. Tertia petitio: Omnes orbes ambire Solem, tanquam in medio omnium existentem, ideoque circa Solem esse centrum mundi. ” To these three postulates, a fourth one is added concerning the immensity of the Copernican universe when compared to Ptolemy’s universe.

  101. (Swerdlow 1973: 436). Copernicus, Commentariolus, (Prowe 1884: II, 184–202): “Quinta petitio: Quicquid ex motu apparet in firmamento, non esse ex parte ipsius, sed terrae. Terra igitur cum proximis elementis motu diurno tota convertitur in polis suis invariabilibus firmamento immobili permanente ac ultimo caelo. Sexta petitio: Quicquid nobis ex motibus circa Solem apparet, non esse occasione ipsius, sed telluris et nostri orbis, cum quo circa Solem volvimur ceu aliquo alio sidere, sicque terram pluribus motibus ferri. Septima petitio: Quod apparet in erraticis retrocessio ac progressus, non esse ex parte ipsarum sed telluris. huius igitur solius motus tot apparentibus in caelo diversitatibus sufficit.”

  102. (Swerdlow 1973: 438). Copernicus, Commentariolus, (Prowe 1884: II, 184–202): “His igitur sic praemissis conabor breviter ostendere, quam ordinate aequalitas motuum servari possit.” The preservation of uniform motion applies also to the Moon.

  103. (Copernicus 1543: f. 99r): “His enim sic constitutis congruere putant apparentia.” For the purposes of our analysis, we prefer a more faithful translation of Copernicus’ text, which explicitly refers to “apparences”. In order to allow the most faithful comparison between Brudzewo’s and Copernicus’ texts, here and in what follows, we have preferred to directly refer to the Latin text of (Copernicus 1543) and directly translate its text instead of using the translation in (Rosen 1992).

  104. (Copernicus, 1543, f. 99r): “Talem sane circulorum compositionem tanquam consencientem lunaribus apparentiis assumpserunt priores. Verum si rem ipsam diligentius expenderimus non aptam satis nec sufficientem hanc inveniemus hypothesim. Quod ratione et sensu possumus comprobare”.

  105. (Copernicus 1543: f. 99r): “Dum enim fatentur, motum centri epicycli aequalem esse circa centrum terrae, fateri etiam oportet inaequalem esse in orbe proprio, quem describit, eccentro”.

  106. Peurbach also refers to the path of the centre of the deferent as a “small circle”, and in his text it is the result of the movements of the two orbs eccentric in a certain sense, which shift the deferent orb, causing its centre to draw a small circle, see supra, note 44.

  107. (Copernicus 1543: 99r-99v): “Quoniam si, verbi gratia, AEB angulus sumatur partium XLV, hoc est dimidius recti, et aequalis ipsi AED, ut totus BED rectus fiat, capiaturque centrum epicycli in G et connectatur GF, manifestum est, quod angulus GFD maior est ipsi GEF, exterior interiori et opposito. Quapropter et circumferentiae DAB, et DG dissimiles sub uno tempore ambae descriptae, ut cum DAB quadrans fuerit, DG quem interim centrum epicycli descripsit, maior sit quadrante circuli. Patuit autem in Luna dividua utramque DAB et DG semicirculum fuisse, inaequalis est ergo epicycli motus in eccentro suo quem ipse describit.”

  108. (Copernicus, 1543, f. 99v): “Quod si sic fuerit, quid respondebimus ad axioma, Motum caelestium corporum aequalem esse, et nisi ad apparentiam inaequalem videri, si motus epicycli aequalis apparens, fuerit reipsa inaequalis? accideturque constituto principio et assumpto penitus contrarium”.

  109. (Copernicus, 1543, f. 99v): “At si dicas aequaliter ipsum [epicyclum] moveri circa terrae centrum, atque id esse satis ad aequalitatem tuendam, qualis igitur erit illa aequalitas in circulo alieno, in quo motus eius non existit, sed in suo eccentro?”.

  110. See supra 6—The irregular motions in Peurbach’s universe: a—The eccentric carrying the epicycle of the Moon: Brudzewo’s commentary on first corollary of Peurbach. About the same corollary Birkenmajer, in (Brudzewo 1900: 55), had already noticed that: “Correlarium hoc, nec non altera de eadem ‘maxima’ philosophica Brudzevii disceptatio [cf. p. 85], maximi sunt momenti in inquirendis exordio primoque conceptu illius admirabilis mundi systematis, quo Nicolaus Copernicus, astronomus summus, saeculo proxime posteriore inclaruit.”

  111. (Copernicus, 1543, f. 99v): “Ita sane miramur et illud, quod ipsius Lunae quoque in epicyclo aequalitatem volunt intelligi non comparatione centri terrae per lineam, videlicet EGM, ad quam merito debebat referri aequalitas, ipso centro epicycli consentiens, sed ad punctum quoddam diversum, atque inter ipsum et eccentri centrum mediam esse terram, et lineam IGH tanquam indicem aequalitatis Lunae in epicyclo quod etiam re ipsa inaequalem satis demonstrate hunc motum.”

  112. The commentaries on the Theoricae novae which we have already studied, in both manuscript and printed form, do not formulate any criticism of the equant similar to the one expressed by Brudzewo and Copernicus. Brudzewo and Copernicus concentrate on the fact that the epicycle moves on one circle and the uniformity of its motion is evaluated with reference to another circle. All the other authors, from Regiomontanus onward at least until Reinhold, justify this by the fact that by following a mathematical approach only one point of a circumference can move regularly in relation to a point which is not the geometrical centre of the circumference. Cf. (Regiomontanus [1475]: f. 4v) and (Reinhold 1542: ff. sign. Nv v-[Nvi] r).

  113. About this point Birkenmajer, in (Brudzewo 1900: 85), had already noticed the relation to Copernicus: “Argumentum disceptationis proxime sequentis (“Hoc enim esset contra illam maximam”, etc.) connexionem habet intimam cum correlario pag. 55 lin. 4 seq. excuso. Utriusque loci, summam in disquisitionibus circa primitias doctrinae Copernicanae gravitatem habentis, ibidem obiter meminimus.”

  114. (Copernicus, 1543, f. 140v): “Prisci Mathematici, qui immobilem tenebant terram, imaginati sunt in Saturno, Iove, Marte, et Venere eccentrepicyclos, et praeterea alium eccentrum ad quem epicyclus aequaliter moveretur, ac planeta in epicyclo.”

  115. (Copernicus, 1543, f. 140v): “Quemadmodum si fuerit eccentrus AB circulus, cuius centrum sit C, dimetiens autem ACB, in quo centru terrae D, ut sit apogaeum in A, perigaeum in B, secta quoque DC bifariam in E, quo facto centro describatur alter eccentros priori aequalis FG, in quo suscepto utcunque H centro, designetur epicyclus IK, et agatur per centrum eius recta linea IHKC, similiter et LHME. [...] epicyclum quoque in consequentia in FHG circulo, sed penes IHC, lineam ad quam etiam stella revolvatur aequaliter in ipso IK epicyclo. Constat autem quod aequalitas epicycli fieri debuit ad E centrum sui differentis, et planetae revolutio ad LME lineam. Concedunt igitur et hic motus circularis aequalitatem fieri posse circa centrum alienum et non proprium. Similiter etiam in Mercurio hoc magis accidere. Sed iam circa Lunam id sufficienter refutatum est.”

  116. (Copernicus 1543: f. 140v): “Haec et similia nobis occasionem praestiterunt de mobilitate terrae, aliisque modis cogitandi, quibus aequalitas et principia artis permanerent, et ratio inaequalitatis apparentis reddatur constantior.”

  117. We refer to a “tradition” in the sense documented by the sources attesting that some teachers and students spread Brudzewo’s Commentariolum. See supra 8- Brudzewo and Copernicus in Cracow, and also Appendix.

  118. For these questions one can refer to (Neugebauer and Swerdlow 1984) which remains the authoritative reference, providing the most technically founded answers that the history of science has been able to formulate until now, and to (Szczeciniarz 1998) which opens a subtle reflection involving astronomical, mathematical, philosophical and epistemological aspects intended to make the extant studies converse with a refined analysis of Copernicus’ text.

  119. The authority of the marginal notes in this copy comes, not only from the fact that the writing is of that epoch, but especially from the fact that the person who annotated this printed copy systematically amends the variants of the printed text, integrating the manuscript version of L or of another copy transmitting the first course of Brudzewo in 1483. What is also interesting is that these same variants are common to M and E, so this person had to go back to a manuscript version.

  120. (Brudzewo 1900): iustitiam.

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Acknowledgments

I would like to warmly thank Noel Swerdlow for his advice.

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  1. SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités,UPMC Univ. Paris 06, 61 avenue de l’Observatoire, 75014, Paris, France

    Michela Malpangotto

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Correspondence to Michela Malpangotto.

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Communicated by: Noel Swerdlow.

Appendices

Appendix: List of manuscripts and printed editions of Brudzewo’s Commentariolum

We present here the extant copies of Brudzewo’s Commentariolum which enrich the corpus described by Birkanmajer in (Brudzewo 1900), made up of L, C, E, of some manuscripts, we have called R, D and K, and of the editio princeps M.

The explicit of L confirms that Brudzewo’s teaching dates back to the year 1483: “Dictum est anno domini Millesimo quadringentesimo octogesimo tertio.” The Liber diligentiarum of the Arts Faculty (Wisłocki 1886) starts with year 1487, so does not contain the teachers for the previous period. According to Birkenmajer, (Brudzewo 1900: XXVII), the manuscript annotation “1483 Brudzew legit” in the margin of f. sign. a3v of the 1495 printed version, Inc. 2705 of the Jagiellonian Library, confirms that in 1483 Brudzewo read his Commentariolum.Footnote 119

The same explicit in L also says that the text of the Commentariolum was made public to students in 1488: “Scriptum vero et in publicum editum anno domini Millesimo quadringentesimo octogesimo octavo”. The Liber diligentiarum of the Arts Faculty of Cracow (Wisłocki 1886, 5) shows that Brudzewo gave a course on the Theorica planetarum in 1488. So he taught the commentary copied in manuscripts L, R, D, K.

The manuscripts, R, D, K, contain only the first part of the explicit in L, and refer solely to the 1483 course, without stating who copied the work or when. The explicit of Peurbach’s Theoricae novae in manuscript R confirms that this text was also copied in 1488. And since the Commentariolum does not present those passages of the Theoricae novae under consideration in their entirety, but only mentions the initial words of each passage, the integral copies of Peurbach’s work associated with Brudzewo’s work in these exemplars would have been read at the same time, so that the teacher’s progressive commentary would support the students’ reading of the text.

In D no other date appears, but in this manuscript (ff. 150r–150v), as in R (ff. 79 r–79 v), the Commentariolum is followed by two identical small texts that seem to be two copies of a common source. So probably both these copies, D and R, date to 1488, as stated at the end of the Theoricae novae in R.

Manuscript C confirms that the Commentariolum was still read at Cracow University in the 1490’s. The explicit at f. 169r of C says in fact that, at the end of the year 1493, Michael de Ruszoczjcze copied this text and he finished the copy in “vigilia Circumcisionis domini”, the evening of 31 December 1493; he could have followed the course in the summer semester of 1493. For this semester, the Liber diligentiarum of the Arts Faculty of Cracow (Wisłocki 1886, 23) says that the Theorica planetarum was taught by Simon Sierpc.

In all the extant copies of the editio princeps M of the Commentariolum, Brudzewo’s name appears nowhere in the volumes, but it is worthy to note that all the extant copies lack f. a i, probably the title page, so it is impossible to know what appeared on it.

The second edition E presents at f. [a i]r a dedication letter of Johannes Otto de Valle Uracense. Here Johannes Otto says that he is a student of Brudzewo and expresses his appreciation of his master’s work: “In Theoricas planetarum Georgii Purbachii viri sane in astronomia disertissimi, interpretationem Alberti Prosevi praeceptoris mei [...] Non enim ingrato commentarium hoc iudicatum iri existimo: ubi motuum superiorum corporum diversitates reciprocationesque dispares contemplari ceperint.”

1.1 Manuscripts of Brudzewo’s Commentariolum

L - Wroclaw, Ossolineum, 759/I (siglum L in Birkenmajer’s edition)

  • ff. 1r–35v, Peurbach’s Theoricae novae,

    Incipit: “Sol habet tres orbes a se invicem omniquaque divisos atque sibi contiguos”

    Explicit: “earum semper invariabiles Finis feliciter anno salutifere incarnacionis 1488” followed by the last diagram of the section De motu octavae sphaerae

    ff. 36r–36v, blank

  • ff. 37r–41r, Brudzewo’s Prohemium to his Commentariolum

    Incipit: “Astrorum observatores studiosi experti quidem sufficienter sensu ratione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit : “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. 41r–69r, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit : “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Tantum de praedictis circa motum octavae sphaerae et per consequens circa Theoricas omnium planetarum. de quo laus et gloria in sempiternum omnipotenti deo, auctori primo coelorum et motuum eorundem, amen. Ffinit commentariolum super Theoricas novas Georgii purbachii in studio Generali Cracoviensi per Magistrum Albertum de Brudzewo pro introductione iuniorum aptiori circa lectionem earundem factam corrogatum. In quo quidem ex minus apte aut non doctrinaliter et scientifice positis, lector industrius in contumeliam facile non insurgat sed que noviter artis cerciora profundioraque in profectum edere studeat, simili provocatus labore eorum (?) si is fuerit qui neque ea que adeo pueriliter adducta sunt capiat permitat illesa ne quem reprehendere cupiens inscitiamFootnote 120 propriam quam honestius tacuisset turpiter propallaret. Dictum dictum est anno domini Millesimo quadringentesimo octogesimo tertio comutacione hiemali immediate post pestem validam que viguit Cracovie anno salutifere incarnacionis Millesimo quadringentesimo octogesimo secundo a festo Corporis Christi incipiens usque ad Michaelis. Scriptum vero et in publicum editum anno domini Millesimo quadringentesimo octogesimo octavo comutacione estivali ffinitum vero est in vigilia corporis Christi hora quasi prandii in lectorio Aristotelis Collegii urbis Cracoviensis per me Iohannem de Crobya earundem Theoricarum principaliter se applicantem auditorem. Et eciam ipso anno Illustrissimo princeps Ffredericus, serenissimi principis et domini Kazimiri dei gracia Regis Polonie filius sextogenitus more spirituali se applicans in Episcopum Cracoviensem est promotus ex convencione que tunc in Pyotrkow celebratur pro quo Deus omnipotens cuius imperium manet sit benedictus in secula seculorum amen. Telos ffinis.”

R - Rome, Biblioteca Apostolica Vaticana, Pal Lat 1385 (absent from Birkenmajer’s edition)

  • ff. 48r - 52r: Brudzewo’s Prohemium to his Commentariolum

    Incipit: “Astrorum observatores studiosi experti quidem sufficienter sensu ratione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit : “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. 52r–79r, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit : “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Tantum de praedictis circa motum octavae sphaerae et per consequens circa theoricas omnium planetarum de quo laus et gloria in sempiternum omnipotenti deo auctori primo coelorum et motuum eorundem deo gratias. \(\parallel \) Ffinit commentariolum super theoricas novas Georgii purbachii in Studio generali Cracoviensi per magistrum Albertum de Brudezuo (sic) pro introductione iuniorum apciori circa lectionem earundem factam corrogatum. In quo quidem ex minus apte autem non doctrinaliter et scientifice positis lector industrius in contumeliam facile non insurgat sed que noviter artis cerciora profundioraque in profectum edere studeat, simili provocatus labore eorum (?) si is fuerit qui neque ea que adeo pueriliter adducta sunt capiat permittatque ille ne quem reprehendere cupiens inscitiam propriam quam honestius tacuisset turpiter propallaret. Dictum est Anno domini 1483 comutacione hiemali immediate post pestem validam que viguit Cracovie anno 1482 a festo corporis Cristi incipiens usque ad Michaelis.”

  • f. 79r: List of definitions of different units

  • f. 79v: List of the distances of each planetary sphere from the Earth

  • ff. 80r–100v: Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes a se invicem omniquaque divisos atque sibi contiguos” Explicit: “semper invariabiles. Deo gratia Finis Theoricarum Anno 1488 currente per Bartholomeum Ioh. de haffurt in Cracoviensi Studio”

D - Dresden, Sächsische Landesbibliothek, N 100 (absent from Birkenmajer’s edition)

  • ff. 87r–120v, Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes a se invicem omniquaque divisos atque sibi contiguos”

    Explicit: “semper invariabiles. ”

  • ff. 121r–124r, Brudzewo’s Prohemium to his Commentariolum

    Incipit: “Astrorum observatores studiosi experti quidem sufficienter sensu ratione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit : “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. 124r–149v, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Tantum de praedictis circa motum octavae sphaerae et per consequens circa theoricas omnium planetarum de quo laus et gloria in sempiternum omnipotenti deo auctori primo coelorum et motuum eorundem deo gratias. \(\parallel \) Ffinit commentariolum super theoricas novas Georgii prirbacii (sic) in Studio generali Cracoviensi per Magistrum Albertum de Brudezeuo (sic) pro introductione iuniorum aptiori circa lectionem earundem factam corrogatum. In quo quidem ex minus apte aut non doctrinaliter et scientifice positis lector industrius in contumeliam facile non insurgat sed que noviter artis cerciora profundioraque in profectum edere studeat simili provocatus labore eorum (?) si is fuerit qui neque ea que adeo pueriliter adducta sunt capiat permittatque ille ne quem reprehendere cupiens inscitiam propriam quam honestius tacuisset turpiter propallaret. Dictum est Anno domini 1483 commutacione hiemali immediate post pestem validam que viguit Cracovie anno 1482 a festo corporis Cristi incipiens usque ad Michaelis.”

    According to (Rosinska 1984, 431), the annotations in the margins to the Theoricae novae in this manuscript are by Egidius de Corinthia.

  • f. 150r: List of the distances of each planetary sphere from the Earth

  • f. 150v: List of definitions of different units

K - Karlsruhe, Badische Landesbibliothek, Cod. Ratstatt 36 (absent from Birkenmajer’s edition)

  • ff. 142r–154v, Peurbach’s Theoricae novae

    Only diagrams related to Peurbach’s Theoricae novae different from those of the printed tradition of Peurbach’s text.

  • ff. 155r–158r, Brudzewo’s Prohemium to his Commentariolum

    Incipit: “Astrorum observatores studiosi experti quidem sufficienter sensu ratione et argumentis tradiderunt Virtute primae sphaerae”

    Explicit : “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. 158r-189r, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit : “Sol habet tres orbes a se invicem. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Tantum de praedictis circa motum octavae sphaerae et per consequens circa theoricas omnium planetarum. de quo laus et gloria in sempiternum omnipotenti deo auctori primo coelorum et motuum eorundem \(\parallel \) Amen \(\parallel \) Ffinit Commentariolum super Theoricas novas Georgii Purbachii in studio generali Cracoviensi per Magistrum Albertum de brudezwo (sic) pro introducione maiori minori aptiorique circa lectionem earundem factam: corrogatum: In quo quidem ex minus apte aut non doctrinaliter et scientifice positis lector industrius: in contumeliam facile non insurgat. Sed qui noviter artis cerciora profundioraque in profectum edere studeat: simili provocatus labore eorum (?) si is fuerit qui neque ea que adeo pueriliter adducta sunt cupiat: permittat illesa ne quem reprehendere cupiens insciciam propriam quam honestius tacuisset turpiter propalaret. Dictum est Anno domini 1483 commutacione hiemali in mediate post pestem validam que viguit Cracovie Anno domini 1483 (sic) A festo corporis Christi incipiens usque ad festum Michaelis qui nos representat deo et sanctis in celis Amen.”

C - Krakow, Biblioteka Jagiellonska, 2703 (siglum C in Birkenmajer’s edition)

  • ff. 154r-156r, Brudzewo’s Prohemium to his Commentariolum

    Incipit: “1493 Commentariolum super Theoricas Novas Georgii purbacii (sic) in Studio generali Cracoviensi per magistrum Albertum De Brudzewo diligenter corrogatum incipit. \(\mid \) Astrorum observatores studiosi experti quidem sufficienter sensu racione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit: “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. 156r-169v, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Et his de praedictis circa motum octavae sphaerae et per consequens circa theoricas omnium planetarum Explicit Commentariolum super Theoricas novas Georgii purbacii in Studio generali Cracoviensi per magistrum Albertum De Brudzewo subtiliter corrogatum Scriptumque per me Michaelem De Ruszoczycze in bursa Ierusalem finitum in vigilia Circumcisionis domini Anno Domini 1493 Finis”

1.2 Printed editions of Brudzewo’s Commentariolum

M - Editio princeps, Milan, Uldericus Scinzenzeler, 1494 (USTC 996571, absent from Birkenmajer’s edition)

Brudzewo’s name is written nowhere in the volume.

  • f. sign. a i lacks in all the extant volumes.

  • ff. sign. a ii r–[a vi] r, Brudzewo’s Prohemium to his Commentariolum

    Incipit: “Prohemium. \(\mid \) Astrorum observatores studiosi experti quidem sufficienter sensu ratione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit: “doctrinaliter tradiderunt se applicare poterit apte.”

  • ff. sign. [a vi] r–[e vi] v, Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Tantum de praedictis circa motum octave sphere et per consequens circa theoricas omnium planetarum. de quo sit laus et gloria in sempiternum omnipotenti deo auctori primo celorum et motuum eorundem Amen. \(\mid \) Impressum Mediolani per Vldericum scinzenzeler. Anno domini. MCCCCLXXXXIIII. die. viij. novembris.”

E - Second edition, Milan, Uldericus Scinzenzeler, 1495 (USTC 991670, siglum E in Birkenmajer’s edition)

  • f. [a i] recto, Frontispiece: “Commentaria utilissima in theoricis planetarum”

  • f. [a i] verso, Dedication letter: “Johannes Otto Germanus de valle vracense Magnifico Ambrosio Rosato ducali physico et Consiliario sapientissimo Rosati domino [...] Ex Papia XIIII Kalendas octobris.”

  • ff. a ij r–[a vi] r: Brudzewo’s preface to his commentary

    Incipit: “Astrorum observatores studiosi experti quidem sufficienter sensu ratione et instrumentis tradiderunt recte virtute primae sphaerae”

    Explicit: “doctrinaliter tradiderunt se applicare poterit apte.”

  • f. [a vi] v–[g viii] v: Brudzewo’s Commentariolum on Peurbach’s Theoricae novae

    Incipit: “Sol habet tres orbes. Theorica Solis principali divisione dividitur in tres partes. In prima parte”

    Explicit: “Finit Commentariolum super Theoricas novas Georgii Peurbatii in studio generali Cracoviensi per Magistrum Albertum de Brudzewo: Pro introductione Iuniorum corrogatum. Impressum arte Ulderici Scinzenzeler. Anno Christi 1495. Tertio Kalendas aprilis. Mediolani. | Ad lectorem epigramma [...]”

(Brudzewo 1900)

Albertus de Brudzewo super Theoricas novas planetarum edidit Ludovicus Antonius Birkenmajer, Cracow, Jagiellonian University, 1900.

A reference to some of these manuscripts can be found in (Brudzewo 1900, XLVI–LIII); (Rosinska 1984, 64); (Markowski 1990a, 11–13).

Sources

Copernicus, Nicolaus. 1543. De revolutionibus orbium coelestium. Nurebergae: Johannes Petreius;

  • English Translation in (Rosen, I, 1992, 3–330).

Copernicus, Nicolaus. 1884. De hypothesibus motuum caelestium a se constitutis commentariolus in (Prowe 1884, II, 184–202);

  • English translation

    • A brief description by Nicolaus Copernicus concerning the models of the motions of the heavens that he invented in (Swerdlow 1973, 433–512).

Peurbach, Georg. Theoricae novae planetarum

  • 1454 manuscripts:

    • Cod. 5203, Österreichische Nationalbibliothek, Wien;

    • Cod. 5245, Österreichische Nationalbibliothek, Wien;

    • Codex Sancrucensis 302, Stiftbibliothek, Heiligenkreuz;

  • first printed editions:

    • [1472], [Nurebergae: Regiomontanus];

    • 1482, Venetiis: Erhard Ratdolt;

    • 1452, Venetiis: Erhard Ratdolt;

  • english translation of the 1485 edition in (Aiton 1987, 9–43);

  • critical edition with french translation in (Malpangotto 2016);

  • commentaries:

    • Brudzewo, Albert. 1900. Albertus de Brudzewo super Theoricas novas planetarum edidit Ludovicus Antonius Birkenmajer. Cracoviae: Typis et sumptibus Universitatis Jagellonicae.

      • Manuscripts:

      • L: 759, Zakład Narodowy im. Ossolińskich, Wrocław;

      • R: Pal. Lat. 1385, Biblioteca Apostolica Vaticana, Roma;

      • D: N 100, Sächsische Landesbibliothek, Dresde;

      • K: Cod. Ratstatt 36, Badische Landesbibliothek, Karlsruhe;

      • C: B. J. 2703, Biblioteka Jagiellonska, Cracovie;

      • Printed editions:

      • M: 1494, Mediolani: Uldericus Scinzenzeler;

      • E: 1495, Mediolani: Uldericus Scinzenzeler.

  • Capuano, Francesco. 1495. Theoricae novae Planetarum Georgii Purbachii astronomi celebratissimi ac in eas ... Domini Francisci Capuani de Manfredonia \(\ldots \) sublimis expositio et luculentissimum scriptum. Venetiis: Bevilaqua;

  • Mazzolini de Prierio, Silvestro. 1514. Clarissimi Sacre Theologie omniumque bonarum artium professoris Reverendi patris fratris Silvestri De Prierio \(\ldots \) in spheram ac Theoricas preclarissima Commentaria. Mediolani : G. de Ponte.

  • Reinhold, Erasm. 1542. Theoricae novae planetarum Georgii Purbacchii Germani ab Erasmo Reinholdo Salveldensi pluribus figuris auctae, & illustratae scholiis, quibus studiosi praeparentur, ac invitentur ad lectionem ipsius Ptolemaei. Witebergae: Lufft;

  • Schreckenfuchs, Erasm Oswald. 1556. Erasmi Osvaldi Schreckenfuchsii Commentaria in Novas theoricas planetarum Georgii Purbachii. Basileae: Henricum Petri;

  • Nunes, Pedro. 1566. In Theoricas planetarum Georgii Purbachii annotationes. Basileae: Henricpetrina; Critical edition in (Leitão 2010);

  • Wursteisen, Christian. 1568. Quaestiones novae in Theoricas novas planetarum doctissimi mathematici Georgii Purbachii Germani quae astronomiae sacris initiatis prolixi Commentarij uicem explere possint: una cum elegantibus figuris, et Isagogica Praefatione. Basileae: Henricpetrina.

Ptolemaeus, Claudius. 1515. Almagestum Claudii Ptolemei. Venetiis: Petrus Lichtenstein (First edition of the Arabo-Latin version of Gerard of Cremona);

  • critical edition of the Greek text in (Heiberg 1898–1907, I);

  • Greek text and French translation in (Halma 1813);

  • English translation in [Toomer, (1998) 1984].

Regiomontanus, Ioannes. [1475]. Dialogus inter Viennensem et Cracoviensem adversus Gerardi Cremonensis in Planetarum Theoricas deliramenta. [Nurebergae: Regiomontanus].

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Malpangotto, M. The original motivation for Copernicus’s research: Albert of Brudzewo’s Commentariolum super Theoricas novas Georgii Purbachii . Arch. Hist. Exact Sci. 70, 361–411 (2016). https://doi.org/10.1007/s00407-015-0171-y

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