Regiomontanus and Homocentric Astronomy

Neugebauer Otto , A history of ancient mathematical astronomy (Berlin, 1975), 262f, 627f.

Zinner Ernst , Leben und Wirken des Johannes Müller von Königsberg, genannt Regiomontanus 2nd edn (Osnabrück, 1968), 61–62.

Zinner announced the discovery in “Neue Regiomontan-Funde und ihre Ergebnisse”, Sudhoffs-Archiv , xxxvii (1953), 107–8, and made a passing reference to it in his revised biography of Regiomontanus: Zinner , Regiomontanus (ref. 2), 151.

“Opus quoque novum quatuor absolvam tractatibus, in quorum primo antiquam speculationem de ecentricis et epiciclis rationibus firmis atque observationibus futuris destructam dabo. In secundo speculationem orbium concentricorum quibus omnes diversitates motuum salvari poterint aperte ponam. In tertio vero testimoniis geometricis ea quae in secundo tractatu sunt confirmabo. Quartus quo pacto motus isti numerari et tabulae ad illas novas radices fundari possint continebit.” Florence, Biblioteca Nazionale Centrale, Magl. XI 144, 16r. Swerdlow Noel , “Regiomontanus's concentric-sphere models for the Sun and Moon”, Journal for the history of astronomy , forthcoming. I thank Swerdlow for making available his text, transcription, and translation long before I had access to the manuscript.

Shank Michael H. , “The ‘Notes on al-Bitruji’ attributed to Regiomontanus: Second thoughts”, Journal for the history of astronomy , xxiii (1992), 15–30.

Resonating with a rare reference to the celestial spheres in Book 9 of the Almagest, Regiomontanus in Book 9, Prop. 1 of the Epitome discusses the order of the celestial spheres. After reviewing several past arrangements (including that of al-Bitruji), Regiomontanus defends the traditional order of the planets (Mercury and Venus below the Sun) on physical grounds. His argument assumes the need to avoid either a vacuum or a useless plenum in the large gap (1006 Earth radii) between the spheres of the Sun and Moon. “Fiet igitur ut distantia inter duo luminaria sibi quam vicinissime approximata: Semidiametrum terre 1006 fere vicibus contineat. Hoc autem spatium natura non sinit vacuum: Necessario igitur quoddam celeste corpus ipsum occupabit. Sed id corpus de integritate erit orbium Solis et Lune; frustra enim tanta moles in celo permitteretur.” f. k1v; Schmeidler Felix (ed.), Joannis Regiomontani opera collectanea (Osnabrück, 1972), 192.

Toomer G. J. , Ptolemy's Almagest (New York and Berlin, 1984), Book 12, chap. 1.

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; Swerdlow Neugebauer Otto , Mathematical astronomy in Copernicus's De revolutionibus (New York, 1984), 48–58.

Helmuth Grössing drew attention to this in print in his “Regiomontanus und Italien: Zum Problem der Wissenschaftsauffassung des Humanismus”, in Hamann Günther (ed.), Regiomontanus-Studien (Vienna, 1980), 223–41, p. 235, n. 58. For a summary of the literature, see Gerl Armin , Trigonometrisch-astronomisches Rechnen kurz vor Copernicus (Stuttgart, 1989), 210–13, who notes, without resolving it, the tension between homocentric and anti-homocentric attributions in the Regiomontanus corpus.

“Dico ego, bonam partem huiusmodi quesitorum per hanc repertum iri tabulam, si prius concentricam astronomiam totam fundaverimus. Quid illud? Diversitates motuum planetarum per concentricos salvare pulcrum erit. Iam Soli et Lune viam dedimus, de reliquis autem quedam initialia iacta sunt, quibus completis equationes omnium planetarum per hanc tabulam numerare licebit.” Curtze Maximilian , “Der Briefwechsel Regiomontan's mit Giovanni Bianchini, Jacob von Speier und Christian Roder”, Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance (Leipzig, 1902), i, 218.

“Quantam gloriam Commentator adeptum se putaverit si Astronomicam concentricam tradidisset testimonio suo docemur, qui totam ferme aetatem in ea re consumens desperasse tandem se confitetur.” Schmeidler (ed.), op. cit. (ref. 6), 51. Paraphrased in Swerdlow Noel M. , “Science and humanism in the Renaissance: Regiomontanus's Oration on the Dignity and Utility of the Mathematical Sciences”, in Horwich Paul (ed.), World changes: Thomas Kuhn and the nature of science (Cambridge, Mass., 1993), 131–68, p. 150.

“Quod si luna habeat eccentricum et epicyclum, quemadmodum conclamatum est, oportebit lunam in certo situ quadruplo fere maiorem apparere quam in alio, rebus ceteris eodem modo se habentibus”, Curtze , “Briefwechsel” (ref. 10), 266; Swerdlow Noel M. , “Regiomontanus on the critical problems of astronomy”, in Levere Trevor Shea William R. (eds), Nature, experiment and the sciences (Boston Studies in the Philosophy of Science, cxx; Boston, 1990), 165–95, p. 174.

“Sed mirum est quod in quadratura luna opposito augis epicycli existente non tanta appareat cum tamen si integra luceret quadrupla oportet apparere ad magnitudinem suam que apparet in oppositione cum fuerit in auge epicycli.” Epytoma , f. [f6r], in Schmeidler (ed.), op. cit. (ref. 6), 145.

“Iam venio ad rationes contra illam antiquam fantasiam eccentricorum, que si esset vera secundum approbatam sententiam ponentium eos, sequitur lunam in pleni lumine non plus quam sesquialtero esse remotiorem quam in quadraturis, id est quando est dimidiata in lumine, quod est falsum; quia sic in quadraturis deberet apparere notabiliter maioris diametri quam in pleni lumine.” Paris, BN, fonds latin 16401, 64v; Vienna, ÖNB lat. 5203, 108v.

“Item stantibus fundamentis eccentricorum et epicyclorum oportet Veneris superficiem apud sensum quandoque apparere unum, alias autem ut 45, quae res nemini aspicienti unquam innotuit.” Curtze , “Briefwechsel” (ref. 10), 265; see also Swerdlow , op. cit. (ref. 12), 173.

For intriguing work on planetary brightness, see Goldstein Bernard L. , “The pretelescopic treatment of the phases and apparent sizes of Venus”, Journal for the history of astronomy , xxvii (1996), 1–12; and “Levi ben Gerson and the brightness of Mars”, ibid. , 297–300.

“Talibus rebus sepenumero vexor et deflere cogor segnitiem et frigiditatem nostre etatis. Profecto materia copiosa est volentibus hodie philosophari. Habemus ante oculos vestigia maiorum nostrorum, quo fit ut cautius incedere possimus, modo ingenium huic rei accomodemus.” Curtze , “Briefwechsel” (ref. 10), 266.

Duhem Pierre , Le système du monde: Histoire des doctrines cosmologiques de Platon à Copernic (10 vols, Paris, 1913–59), x, 364. These issues receive fuller treatment in my ever-more-imminent monograph on the Disputationes.

See my abstract “Regiomontanus and homocentric astronomy”, Bulletin of the American Astronomical Society , xiv (1982), 897, and my “The Disputationes of Regiomontanus: Medieval astronomy in Renaissance garb”, presented at the annual meeting of the History of Science Society (Philadelphia, 31 October 1982) and also read for me by Owen Gingerich at the conference celebrating the 550th anniversary of Regiomontanus's birth (Esztergom, Hungary, 21 June 1986), and still ‘in press’ at this writing.

Regiomontanus , Disputationes , in Schmeidler (ed.), op. cit. (ref. 6), 518.

In the late thirteenth century, the Franciscan Bernard of Verdun who favoured the standard Ptolemaic model (by elimination of the homocentric approach, the only other possibility he considered), refuted just such a view in his Tractatus super totam astrologiam: “They argue that if there is an eccentric or epicyclic orb, then either the body of the sky will be divisible or rarefiable or there will be a vacuum…. Similarly an epicycle that is revolved through an orb will cut it.” Grant Edward (ed.), A source book in medieval science (Cambridge, Mass., 1973), 523.

Regiomontanus , Disputationes, in Schmeidler (ed.), op. cit. (ref. 6), 519.

Kren Claudia , “Homocentric astronomy in the Latin West: The De reprobatione ecentricorum et epiciclorum of Henry of Hesse”, Isis , lix (1968), 269–81, p. 273.

In 1800, it was owned by von Murr Theodor , who sold it to the Czar. My colleague Richard Kremer and I are are deeply grateful to the St Petersburg Academy of Sciences, Dr V. Soboliev, and Dr Daniel Alexandrov for their assistance in obtaining a copy.

The manuscript was once paginated (see the photocopy in the Stadtbibliothek Nürnberg). In the original, the pagination has now been crossed out and replaced with foliation.

For the best effort to date, see the excerpts in Monfasani John , Collectanea trapezuntia: Texts, documents, and bibliographies of George of Trebizond (Binghamton, N.Y., 1984), 671–87.

“Hoc autem anno haud septem […?] ante Sixti Tertii [sic; read Quarti] summum pontificatum….” Defensio 415. Sixtus was elected on 9 August 1471.

“Quod si posthac per otium licebit demonstratum dabo quonam pacto huiusmodi diversitates in motibus lune absque ecentrico et epiciclo salvare possimus, non per modum Alpetragii, qui nequaquam satisfacit, sed per viam quandam novam et convenientissimam. Neque id ex arbitrio libero procedit quod elegerim sive invenerim alium modum quam vulgus astronomorum habeat, verum ad hoc impellit ratio convincens non esse ecentricum et epiciclum lune. Nam si sic, sequitur angulum quem subtendit luna in centro visus pro certo instanti fere duplum esse ad eum sub quo videtur luna in certo alio instanti, rebus ceteris eodem modo se habentibus…; hinc quoque sequitur aream lune si in certo situ apparuerit ut unum, in alio situ apparere fere ut quatuor, quod vero unquam deprehendit. Huius rei ampliorem declarationem alibi conscribemus.” Defensio 11.

“Motus celestium omnino equales sunt sed quo ad nos inequales apparent. Quare ante omnia salvanda est equalitas que utique per eccentricos et epicyclos non servatur.” Defensio 482, lower margin.

“Duo sunt in celestibus motibus precipue servanda: Equalitas videlicet primordialis et intrinseca, et inequalitatis apparentia. Primum per orbes, non per tenues circulos absolvitur; secundum per circulos in planetas quapiam descriptibiles propter demonstrationis facultatem. Primum ad naturam corporum celestium attinet que multum nisi equalem motum sustinere possunt; secundum ad spectatores homines refertur, quibus motibus illi videntur inequales atque inordinati.” Defensio 400.