Regiomontanus's Padua Oration in Context

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Footnotes



An earlier version of this paper was delivered at the 2004 History of Science Society meeting in Austin, Texas. Thanks to Robert Goulding, Lauren Kassell, Nicholas Popper, and Anthony Grafton for their comments at the HSS meeting.

1. Regiomontanus, "Oratio Iohannis de Monteregio, habita in Patavii in praelectione Alfragani," in Opera collectanea, ed. Felix Schmeidler (O. Zeller: Osnabrük, 1972), 43–53. Further citations of the Padua oration refer to this edition.

2. "Memorare possem in primis originem nostrarum artium, et apud quas gentes primum coli coeperint, quo pacto ex linguis peregrinis variis ad Latinos tandem pervenerint, qui in hisce disciplines apud maiores nostros claraverunt, et quibus nostra tempestate mortalibus palma tribuitur." Regiomontanus, Padua oration, 43.

3. See, for example, Paul Lawrence Rose, The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo (Geneva: Droz, 1975); Helmuth Grössing, Humanistische Naturwissenschaft: zur Geschichte der Wiener mathematischen Schulen des 15. und 16. Jahrhunderts (Baden-Baden: V. Koerner, 1983); N.M. Swerdlow, "The Recovery of the Exact Science of Antiquity," Rome Reborn: The Vatican Library and Renaissance Culture, ed. Anthony Grafton (Washington, D.C.: Library of Congress, 1993), 125–68; Jens Høyrup, "A New Art in Ancient Clothes: Itineraries Chosen Between Scholasticism and Baroque in Order to Make Algebra Appear Legitimate and their Impact on the Substance of the Discipline," Physis 35 (1998): 11–50.

4. Ernst Zinner, Regiomontanus: his Life and Work, tr. Ezra Brown (New York: North-Holland, 1990), 13–50.

5. Ibid., 51–55.

6. On the medieval history of the University of Vienna, see Rudolf Kink, Geschichte der kaiserlichen Universität zu Wien (Vienna: C. Gerold und Sohn, 1854), vols. 1–2; Joseph Ritter von Aschbach, Die Wiener Universität und ihre Gelehrten (Vienna: Verlag der k.k. Unversität, 1888), vols. 1–2; Alphons Lhotsky, Die Wiener Artistenfakultät, 1365–1497 (Vienna: Hermann Bohlaus, 1965); Paul Uiblein, Mittelalterliches Studium an der Wiener Artistenfakultät (Vienna: WUV-Universitätsverlag, 1995); Uiblien, Die Universität Wien im Mittelalter: Beitrage und Forschungen (Vienna: WUV-Universitätsverlag, 1999).

7. The curricular bonds between German universities and the University of Paris are further discussed in Astrik L. Gabriel, The Paris Studium: Robert of Sorbonne and his Legacy (Notre Dame: United States Subcommission for the History of Universities, 1992), 113–68.

8. On medieval mathematics in general, see Michael S. Mahoney, "Mathematics," in Science in the Middle Ages, ed. David Lindberg (Chicago: University of Chicago Press, 1978), 145–78; A.P. Iushkevich, Geschichte der Mathematik im Mittelalter, trans. Viktor Ziegler (Leipzig: Teubner, 1964); on arithmetic, see, Jordanus de Nemore, De numeris datis, ed. and trans. Barnabas Hughes (Berkeley: University of California Press, 1981); Ghislaine L'Huillier, Le Quadripartitum numerorum de Jean de Murs: Introduction et edition critique (Geneva: Droz, 1990); on geometry: H.L.L. Busard, The Latin Translation of the Arabic Version of Euclid's Elements Commonly Ascribed to Gerard of Cremona (Leiden: Brill, 1984); on astronomy: Lynn Thorndike, The Sphere of Sacrobosco and its Commentators (Chicago: University of Chicago Press, 1949); Francis S. Benjamin, Jr. and G.J. Toomer, Campanus of Novara and Medieval Planetary Theory (Madison: University of Wisconsin Press, 1971); on optics: David C. Lindberg, Theories of Vision from al-Kindi to Kepler (Chicago: University of Chicago Press, 1976).

9. Acta Facultatis Artium. Vol. 3. Universitätsarchiv, Vienna. Codex Ph. 8, 51r.

10. Lhotsky, Die Wiener Artistenfakultät, 139–41.

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11. Zinner, Regiomontanus, 18. One of Peurbach's poems on nature can be found in Grössing, Humanistische Naturwissenschaft, 210–13.

12. "Me autem nichil unquam provide fecisse . . . aut, si quicquam, hoc in primis, non audeo dicere sapienter, sed feliciter factum est: et quod Bononiam vidi et quod non inhesi." Petrarch, Rerum familiarum libri I-VIII, trans. Aldo S. Bernardo (Albany: State University of N.Y. Press, 1975), 223; Idem, Rerum familiarum IV-VII, ed. Ugo Dotti (Paris: Société d'édition Les Belles Lettres, 2002), 109.

13. "Te Vienna Doctorem Artium creavit dignissimum." Regiomontanus, Padua oration, 48.

14. On humanist periodicity, see Michael Baxandall, Giotto and the Orators: Humanist Observers of Painting in Italy and the Discovery of Pictoral Composition, 1350–1450 (Oxford: Clarendon, 1971), 20–27.

15. "Nisi primitias lectionum facturo mihi mansuetudo vestra aspiraret, orationisque tremebundae filum dirigeret, praestantissimi viri, silvisse prorsus mallem quam pulpitum hoc philosophicum audentius conscendisse, praesertim cum novitate coepti facinoris, tanto tamquam celebri clarissimorum hominum conventu, diuturna demum a scholasticis exercitiis abstinentia facile deterreri potuerim." Regiomontanus, Padua oration, 43.

16. Baxandall, Giotto and the Orators, 21.

17. On humanist epideictic, see John W. O'Malley, Praise and Blame in Renaissance Rome: Rhetoric, Doctrine, and Reform in the Sacred Orators of the Papal Court, c. 1450–1521 (Durham: Duke University Press, 1979), 39–41.

18. A number of such orations can be found in Karl Müllner, Reden und Briefe Italienischer Humansiten (Munich: W. Fink, 1970).

19. "Dominicus igitur domum praedicatorum condidit, Thomas eius pavimenta marmore vestivit, Dominicus parietes struxit, Thomas picturis eos egregiis adornavit, Dominicus fratrum columen extitit, Thomas specimen, Dominicus plantavit, Thomas irrigavit, ille dignationes atque episcopatus ultro delatos refugit atque aversatus est, hic nobilitatem, opes, propinquos, parentes tamquam sirenes effugit. . . ." Lorenzo Valla, "In Praise of Saint Thomas Aquinas," trans. M. Esther Hanley, in Renaissance Philosophy, ed. Leonard A. Kennedy (The Hague: Mouton, 1973), 13–27, 21; J. Valen, "Lorenzo Valla über Thomas von Aquino," Vierteljahrsschrift für Kultur und Litteratur der Renaissance 1 (1886): 384–96, 393.

20. Hannah H. Gray, "Valla's Encomium of St. Thomas Aquinas and the Humanist Conception of Christian Antiquity," in Essays in History and Literature: Presented by the Fellows of the Newberry Library to Stanley Pargellis, ed. Heinz Bluhm (Chicago: The Newberry Library, 1965), 37–51.

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21. "Archimedes Siracusanus civis et Apollonius Pergaeus ob ingenii altitudinem divinus vocari solitus, quorum uter alteri praeferendus sit, non facile dixero. Nam etsi Apollonius elementa conica in octo libris, quos nondum vidit latinitas, subtilissime conscripserit, Archimedi tamen Siculo varietas rerum editarum principatum contulisse videtur . . . Apollonius quoque ubi in Latinum ex Graeco versus fuerit, nemini vestrum non admirandus veniet." Regiomontanus, Padua oration, 45.

22. O'Malley, Praise and Blame, 63–65.

23. "spectatissimus mathematicarum splendor . . ." Regiomontanus, Padua oration, 43.

24. "Ante oculos igitur causam habetis." Regiomontanus, Padua oration, 53.

25. "Geometriae disciplina primum ab Aegyptis reperta dicitur, quod, inundante Nilo et omnium possessionibus limo obductis, initium terrae dividendae per lineas et mensuras nomen arti dedit. Quae deinde longius acumine sapientium profecta et maris et caeli et aeris spatia metiuntur." Isidore of Seville, "On the Quadrivium or Four Mathematical Sciences," trans. Ernest Brehaut, in A Source Book in Medieval Science, ed. Edward Grant (Cambridge, Mass.: Harvard University Press, 1974), 3–16, 8; Idem, Etimologie o Origini, 1.10, ed. Angelo Valastro Canale (Turin: Unione Tipografico-Editrice Torinese, 2002), 290.

26. "Dum Nili flumen solito vehementius exundans limites agrorum Aegyptiorum vastaret, et pene universos delevisset, contendere coeperunt agricolae, sua quisque pro opinione (ut est ingenium hominum ad rem plus satis attentum) agros suos definire cupiebat, quique sive sermone, sive viribus plus caeteris valuit, tametsi antea angustum haberet agrum pro libito terminus instituit, quae res cum praeter aequum et bonum verteretur, ad principem eius patriae devoluta est, qui iusta quadam ratione mensurisque certis suos cuique reparuit limites. Sic generali et inusitato quodam impulsu mortalium animi ad mensuras tractandas converse coepere alter alteri questiones anteponere, et quicquid in huiuscemodi exercitiis bene inventum putabant, quamvis indigestum, ut ita loquar, adhuc foret, literis mandare studuerunt." Regiomontanus, Padua oration, 44.

27. Herodotus, The Histories, 2.109, trans. George Rawlinson (New York: Knopf, 1997), 177.

28. On Valla's translation of Herodotus, see E.B. Fryde, "Some Fifteenth Century Latin Translation of Ancient Greek Historians," in Humanism and Renaissance Historiography (London: The Hambledon Press, 1983), 83–114.

29. "Cum Platonis in dicendo suavitas, tum Ciceronis nostra lingua dissertissima non assint, qui etsi reviviscerent haud quaquam pro dignitate idipsum assequerentur." Regiomontanus, Padua oration, 43. Plato, though he was of course Greek, was seen by fifteenth-century humanists as exemplifying excellent style. See, for example, Baxandall, Giotto and the Orators, 22–24.

30. "Nilus totius orbis fluviorum celeberrimus a solstitio aestivo usque ad autumnale aequinoctium, ut Herodotus libro 2 et Diodorus in 1 testatur, immensa aquarum mole quotannis totam Aegyptum exundat, ex cuius incremento Aegyptii vim aut penuriam futurarum frugum praevident. Aegyptus enim cum Nilus in 12 cubitos excrescit famem sentit; in 13 etiamnum esurit; 14 cubiti hilaritatem afferunt, 15 securitatem, 16 delitias, quod iustum fertur esse incrementum. Maximum autem aetate Claudii principis fuit cubitorum 18, sicut minimum Pharsalico bello veluti caedem magni Pompeii prodigio quodam aversante, autores Plinius libro 5 et Strabo 17. Cum huiusmodi itaque Nili inundationes limites agrorum confunderent, nunc minuendo, alias immutando, nonnunquam delendo signa quaedam quibus proprium ab alieno discerneretur, iterum atque iterum metiri eam terram oportebat, propter quod Strabo 17 Geographiae et Herodotus 2 aiunt nonnullos prodidisse geometriam ab Aegyptiis primo inventam esse, quemadmodum arithmeticam, id est, numeralem scientiam a Phoenicibus propter mercaturas." Polydore Vergil, On Discovery, ed. and trans. Brian P. Copenhaver. (Cambridge, Mass.: Harvard University Press, 2002), 146–49.

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31. Andrea Brenta, In disciplinas et bonas artes oratio, in Reden und Briefe, 71–85.

32. "Abraham enim Hebraeorum patrem Astronomiam tenuisse clamant atque Mosen. Prometheo ignis divini furtum imputant, quod Astronomiae lumen mortalibus tradiderit. Herculem pro Atlante coelum humeris suis sustinuisse aiunt, sive quod sub Atlante astronomiam didicerit, sive quod in regno eius absentis praefectus aliquamdiu fuerit." Regiomontanus, Padua oration, 46.

33. Isidore, "On the Quadrivium," 11. The main difference between Regiomontanus's account and that of Isidore is Regiomontanus's mention of Prometheus.

34. "Astronomiam ab Aegyptiis inventam tradunt. Nam cum in ea regione perpetua aeris serenitas contingeret et Aegyptii sacerdotes, qui disciplinis studebant, otio et rebus ad vitam necessariis abundarent, ut Aristoteles, multa et observasse et invenisse perhibentur quae ad caeli rationem pertinebant. . . . Post multa vero annorum milia, ut quidam prodiderunt, in Graeciam delata est et a multis cognita, ut maxime ex poetis cognosci potest. Deinde secuti sunt Pythagoras et Pherecydes, qui mathematicarum rerum studiosi permultum huic disciplinae addiderunt. Hos secutus est Eratosthenes, Berosus, et Hipparchus et innumerabiles alii, quibus Graecia plurimum abundavit. Plato vero et Eudoxus, cum discendi gratia in Aegyptum profecti essent, multa cum rerum aliarum tum vero eius scientiae secreta, ut Strabo refert, ab Aegyptiis sacerdotibus in Graeciam reportarunt. Ita paulatim ac per aetates aucta et ad cumulum perducta usque ad Ptolemaei tempora pervenit, a quo mirandum illud ac prope divinum astrologiae opus editum est, ut nihil quodam modo ad hanc scientiam addi posse videatur." Gregorio da Città di Castello, "Gregorii Tiphernii, viri clarissimi atque Graecarum litterarum eruditissimi, de astrologia oratio," in Reden und Briefe Italienischer Humansiten, 177–78.

35. Müllner, Reden und Briefe, 177 n. 2; Aristotle, Metaphysics, 1.24; Aristotle, Posterior Analytics, 2.19; Strabo, Geography, 14.1.14; Cicero, De finibus, 5.87; Pliny, Historia naturalis, 30.1.

36. "Hipparchus tamen Rhodius huius disciplinae primus parens, Claudius autem Ptolemeus Alexandrinus auctor atque princeps non iniuria praedicabitur. Nam ante Hipparchum pauci admodum astrorum motus expedite contemplati sunt, nemo autem prorsus stellas fixas alio quam diurno motu circumferri putaverat, cui rei Hipparchus oculos adiecit crebriores, conclusitque memoratas stellas motu quodam proprio ac tardissimo Orientem versus mutari. Deinde Ptolemaeus inventa priscorum resumens . . . motum huiusmodi in centum annis per unum gradum pronunciavit quemadmodum in septima dictione capituli 3. intueri licet. . . . Multos denique huius artis Graecos professores silentio praetereundos censeo . . . Arabes praeterea quantum in hoc genere atrium valuerunt, testes ostendunt dignissimi Albategnius quem Latinum fecit Plato quidam Tiburtinus. Item Geber Hispalensis Gerardo quodam Cremonensi traductus, quem Albertus Magnus in speculo Astronomiae correctorem Ptolemaei vocare non formidat." Regiomontanus, Padua oration, 46–47; Ptolemy, Almagest, 7.3, trans. G.J. Toomer, in Ptolemy's Almagest (London: Duckworth, 1984), 329–38.

37. Georg Peurbach and Regiomontanus, Epytoma in almagestum Ptolomei, in Opera collectanea, 59–274; Zinner, Regiomontanus, 51–55.

38. Peurbach and Regiomontanus, Epitome, 7.3, 172–173; Zinner, Regiomontanus, 54.

39. Valla, "In Praise of Saint Thomas Aquinas," 26; Petrarch, Against a Detractor of Italy, ed. and trans. David Marsh, in Francesco Petrarca: Invectives (Cambridge, Mass.: Harvard University Press, 2003), 364–475, 411–25.

40. "Nam etsi Pythagoras numerorum peritia apud posteros immortalitatem reliquerit, tum quod peregrinis praeceptoribus Aegyptiis atque Arabibus, qui plurimum in eo studio valuerunt, se submiserit, tum quod numerorum certa compagine omnia naturae secreta scrutari tentaverit, longe tamen digniora Euclides fecit numerorum fundamenta in tribus libris suis, septimo, octavo et nono, unde et Iordanus decem numerorum elementa decerpsit, hinc tres libros de datis numerorum pulcherrimos edidit. Diofanti autem tredecim libros subtilissimos nemo usque hac ex Graecis Latinos fecit, in quibus flos ipse totius Arithmeticae latet, ars videlicet rei et census, quam hodie vocant Algebram Arabico nomine. Huius equidem artis pulcherrimae multa fragmenta passim Latini contrectant, paucissimos autem egregie doctos offendo nostra tempestate post Ioannem de Blanchinis virum optimum. Habetur demum apud nostros quadripartitum numerorum, opus insigne admodum, item Algorithmus demonstratus et Arithmetica Bohecii, introductio ex Graeco Nicomacho sumpta." Regiomontanus, Padua oration, 46.

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41. Regiomontanus, Padua oration, 49.

42. Some scholars have linked Regiomontanus's praise of Diophantus and failure to mention Arabic sources to humanist anti-Arabism and the sixteenth-century effort to establish an entirely classical genealogy of algebra. See, for example, Giovanna Cifoletti, Mathematics and Rhetoric: Peletier, Gosselin and the Making of the French Algebraic Tradition (Ph.D. Dissertation, Princeton University, 1992), 254–86; and Høyrup, "A New Art in Ancient Clothes."

43. Rose, The Italian Renaissance of Mathematics, 95–98.

44. On the use of Archimedes in the fourteenth and fifteenth centuries, see Marshall Clagett, Archimedes in the Middle Ages (Madison: University of Wisconsin Press, 1978), vol. 3.

45. See Sabetai Unguru, "A very early acquaintance with Apollonius of Perga's treatise on conic sections in the Latin West," Centaurus 20 (1976): 112–28.

46. Peurbach, Novae theoricae planetarum, trans. E.J. Aiton in "Peurbach's Theoricae novae planetarum: a Translation with Commentary," Osiris, 2nd Series 3 (1987), 4–43; Olaf Pedersen, "The Decline and Fall of the Theorica planetarum," in Science and History: Studies in Honor of Edward Rosen (Wroclaw: Ossolineum, 1978), 157–85.

47. Zinner, Regiomontanus, 60–69.

48. Regiomontanus, Padua oration, 49–50.

49. Andrea Brenta, "In disciplinas et bonas artes," 77; Valerius Maximus, Facta et dicta memorabilia , 8.7 ext. 7, ed. John Briscoe (Stuttgart: Teubner, 1998), 526–27.

50. Aeneas Silvius Piccolomini, The Education of Boys, ed. and trans. Craig W. Kallendorf, in Humanist Educational Treatises (Cambridge, Mass.: Harvard University Press, 2002), 251–53.

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51. "Qui septimum Physicorum absque notitia proportionum discere possit arbitror esse neminem." Regiomontanus, Padua oration, 50.

52. Arthur Field, The Origins of the Platonic Academy of Florence (Princeton: Princeton University Press, 1988), 114–15.

53. "Cum se primo ad naturalem philosophiam conferet auditor, astrologiae geometriaeque prima elementa degustet. . . . Principiis autem earum disciplinarum perceptis, facile quae ab Aristotele dicuntur intelliget. Itaque satis, quod ad philosophiam attinet, earum disciplinarum didicisse putabitur, si De spera brevissimum opusculum et Planetarum theoricam, quibus astrologiae continentur elementa, in geometria vero primum Euclidis librum perceperit." Alamanno Rinucinni, "Alamannus Rinuccinus ad Philippum filium," in Lettere ed Orazioni, ed. Vitto R. Giustiniani (Florence: Leo S. Olschki, 1953), 100.

54. "Quos ramos inter se et a stipite suo diversos haec secta produxit? Pars Ioannem Scotum imitatur; alii sanctum Thomam; nonnulli autem ingenio promiscuo hac atque illac defluunt . . . Igitur quo plures philosophia duces habet, eo minus hac nostra tempestate addiscitur. Princeps interea philosophorum prorsus destituitur, nomenque suum is sibi usurpat, que in sophismatibus plus caeteris valet, neque Aristoteles ipse si revivisceret discipulos suos atque sequaces satis intelligere crederetur. Quod de nostris disciplinis nemo nisi insanus praedicare ausit, quandoquidem neque aetas neque hominum mores sibi quicque detrahere possunt. Theoremata Euclidis eandem hodie quam ante mille annos habent certitudinem. Inventa Archimedis post mille secula venturis hominibus non minorem inducent admirationem." Regiomontanus, Padua oration, 50–51.

55. "Quae cognitio iucundissima est et praeceptum in se certitudinem continet." Pier Paolo Vergerio, The Character and Studies Befitting a Free-Born Youth Dedicated to Ubertino da Carrara, in Humanist Educational Treatises, 54–55.

56. "In quam aspicientem, iucundum est et fixarum stellarum imagines discernere. . . . Quae cum omnia iucundum est intellegere, tum maxime negotiari circa eas quae in aere et circa terram fiunt impressiones iucundissimum est." Ibid, 54–55.

57. William Harrison Woodward, Vittorino da Feltre and Other Humanist Educators (New York: Columbia University Teacher's College Bureau of Publications, 1963), 43, 234–41.

58. Hanna Gray, "Renaissance Humanism: the Pursuit of Eloquence," JHI 24 (1963): 497–514.

59. Petrarch, De sui ipsius et multorum ignorantia, tr. H. Nachod in The Renaissance Philosophy of Man, ed. Cassirer, Kristeller, and Randall (Chicago: University of Chicago Press, 1948), 47–133,105; cited in Gray, "Renaissance Humanism," 501.

60. "Quamvis enim artes huiusmodi in veri vestigatione versentur, earum tamen studio a rebus gerendis abduci contra officium est, quia virtutis omnis laus, ut ille dicit, in actione consistit." Piccolomini, The Education of Boys, 246–47; Cicero, De officiis, 1.6.19,

61. "Tu es procul dubio fidelissima immortalis Dei nuncia, quae secretis suis interpretandis legem praebes, cuius gratia coelos constituere decrevit omnipotens, quibus passim ignes sidereos, monimenta futurorum impressit." Regiomontanus, Padua oration, 52.



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