The “Notes on Al-Biṭrūjī” Attributed to Regiomontanus: Second Thoughts

Carmody F. J. , “Regiomontanus' notes on al-Biṭrûjî's astronomy”, Isis, xlii (1951), 121–30.

Zinner Ernst , Leben und Wirken des Johannes Müller von Königsberg, genannt Regiomontanus , 2nd edn (Osnabrück, 1968), 65–66, 307 [hereafter cited as Zinner , Regiomontanus].

Zinner , Regiomontanus (ref. 2), 307. Note the following nonstandard foliation: F. 63 has “63” on recto, “64 65” on verso. The next folio is numbered.

Zinner , Regiomontanus (ref. 2), 61–62, 305. On al-Biṭrūjī, see Goldstein Bernard , Al-Biṭrūfī on the principles of astronomy (2 vols, New Haven, 1971), i, 3ff; Sabra A. I. , “The Andalusian revolt against Ptolemaic astronomy: Averroes and al-Biṭrūjī”, in Tradition and transformation in the sciences, ed. by Mendelsohn Everett (Cambridge, 1984), 133–53.

Carmody , “Regiomontanus' notes” (ref. 1), 122.

See for example Henry of Langenstein's “De reprobatione ecentricorum et epiciclorum” (Vienna, ÖNB lat. 5203, 100r–l17v).

Carmody , “Regiomontanus's notes” (ref. 1), 129; see also below.

See Appendix A, at ref. 38, 40–41, 43, 44, 47, 48, 54. This contrasts markedly with Regiomontanus's behaviour in genuine autographs (e.g., the “Defensio Theonis”, in which deletions, erasures, and revisions abound; the original of this is in the archive of the U.S.S.R. Academy of Sciences in St Petersburg; I consulted the copy in the Stadtbibliothek Nürnberg).

It has neither the terse specificity of his technical arguments, nor the rhythm of his periodic sentences, nor the slightly pedantic vocabulary of his works from the 1460s (e.g., the preface to the Epitome, the introduction to the Padua lecture on al-Farghānī, the opening monologue of the Disputationes), not to mention good grammar (see the inconsistent shifting between present and perfect, or indicative and subjunctive). The “Notes” are admittedly earlier than these, but Regiomontanus filled the pages of his “computation book” at a time when style was beginning to wax in importance at Vienna. During these years, Regiomontanus's close friend and colleague Georg Peuerbach was teaching Virgil, Juvenal, and Horace. Regiomontanus himself was scheduled to lecture on Virgil's Bucolics as he left Vienna for Italy in September 1461; see Uiblein Paul , “Die Wiener Universität, ihre Magister und Studenten zur Zeit Regiomontans”, in Regiomontanus-Studien [Österreichische Akademie der Wissenschaften, Sitzungsberichte, Phil.-hist. Kl., ccclxiv], ed. by Hamann Günther (Vienna, 1980), 428. The “Notes” are not from the pen of an aspiring Latinist.

Carmody , “Regiomontanus's notes” (ref. 1), 127.

In Regiomontanus's own edition of the Disputationes, the criticism appears on 3v and 4r of the unnumbered folios; see Joannis Regiomontani opera collectanea, ed. by Schmeidler F. (Osnabrück, 1972) [hereafter cited as “Schmeidler”], 518–19.

Carmody , “Regiomontanus' notes” (ref. 1), 128–9.

de Monte Regio Joannes , Epytoma in almagestum Ptolemei, Book 9, Proposition 1, f. klv [Schmeidler (ref. 11), 192]; Carmody , “Regiomontanus's notes” (ref. 1), 128–9.

Zinner , Regiomontanus (ref. 2), 61; Nürnberg, Stadtbibliothek Cent. V 53, 74r: “Geber mercurium et venerem supra solem posuit”; 101r-v: “De ordine trium planetarum solis veneris et mercurii” (101r) across from the text “Sermo in celis iiii^or…” Al-Biṭrûjî: De molibus celorum, ed. by Carmody Francis (Berkeley, 1952), 127, sent. 1]; later “venus supra solem” (101v) across from the passage “sed videtur de re veneris…” (ibid., 128, sent. 7); and finally “Quod venus et mercurius non obscurant solem non esse sufficiens indicium sue supra solem collocationis” (101v) across from the passage that begins “Sed illud quod posuerunt…” (ibid., 128, sent. 10).

Zinner , Regiomontanus (ref. 2), 61–62. Zinner's summary of their gist mistakenly implies consistency with the “Notes” for he asserts that Regiomontanus criticized “al-Biṭrūjī's claim that Mercury and Venus must move above the Sun” (p. 62). But al-Biṭrūjī made no such claim. Indeed Regiomontanus's marginal annotation (“That Venus and Mercury do not obscure the Sun is not a sufficient proof of their location above the Sun”) pertains to a view that al-Biṭrūjī attributed to “opponents of the ancients”, without endorsing it himself; see Al-Biṭrûjî, ed. by Carmody (ref. 14), 128.

Nürnberg , Stadtbibliothek Cent. V 53, 76v: “Ptolemei positionem impugnat non satis intelligens eccentricorum et epicyclorum [[diversitas]] genera que in scholis hodie exercentur” [facing Al-Biṭrûjî, ed. by Carmody (ref. 14), 78, sent. 25].

Toomer G. J. , Ptolemy's Almagest (New York/Berlin, 1984), 252 (Book V, 14); Regiomontanus , Epytoma (Book 5, Prop. 21; Schmeidler (ref. 11), 143). In his Theoricae novae planetarum (c. 1454), Peuerbach had already given solar apogee and perigee values of 31′ and 34′ respectively; see Schmeidler (ref. 11), 782; and Aiton E. J. , “Peuerbach's Theoricae novae planetarum: A translation with commentary”, Osiris, ns, iii (1987), 5–43, p. 31.

This prediction exists only in a German version, Edited by Klug R. , “Johannes von Gmunden, der Begründer der Himmelskunde auf deutschem Boden. Nach seinen Schriften und den Archivalien der Wiener Universität”, < Österreichische > Akademie der Wissenschaften zu Wien, Sitzungsberichte, Phil.-hist. Kl., ccxxii, 4 (1943), 61–62; also Edited by Mundy John in conjunction with his “John of Gmunden”, Isis, xxxiv (1943), 196–205.

Klosterneuburg 683, 212v: “Anno Domini etc 1433°. Notificat Magister Johannes de Gmunden quod die 17^a mensis Junii, scilicet feria 4^ta post festum Sancti Viti hora 4^a et minuto 31° post meridiem erit conjunctio visibilis luminarium, videlicet Solis et lune…. Et eclipsabitur totum corporis Solis…”.

See Georg Tanstetter's introduction to the Tabulae eclipsium Magistri Georgii Peurbachii (Vienna, 1514), f. aa3v; and Durand Dana , The Vienna-Klosterneuburg map corpus (Leiden, 1952), 45, 59–60. The Gmunden texts in Prunner's hand are preserved in London, British Library, Add. 24071 and 24071; they were copied between 1436 and 1438.

“Der ‘Tractatus Cylindri’ des Johannes von Gmunden”, ed. by d'Occhieppo Ferrari Konradin and Uiblein Paul , in Beiträge zur Kopernikus-Forschung [Katalog des Oberösterreichischen Landesmuseums, Nr. 86] (Linz, 1973), 33.

“Explicit tractatus super planitorbium editus a fratre G. Marchonis ordinis fratrum minorum, tunc studente Parisius pro provincia Aquitanee. Amen. Et est finitus per me Vincentium Swofheym de Legnicz in felici monasterio Newnburgensi in curia et in edificio domini et patris reverendissimi domini Georii prepositi monasterii eiusdem. De Slesia natus Vincentius sum vocatus” (ÖNB lat. 5266, 263v). Emmanuel Poulle has analysed in detail the part of the treatise that describes the instrument, in his Les instruments de la théorie des planètes selon Ptolémée: Équatoires et horlogerie planétaire du XIIIe au XVIe siècle (2 vols, Geneva/Paris, 1980), i, 260–8. It reveals this “G. Marchio” to be a sophisticated theorist who seeks to reduce to a minimum the number of graduated circles usually required to construct an equatorium. Zinner mentions “G. Marchio” and his treatise briefly. He implicitly gives the work an excessively late date (“vor 1434”) and argues that it relies on both Profatius Judaeus (= Jakob ben Machir), which makes sense chronologically, but especially on Algeri (Johannes Algerius), who appears to be from the mid-fourteenth century, and is therefore an unlikely source for a work from 1310; see Zinner , Deutsche und niederländische astronomische Instrumente des 11.–18. Jahrhunderts (Munich, 1967), 159.

“Fuit autem compilatum presens opusculum et instrumentum compositum anno domini 1310 versus anno milleno domini tercent quoque deno inter cetera fore cepi dictante minore” (236r). For the full reference to the annular eclipse (“fuit visum Parisius anno domini 1309 ultima die Januarii hora quasi septima”, 238r), see ref. 49 below. Easter marked the beginning of the new year in late medieval Paris, which is why the year of the eclipse according to our calendar is 1310; Grotefend H. , Taschenbuch der Zeitrechnung des deutschen Mittelalters und der Neuzeit, 11th edn (Hanover, 1971), 13.

The bastard son of the count of Angoulême and La Marche, Guy de la Marche was granted a papal dispensation in order to receive a special dignity from the general of his order; see Wadding Luke , Annales Minorum seu Trium Ordinum a S. Francisco Institutorum… , v [1276–1300] (Florence, 1931), 322–3; Hauréau Barthélémy “Gui de la Marche”, Histoire littéraire de la France, xxix (Paris, 1885), 552–7. His birth and death dates are uncertain, but Hauréau charitably conjectures that he was born before 1257 (the presumed date of his father's marriage!) and supposes that he died c. 1315. Guy de la Marche is also the author of two poems, a “Disputatio mundi et religionis” that antedates 1307; and a satirical logical poem with incipit “Sortes, Plato, Cicero”. They are edited respectively by Hauréau , in the Bibliothèque de l'École des Chartes, xlv (1884), 5–30; and Pflaum Heinz , “Sortes, Plato, Cicero: Satirisches Gedicht des dreizehnten Jahrhunderts”, Speculum, vi (1931), 499–533.

Compare, for example, lines 14 and 16 of Appendix A with refs 45 and 46 below.

See ref. 51 below.

See ref. 49 below.

See ref. 22 above. The other complete Viennese copy is ÖNB lat. 5273, ff. 258–301; for the other copies, see Poulle , Les instruments (ref. 22), 261, n. 4.

These figures simplify al-Biṭrūjī's model by omitting the polar deferent on which the centre of the epicycle CPKQ rides; for the complete diagram of a superior planet, see Goldstein , Al-Biṭrūjī (ref. 4). The basic geometry of diagram is incorrect in the Marchia manuscript and in Carmody (ref. 1), but Regiomontanus drew it correctly when copying the “Notes”. Point C must be the centre of both the Zodiac and circle DEL (Appendices A and B, line 6). The reference to the “circle or oval figure” in Marchia represents a concern to discuss simultaneously the “actual” shape of the curve and its projection in two dimensions.

Marchia's scheme will be the subject of a later article.

According to modern calculations, the eclipse of 17 June 1433 was total, not annular; see Schroeter J. Fr. , Spezieller Kanon der zentralen Sonnen- und Mondfinsternisse, welche innerhalb des Zeitraums von 600 bis 1800 n. Chr. in Europa sichtbar waren (Kristiania, 1923), 53, 138. Silverman Samuel and I will discuss this curious observation in more detail in a forthcoming article.

Grossing Helmut , “Regiomontanus und Italien” in Regiomontanus-Studien , ed. by Hamann (ref. 9), 234–5. The letter to Vitéz is mentioned first in Zinner , “Neue Regiomontan-Forschungen und ihre Ergebnisse”, Sudhoffs Archiv, xxxvii (1953), 107–8; and in the second edition of Zinner's Regiomontanus (ref. 2), 151; see also Gerl Armin , Trigonometrisch-astronomisches Rechnen kurz vor Copernicus: Der Briefwechsel Regiomontanus-Bianchini (Stuttgart, 1989), 210ff. Gerl's analysis unwittingly reveals the contradictions involved in understanding Regiomontanus's position if one accepts both the “Letter to Vitéz” and the “Notes on al-Biṭrūjī” as genuine works. I thank Noel Swerdlow for drawing my attention to the letter several years ago, and for sending me a copy of the text, together with his transcription and translation.

“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 que in secundo tractatu sunt confirmabo. Quartus quo pacto motus isti numerari et tabule ad illas novas radices fundari possint continebit” (Florence, Bibl. Naz., Magl. XI 144, f. 16r).

My forthcoming study of Regiomontanus's Disputationes argues that Regiomontanus drew upon Henry of Langenstein's homocentrically oriented “De reprobatione ecentricorum et epiciclorum” for several criticisms of the old Theorica planetarum.

This is the title given in the index to Regiomontanus's notebook (on the fly-leaf of the manuscript).

Cf. Marchia: “Fuit ymaginatus Alpetragius quod omnes circuii celestes moverentur ab oriente in occidens. Et si moveri videantur ab occidente in oriens, hic non est nec quia moventur ab oriente in occidens incurtatim sicut cum duo homines moventur non eque velociter ad idem, ubi videbitur alicui longe distanti quod tardior ad ubi contrarium moveatur a quo velocior recedere dinoscitur” (ÖNB lat. 5266, 236va).

Cf. Marchia : “…quia contrarietas et multitudo in motibus celestibus tollenda est si motus ad eandem partem reddat rationem de apparentibus, quia in paucioribus via magis visum fuit in Alpetragio quod omnes celestes circuii tantum ad occidens moverentur” (ÖNB lat. 5266, 236vb).

duorum (interlinear) replaces cuiusdam (crossed out).

Cf. Marchia : “Commentator Averroys 12° Metaphysice vult quod astrologia vera fundatur super principia naturalia que destruunt ecentricos et epiciclos. Et per consequens ipsos destruet vera astrologia, quorum destructionem dicit posse contingere si unus orbis movetur super polos multos ut talis motus sit compositus ex multis partialibus motibus quibus correspondeant multi motores et tamen confitetur hanc assertionem non posse explicare, ymmo desperavit de ipsa in senectute, licet in iuventute sua speraverit” (ÖNB lat. 5266, 236vb).

After polus (at the end of a line), a second polus (here omitted) occurs at the beginning of the next line.

ut in L added in the margin.

K interlinear.

secundum crossed out.

pro crossed out.

Cf. Marchia : “…si non esset in motibus planetarum differentia nisi incurtationis, tunc Venus et Mercurius certis temporibus essent oppositi gradui solis, quod numquam visum est…” (ÖNB lat. 5266, 237rb).

Cf. Marchia : “quia tunc directio et retrogradatio essent velocissime cum planete essent in maxima latitudine et aliter non, quod est falsissimum” (ÖNB lat. 5266, 237rb–237va).

particularibus: Added in margin.

simili la crossed out.

Cf. Marchia: “Sexta via est quia stante eadem linea AB originata a B transeunte per centrum D ipsius lune et per centrum solis E, aliquando totus sol nobis occultabitur, aliquando non eclipsabitur totaliter, ymmo remanebit notabililis circumferentia solaris circumdans lune emisperium, sicut fuit visum Parisius anno domini 1309 ultima die Januarii hora quasi septima cuius rei non potest alia reddi ratio quam < vel: added interi. > solis et < vel: added interl. > lune in suis ecentricis maior et minor elongatio sicut evidenter ostendit decima figura et 11^a “(ÖNB lat. 5266, 238ra-b).

Cf. Marchia : “Secunda via est quia Luna habente eandem latitudinem ex parte septentrionis vel meridiei, dum eclipsatur particulariter quandoque eclipsatur sub portione maioris circuii quandoque sub portione minoris, ut visus ostendit, quod non contingeret nisi pro eo quod Luna pertransit ad locum in quo circulus umbre est differens secundum magnitudinem et parvitatem, et per consequens magis et minus terre appropinquans. Tertia via est quia Luna habente eandem latitudinem omnino in variis eclipsibus et cum hoc etiam cursum habente velocem, quia est in parte inferiori epicicli dum est eclipsis totalis in variis eclipsibus, una earum plus protenditur et etiam plus durat, quod esse non potest nisi ratione transitus maioris et minoris dyametri in umbra que, cum sit piramidalis, versus terram ubi est basis erit latior quam versus conum. Et ideo talis eclipsis quanto plus durabit tanto Luna erit terre propinquior” (ÖNB lat. 5266, 237ra-b).

Cf. Marchia : “Sed aliqui antiquorum sicut Caldei et Egiptii dixerunt quod sub Marte situatur Venus immediate, et sub Venere Mercurius et Sol sub Mercurio, sub quo Luna. Et ad hoc ponendum fuerant motus < corr.from motum > duplici ratione. Prima est quia si Venus et Mercurius essent sub sole, aliquando contingeret quod aliqua portio solis eclipsaretur nobis per eorum interpositionem, quod numquam fuit visum. Secunda est quia quanto planete cursum suum tardius faciunt, tanto situantur altius, sicut patet in tribus superioribus. Sol autem citius cursum suum facit quam Venus et Mercurius, et Mercurius citius quam Venus. Et ideo Venus ut dicunt Mercurio supponitur et Mercurius ipsi Soli” (ÖNB lat. 5266, 239ra).

Cf. Marchia : “Tertium est quia cum sol sit fons caloris et luminis etc omnium planetarum ad modum cordis debet esse in medio eorum, et hec est sententia Ptolomei et Alfragani ceterorumque peritorum in astronomia” (ÖNB lat. 5266, 239rb).

Cf. Marchia : “omnia salvari possunt que de planetarum apparent motibus stante continuitate spere vel unitate orbis a convexo firmamenti usque ad lune concavum per distinctos columpnares circulos…” (ÖNB lat. 5266, 236r); “In circulo columpnari deferente totum corpus epicicli ymaginatur quedam linea circularis transiens per centrum epicicli eque distans convexo et concavo circuii columpnaris qui vocatur deferens in quo movetur centrum epicicli ad motum columpnaris circuii…” (ÖNB lat. 5266, 240ra). To the best of my knowledge, the term prisma occurs nowhere in the Marchia text. It therefore seems to be an amplification and interpretation by the author of the “Notes”, particularly intriguing since prisma is “probably the term that Ptolemy used for the ‘drums’ containing the planetary model in Bk. II of his Planetary hypotheses (preserved only in Arabic translation)”; see Toomer , Ptolemy's Almagest (ref. 17), 407, n. 186. A less tantalizing source than the importation of a Ptolemaic fragment, however, is the linkage between “corpus columpnare” and “prisma” in the mid-fourteenth-century De arte mensurandi attributed to Johannes de Muris, ch. 10: “Prisma est corpus columpnare lateratum cuius basis est superficies plurilatera…”; see Archimedes in the Middle Ages , ed. by Clagett Marshall , iii (Philadelphia, 1978), 94, 2. In another passage, “prisma” and “columpna” are used synonymously (95, 4).

contig sed crossed out.

Although the word “above” [supra] may seem odd in three dimensions, it makes good sense with respect to the orientation of the two-dimensional diagram in the manuscript, in which C appears at the bottom of the circle (see Figure 1).