Abstract
The idea of reconciling Ptolemaic planetary theory with Aristotelian natural philosophy by imagining epicycles and eccentric deferents as three-dimensional orbs or orb-segments within larger spheres is frequently associated with Georg Peurbach and his widely read astronomy textbook, the Theoricae novae planetarum (1454). This article cautions against existing tendencies to overstate the originality or revolutionary force of this work by taking a closer look at the early history of the same Ptolemaic-Aristotelian compromise in a Latin European context. Using previously unpublished or unused source material from the twelfth to early fourteenth centuries, it documents the gradual spread and acceptance of an orbicular interpretation of Ptolemy’s planetary models among astronomers and university teachers.
Nicholas Copernicus’s decision to rearrange planetary motions in favour of a heliocentric theory continues to pose formidable explanatory problems that have led modern scholars down multiple different roads in search of a solution.1 This has included efforts to probe more deeply into the astronomical literature of the century that preceded Copernicus’s own, as exemplified by the work of Noel Swerdlow, Michael Shank, Peter Barker, and others.2 The necessity to go back to the fifteenth century in order to explain the “revolution” that occurred in the sixteenth has been emphasized with particular rhetorical vigour by Michela Malpangotto, according to whom the key source to consider is Georg Peurbach’s Theoricae novae planetarum (1454), a text for which she has provided the standard edition and study.3 As is well known, this work offered technical accounts as well as diagrams of the Ptolemaic kinematic models for the seven planets, which depicted the familiar epicycles and eccentric deferents as physical objects, that is to say, as mobile segments of larger planetary spheres that have the Earth at their centre. The implicit purpose of this depiction was to achieve a compromise between mathematical astronomy and natural philosophy, one which integrated Ptolemy’s planetary theory into an Aristotelian physics of the heavens that conceived of all planets as being moved by aggregates of concentric spheres composed of ether.4
In a recent article entitled “Une révolution avant Copernic,” Malpangotto insists that Peurbach’s presentation of this Ptolemaic-Aristotelian compromise in the Theoricae novae planetarum amounted to something fundamentally innovative, and therefore “revolutionary,” with regards to the status quo ante of Latin astronomy.5 According to Malpangotto, the Latin world before Peurbach knew Aristotle’s material spheres and Ptolemy’s geometrical devices only as two conflicting descriptions of the world, with no real means of reconciling them:
[C]es deux traditions restées pendant plus de treize siècles inconciliables, fusionnent dans les Theoricae novae de Peurbach: les sphères concentriques solides d’Aristote emboitées les unes dans les autres, ayant pour centre commun la Terre, sont préservées, mais elles sont redéfinies dans leur composition interne par Peurbach et les systèmes mathématiques de Ptolémée deviennent la structure théorique qui supporte ce tout nouvel édifice céleste. Les Theoricae novae donnent ainsi vie pour la première fois dans l’Occident latin à un univers physique réellement existant.6
Having discussed the appreciation of Peurbach’s work by later readers such as Pierre Gassendi, Malpangotto concludes:
[C]’est précisément à partir du milieu du xve siècle que s’est produite une véritable révolution capable de donner vie à une nouvelle astronomie ayant une identité propre et des caractéristiques singulières. Cette nouvelle astronomie, d’une part, maintient certains traits de l’astronomie traditionnelle, parmi lesquels le géocentrisme, et d’autre part, s’en éloigne de manière remarquable. Grâce à l’univers décrit dans les Theoricae novae, en effet, l’astronomie se renouvelle dans son objet et dans sa méthode de sorte qu’elle change complètement de statut pour entamer le chemin qui l’amènera à devenir la science de la réalité céleste. La nouvelle astronomie issue des Theoricae novae a interrompu l’hégémonie de l’astronomie ptoléméenne, qui se poursuivait depuis 13 siècles. La conception théorique des cieux qui, jusqu’à Peurbach, avait été utile aux astronomes pour prédire les positions des corps célestes et les phénomènes observés, est désormais remplacée par la nouvelle astronomie issue des Theoriae novae.7
One purpose of the present article is to demonstrate that these remarks are simply untenable. Contrary to what Malpangotto asserts, the two “traditions” of Ptolemy and Aristotle did not stand in opposition or unconnected for more than three centuries prior to Peurbach. Far from representing some kind of nouvelle astronomie, the Ptolemaic-Aristotelian compromise that characterizes the Theoricae novae planetarum had been an entrenched part of Latin astronomy and natural philosophy for much of this period. While certain outlines of this history have been known since the pioneering work of Pierre Duhem (1861–1916), the sources that document the presence of orbicular planetary models in medieval Europe are by no means fully explored.8 The evidence I am going to present in what follows mostly stems from the twelfth, thirteenth, and early fourteenth centuries, as my goal is to show how the idea of a “physicalized” Ptolemaic planetary theory consisting of orbs and orb-segments slowly established itself in learned circles and at universities, thus setting the stage for Peurbach’s supposed innovation.
An obvious first point to make here is that the interpretation of Ptolemy’s eccentres (i.e., eccentric deferents) and epicycles as physical objects began with Ptolemy himself. This is evident from his Planetary Hypotheses, in which the Alexandrian astronomer describes each eccentre-and-epicycle mechanism for predicting the ecliptic longitudes and latitudes of a planet as a system of three-dimensional shells, which are nested inside the body of larger spheres that are themselves concentric with the centre of the Earth.9 In the Islamic world, this tradition of explaining Ptolemy’s kinematic models in terms of physical bodies was perpetuated by works dealing with the science of “the configuration” (ʿilm al-hayʾa). A widely diffused representative of this genre was Ibn al-Haytham’s eleventh-century book On the Configuration of the World, whose descriptions of the seven planetary spheres agree with Georg Peurbach’s Theoricae novae planetarum in their essential details.10 In fact, whereas the Planetary Hypotheses remained unknown in the pre-Copernican Latin West, Ibn al-Haytham’s work was translated into Latin on multiple occasions between the twelfth and the sixteenth century.
The chronological sequence of known instances begins with the Liber Mamonis by Stephen of Pisa, which he wrote in the Principality of Antioch in approximately the late 1120s. It can be described as an augmented Latin translation of most of On the Configuration of the World, to which Stephen added his own commentary as well as occasional revisions. An edition and English translation of the only surviving manuscript (ms Cambrai, Le Labo, 930) was published in 2019 by Dirk Grupe.11 A literal translation of the whole work save for its introduction is known from ms Madrid, Biblioteca nacional de España, 10059, ff. 37r–50r, which dates from the thirteenth or early fourteenth century. This text, entitled Liber Aboali ibn Heitam, was published in 1942 by José M. Millás Vallicrosa,12 while a recent stylistic analysis by Dag Nikolaus Hasse has indicated Michael Scot (d. ca. 1235) as the translator responsible.13 Another translation, which presents the text in a restructured form, survives in the fifteenth-century ms Oxford, Bodleian Library, Canon. Misc. 45, ff. 1r–56r, and was edited by José Luis Mancha in 1990. Its source was a lost Castilian translation made for King Alfonso x of Castile and Léon (reigned 1252–1284) by a Jewish scholar named Abraham.14 Furthermore, the sixteenth-century ms Città del Vaticano, Biblioteca Apostolica Vaticana, Vat. lat. 4566, ff. 1r–41v, is known to contain a Latin translation from Hebrew made by Abraham de Balmes ben Meir (d. 1523) for his patron, the Italian cardinal Domenico Grimani (1461–1523). Some extracts from this version were printed by Moritz Steinschneider in 1881.15
Still unpublished remain two further medieval Latin translations, each of which appears to be completely independent from those mentioned thus far. One appears in ms Cambridge, Clare College Library, 15, ff. 29rb–39ra, roughly datable to the second half of the thirteenth century, where the text is identified as Liber Ibnuhaicem (f. 39ra). It begins as follows: Incipit prologus de astrologia mundi. Non cessaverunt multi sapientes in quadruvio studere …16 The second is found in the fourteenth-century ms Lüneburg, Ratsbücherei, Miscell. D 2o 13, ff. 108va–119vb (ca. 1389) and has the incipit Mundus est nomen impositum omnibus rebus corporeis.17
If the number of extant manuscripts – only one in each case – is anything to judge by, none of the six known Latin versions of the text was particularly influential. Indeed, it remains an open question to what extent the idea of representing Ptolemy’s deferents and epicycles as physical orb-segments entered the Latin West through Ibn al-Haytham, as opposed to other channels. One factor that here seems worth considering is a possible spread of the basic idea not only through written texts, but also via diagrams and oral transmission, for instance in a classroom setting. An early witness to an integration of orb-segments into the teaching of basic planetary theory is the Liber de motibus planetarum, an anonymous theorica-type text with a clear didactic orientation that was probably written in England in the third quarter of the twelfth century.18 According to the unknown author of this text, the circuli (“circles” or “rings”) containing the planets are endowed with a “thickness” (spissitudo) defined by the distance between their outer and inner surface, allowing other circuli to be nested within this thickness.19 That the word circulus is here intended to mean something like “orb” is made clearer by the four accompanying diagrams (for the Sun, the Moon, Mercury, and the four remaining planets), which must have been a part of the work from the outset. They visualize each planetary sphere as a body extended between an outer and inner surface, leaving at its centre a hollow space to contain the lower spheres. Each of these bodies carries within it an eccentric deferent, which in the case of the Moon and the five planets is thick enough to encompass the corresponding epicycle.20 An echo of this understanding of eccentres and epicycles is also present in an anonymous Liber omnium sperarum celi et compositionis tabularum, which in one manuscript is spuriously described as an Arabic-to-Latin translation made by Gerard of Cremona.21 In actual fact, the text is another didactic work dating from the second half of the twelfth century, which may have originated in the same English milieu as the Liber de motibus planetarum. Its author insists that the eccentres of all planets other than the Sun are endowed with a thickness (crassitudo), such that “the centre of the epicycle is situated in its middle.”22
A clearer and more explicit expression of the idea that planets are parts of spheres that contain within themselves mobile orbicular segments appears in a general introduction to astronomy (Astrologia) penned in 1220 by William the Englishman of Marseille. It contains the following passage already noted by Pierre Duhem:
One should not omit to mention that each planet has a sphere that is thick and solid in its nature, which in terms of its dimensions is comparable to the shape of the firmament and which is concentric with the world, and its thickness is enough to incorporate the eccentricity and the radius of the epicycle and the radius of the body of the planet. Consequently, when the centre of the epicycle is at the apogee of the eccentre and the body of the planet at the apogee of the epicycle, the body of the planet touches the outer surface of the sphere. By contrast, when the centre of the epicycle is at the perigee of the eccentre and the body of the planet at the perigee of the epicycle, the body of the planet touches the inner surface of the sphere. And the sphere of each planet is contiguous with the sphere of another according to the order of the planets.23
In the case of the copy of William’s Astrologia in ms Erfurt, Universitätsbibliothek, Dep. Erf. CA 4o 357, ff. 1r–22r (s. xiii/xiv), this statement is accompanied by a carefully drawn diagram (f. 8v) indicating both the thickness of a planetary sphere and its eccentre (spissitudo spere) and the positions of the epicycle and planetary body at perigee and apogee.24 William’s distinction between the total sphere of a planet and the different mobile components carried within it was also acknowledged by a glossator of Ptolemy’s Almagest, who worked in Paris in 1247. His extensive gloss on the entire work is found in ms Paris, Bibliothèque nationale de France, lat. 16200, ff. 1ra–191vb, which copy had already been completed in 1213.25 Ptolemy’s remark at the beginning of Almagest 9.1 on how the poles of the planetary spheres coincide nearly with the poles of the ecliptic occasioned the following gloss referencing al-Biṭrūjī, an Andalusian critic of Ptolemy and proponent of a homocentric planetary theory:26
Al-Biṭrūjī [Alpetragius] says that Ptolemy here speaks erroneously, because the circles of the wandering [stars] have different poles from the zodiac. And he says the truth if one speaks only about their circles. Yet, if one speaks about their whole spheres – in the sense that there is a whole sphere of the Moon that contains its oblique circle that carries the epicycle and its eccentre – then al-Biṭrūjī does not speak the truth.27
Much better known than the examples cited so far is the presentation of the Ptolemaic-Aristotelian compromise in the writings of Roger Bacon, who probably first encountered the idea in Paris. His most extended account of this idea appears in the Opus tertium (ca. 1268) he wrote for the eyes of Pope Clement iv, where it is accompanied by diagrams depicting the spheres of the Sun and the Moon, each divided into its constituent orbs.28 Bacon’s discussion of the imaginatio modernorum, his term for the orbicular interpretation of Ptolemy’s models, has been commented upon enough times in the literature that its details need not be repeated here. Suffice it to say that Bacon himself remained sceptical of this imaginatio and appears to have preferred the strictly homocentric spheres espoused by al-Biṭrūjī and followers of Aristotle such as Averroes.29 His relatively detailed treatment of the imaginatio modernorum may nevertheless have contributed to its popularity among subsequent writers.
An account of this “modern” interpretation of planetary spheres that has hitherto gone unnoticed appears in ms Salamanca, Biblioteca Universitaria, 111, f. 32r (s. xiii2/2), in a brief text beginning Nota qualiter poteris ymaginare motum corporum celestium. It is accompanied by a detailed drawing of a physicalized planetary diagram, showing the body of a planet inside an epicyclic orb, which in turn resides within the thickness of the eccentre (see Figure 1). The revolutions performed by the epicycle and eccentre are visualized by drawing the epicyclic orb in four different positions corresponding to the apogee and perigee as well as the mid-points between them. Also clearly depicted in this diagram are the orb-segments that enclose the eccentre and fill out the remaining space to create the total sphere of the relevant planet. The fact that the diagram appears above a note on the comet of 1264, written by a different hand, may suggest an approximate date for this material.
Figure 1
ms Salamanca, Biblioteca Universitaria, 111, f. 32r (detail)
Citation: Vivarium 62, 4 (2024) ; 10.1163/15685349-06204004
Further evidence of an awareness of the imaginatio modernorum among Bacon’s contemporaries comes from an unpublished quaestiones-commentary on John of Sacrobosco’s Tractatus de sphera, beginning Queritur utrum sint plures mundi …, which according to a manuscript colophon was copied in Montpellier in September 1267.30 Little can be said about the author of this work, although his heavy and reverential reliance on Albert the Great’s De caelo et mundo suggests that he may have been a member of the Dominican order. Although this author ended up rejecting the orbicular interpretation of eccentres and epicycles on various philosophical grounds, he considered it important enough to warrant a detailed description, which was originally intended to include a diagram representing the sphere of the Sun. It showed the three main orbs that constitute this sphere together with the Sun itself, whose body was encased by two circles representing the eccentre, which held it in place immovably “like the gemstone on a ring or a stud on a wheel.”31 More striking than this description is the fact that the author introduces the three-orb model as the invention of Campanus of Novara, the well-known Italian astronomer and chaplain at the papal curia (d. 1296):
For this reason, there follows the sixth position, which belongs to certain contemporary [scholars] who reject the aforementioned opinions and attempt to avoid the inconsistencies that follow from them. The original author and creator of this position was Master Campanus of Lombardy, from the city of Novara, who subtly proposed that the spheres of all the planets are concentric with the Earth, and that at the same time within these spheres the planets all move according to eccentric circles. By this, he intended to reconcile the positions of all his predecessors, namely, both those who posit the spheres as concentric with the Earth and those who assumed that they are eccentric. In holding this position, however, he assumes as a foundation and principle (radix) the mutual discontinuity of the parts contained inside the orbs or spheres and that the spheres, considered in their substance, are hence divided according to form, which he claims is neither inconsistent nor impossible.32
This attribution is somewhat puzzling insofar as no full description of an orbicular model appears anywhere in Campanus’s known work on planetary theory (Theorica planetarum), which he wrote in 1261/64. What Campanus does affirm in this work, however, is one of the fundamental presuppositions of the model, which is that the elementary and planetary spheres are contiguous, such that the convex outer surface of one sphere always coincides with the concave inner surface of the sphere above it.33
Authors of the later thirteenth century who openly endorsed the Ptolemaic-Aristotelian compromise include the Franciscan Bernard of Verdun, who defended the reality of epicycles and eccentres in his Tractatus super totam astrologiam,34 and a certain Friar John, author of an unprinted Summa astrologiae (ca. 1276). According to the latter text, the circles that astronomers drew in their books were merely a simplification aimed at greater intelligibility. The actual epicycles and deferent had to be understood as parts of solid and three-dimensional spheres.35 A particularly revealing testimony to the growing acceptance of such a physical understanding at the University of Paris is offered by John of Sicily, who in about 1291/93 wrote a detailed commentary on the most common set of canons to the Toledan Tables.36 Upon introducing the basic concept of celestial spheres, John explained to the reader that
what I call the “sphere” of a planet is not just one spherical body in which the planet is fixed, but several orbs that are specially arranged for the motion of the planet … In order, however, to save the appearances and avoid inconsistencies with regards to natural philosophy, it is necessary to assign to each planet at least three spherical orbs, with one located within the concavity of another, such that the lower of them is concentric with the Earth with respect to its concave surface, but eccentric with respect to its convex one. The second [orb], however, is eccentric to the Earth with respect to both surfaces, but concentric with the convex surface of the lower orb, so that it entirely shares the same centre upon which the convex surface of the lower orb is positioned. The third, upper orb, however, is eccentric to the Earth on the side of its concavity, but on the same side concentric with the second orb. On the side of its convexity, however, it is entirely concentric with the Earth … Consequently, the sphere that is constituted by these orbs is in an absolute sense (simpliciter) concentric with the Earth, but the orbs that constitute it stand in different relations with respect to their various surfaces.37
Having described the motions performed by these different orbs as well as the motion of the epicycle, which is located within the second orb, John mentions his effort of constructing orbicular instruments with mobile parts (instrumentis materialibus atque mobilibus), which served to visualize these different motions and the philosophical advantages of the underlying physical model, such as the avoidance of a vacuum or changes in density. He goes on to call this model a “new position” (novae positionis imaginatio), which has yet to receive a detailed explanation and defence.38
Sources from the early years of the fourteenth century offer glimpses of a situation in which John’s interpretation of the Ptolemaic planetary models has largely prevailed against alternatives such as the homocentric spheres advocated for by Averroes and al-Biṭrūjī. In a quodlibetal quaestio held at the University of Paris in 1307, the Augustinian theologian Henry of Friemar (ca. 1245–1340) considered whether eccentres and epicycles were a real part of God’s creation.39 He came down firmly in favour of their existence while explaining in some detail how their correct interpretation as physical objects was capable of eschewing standard philosophical objections. In doing so, he invoked the astronomical instruments known as equatoria – analogue computers for finding celestial positions – as models of how to picture an epicyclic orb nested within its deferent orb:40
The entire cause of the error that arises with regards to eccentres and epicycles is a failure of the imagination (defectus ymaginationis), because some people conceive of the eccentre as a real circle to which the centre of the epicycle is fixed and, likewise, of the epicycle as a real circle on whose outline the body of the planet moves, which is not the case, but instead both circles are imaginary. For the eccentre is an imaginary circle that is drawn from the centre of the epicycle around the middle of the thickness of the deferent orb and, likewise, the epicycle is an imaginary circle that is drawn according to the motion of the centre of the planet inside its own orb, just as the eccentre is drawn according to the motion of the centre of the epicycle in the middle of the thickness of the deferent orb. Therefore, since the planet together with its orb and the epicycle that is inscribed in it is enclosed within the diameter of the deferent orb, there arises no penetration [between orbs], neither in its own orb nor in the orb above it, as is clearly evident from equatoria (instrumentis equationum). There have been some, however, who in order to avoid the aforementioned penetration placed the planet entirely within its epicycle, thinking that if the centre of the planet were on the epicycle and its radius stuck out from the epicycle, a penetration or the position of a vacuum would follow. But this cannot stand, because according to this, we could never account for the planet being at the apogee or perigee nor many [other] phenomena, the explanation of which is derived from the fact that the centre of the planet is placed on the circumference of the epicycle, not in the sense that the planet is really established on the epicycle, since it is not a real circle, as has been seen, but because the centre of the planet describes the epicycle through the motion of the planet itself inside its own orb to which it is fixed.41
The impression that the Ptolemaic-Aristotelian compromise championed by John of Sicily and Henry of Friemar was now an entrenched part of Latin astronomy is strengthened by a quodlibetal disputation from the University of Oxford, held by the Dominican Nicholas Trevet in ca. 1305. In his quaestio on whether the motions of the planets involve epicycles (Utrum planete moveantur secundum epicyclos), Trevet notes that “modern astronomers” (moderni astrologi) avoid the traditional clash between Ptolemaic astronomy and Aristotelian physics by imagining the epicycle and the planet together as a single spherical body (unum corpus spericum) and the eccentre as a ring (circulum ad modum anuli) whose thickness corresponds to the diameter of the epicyle.42
A surprising feature of Trevet’s account is his claim that the “modern astronomers” who endorse this orbicular model assume the diameter of the epicyclic orb to be twice the size of the diameter of the planet within it, with the result that the planet’s body touches both the centre and the circumference of the epicyclic orb.43 This claim, which is nonsense from the vantage of Ptolemaic astronomy, corresponds exactly with the graphical depiction of a planetary sphere in Figure 1, which suggests that Trevet had seen a similar drawing. Another intriguing comment in this quaestio concerns an addition to the conventional Ptolemaic lunar model that advocates of the orbicular model were inclined to make. It consisted in attributing to the spherical body of the Moon a rotation contrary to the direction of the epicyclic orb. Without this counter-rotation, it would have been inexplicable why the Moon always presented the same side to the observer, as indicated by its spots.44 The same idea of a rotating proper motion on the part of the Moon is mentioned in a contemporary quaestio by the Franciscan Peter of England, held in Paris in ca. 1305, which again endorses the view of eccentres and epicycles as physically existing orb-segments.45
There appears to be ample room for further research that would trace the diffusion and reception of this physical interpretation of Ptolemaic planetary theory at late medieval universities. An example of its application in the context of studying Aristotle’s libri naturales is provided by Albert of Saxony’s quaestiones-commentary on De caelo, which originated in Paris in the mid-fourteenth century. Albert affirmed the Ptolemaic-Aristotelian compromise in two separate discussions, one dedicated to the number of orbs in the heavens, the other to the reality of eccentres and epicycles.46 With regards to the former topic, he noted the importance of distinguishing between different understandings of the concept of a celestial orb. While one of these understandings corresponded to the ethereal spheres traditionally envisioned in the context of Aristotelian philosophy, another also encompassed the constituent parts of these spheres, regardless of whether they were concentric with the world or not.
[A]nd this is how it is understood when one says that the Sun has three orbs, namely, an eccentric one that carries the Sun and two other orbs that enclose it, of which the inner one is concentric with the world with respect to the concave [surface] and eccentric with respect to the convex one, whereas the outer one is eccentric with respect to the concave [surface] and concentric with respect to the convex one.47
At the University of Vienna, where Georg Peurbach would matriculate in 1446, Albert of Saxony’s position was known and shared by the Arts master Johann Widmann of Dinkelsbühl, who in a quodlibetal quaestio of 1429 pondered the number of intelligences that were required to move the celestial orbs. His answer, according to which this number was 21, once again relied on the assumption that most of the segments that made up the total orb (orbis totalis) of each planetary sphere required separate movers to explain the complexity of observable motions. Other than to each eccentre and epicycle, Widmann attributed particular movers to the pairs of orb-segments that enclosed the eccentres of the Moon and Mercury, as these two planets were known to possess a rotating line of apsides.48
Other sources, too, document that the Ptolemaic-Aristotelian compromise was taught at the University of Vienna well before Peurbach’s arrival. James Steven Byrne has drawn attention to an anonymous quaestio on the Moon’s increase in brightness (Utrum luna propter specialem sui ecentrici motum a coniunctione ad oppositionem crescat in lumine) preserved in ms Wien, Österreichische Nationalbibliothek, 4907, ff. 354v–356r, which dates from the first quarter of the fifteenth century (1414/21).49 The subject of the Moon’s eccentre and its two enclosing orb-segments is here broached in the following way, which is in part reminiscent of Albert of Saxony’s commentary on De caelo:
Note that there is a twofold eccentre of the Moon. One of these is eccentric in an absolute sense (simpliciter), that is, with respect to both surfaces, the concave one as much as the convex one, and this is the one that carries the epicycle of the Moon, meaning that the epicycle of the Moon is fixed within it such that its thickness corresponds to the diameter of the epicycle. The other is eccentric not in an absolute sense (simpliciter), but rather in a relative sense (secundum quid), that is, not with respect to both surfaces, but only with respect to one of its surfaces, namely, either the concave one or the convex one, and this is the one that carries the apogee. From this noteworthy thing it follows that the Moon has three eccentres, one concentric with the world with respect to its convex surface and eccentric with respect to its concave one, a second [that is] eccentric in an abolute sense (simpliciter), and a third that is concentric with respect to its concave surface and eccentric with respect to its convex one.50
The important point to stress here is that the orbicular interpretation of eccentres and epicycles was nothing remotely new or unheard of when Georg Peurbach composed the Theoricae novae planetarum. What justified the title Theoricae novae was not the groundbreaking novelty of its content, but the fact that the text was intended as a replacement of the “old” Theorica planetarum beginning Circulus eccentricus vel egresse cuspidis …, which had been in use as a university textbook since the thirteenth century.51 Yet, while it is true that this old theorica paid no attention to the physical aspects of the planetary models it expounded, other texts of this wider genre had done so since the twelfth century, as can be seen from the Liber de motibus planetarum. Even the idea of updating the conventional Theorica planetarum by shifting the emphasis from circles towards physical orbs had been tried out before Peurbach, as seen from Walter Brytte’s Theorica planetarum of the late fourteenth century.52
None of this is to deny that the Theoricae novae planetarum of Georg Peurbach contain some original elements, especially when it comes to the finer levels of technical detail, or that later astronomers drew inspiration from their exposure to this widely diffused text. One relatively novel aspect of the Theoricae novae is Peurbach’s integration of the precession model of the Alfonsine Tables into his description of the eighth, ninth, and tenth spheres above Saturn, although even here it is possible to identify precursors.53 What should be avoided, at any rate, is to exaggerate Peurbach’s role in the history of astronomical cosmology, or to claim that he was the first author in the Latin West to have shown a “univers physique réellement existant.” Such claims do not remotely match the evidence that remains of four centuries of astronomical theory and practice in medieval Europe.
For some examples from the vast secondary literature, which are here limited to a handful of titles published since 2010, see Goddu, Copernicus; Goddu, “Ludwik Antoni Birkenmajer”; Westman, The Copernican Question; Blåsjö, “A Critique”; Malpangotto, “The Original Motivation”; Ragep, “Ibn al-Shāṭir”; Swerdlow, “Copernicus’s Derivation”; Nikfahm-Khubravan and Ragep, “The Mercury Models.”
To name but a few examples: Swerdlow, “Regiomontanus”; Swerdlow, “Regiomontanus’s Concentric-Sphere Models”; Shank, “Regiomontanus and Homocentric Astronomy”; Shank, “Regiomontanus on Ptolemy”; Shank, “Mechanical Thinking”; Shank, “Regiomontanus versus George of Trebizond”; Barker, “Albert of Brudzewo’s Little Commentary”; Feldhay and Ragep, eds. Before Copernicus.
Malpangotto, Theoricae novae planetarum.
On the wider intellectual background, see Aiton, “Celestial Spheres”; Lerner, Le monde; Botteri and Casazza, The Astronomical System.
Malpangotto, “Une révolution.”
Malpangotto, “Une révolution,” 45.
Malpangotto, “Une révolution,” 55.
Duhem, Le système, especially vol. 3: 289–290, 430–437, 453–457, 471, 486–488, and vol. 4: 7–8, 103, 112, 122–124, 156, 161–162, 170. See also Grant, Planets, 275–286; Shank, “Rings”; Byrne, The Stars, 65–96; Sylla, “The Status.” The account of Peurbach’s precursors in Malpangotto, Theoricae novae planetarum, 49–69, ignores much of the published evidence, which the present article seeks to increase.
Murschel, “The Structure”; Hullmeine, Ptolemy’s Cosmology. On the Arabic tradition of the Planetary Hypotheses, see Loizelet, Traditions.
For an English translation, see Langermann, Ibn al-Haytham’s On the Configuration. On the work in its wider Islamic context, see Gamini, “Planetary Theory.”
Grupe, Stephen of Pisa.
Millás Vallicrosa, Las traducciones, 285–312.
Hasse, “Stylistic Evidence,” 36–37.
Mancha, “La version.” See the discussion in Samsó, On Both Sides, 553–567.
Steinschneider, “Notice,” 732–736. See also Duhem, Le système, 2: 121–124.
I thank Dr David Juste for drawing my attention to this manuscript and the translation contained in it. For a description, see James, A Descriptive Catalogue, 28–34.
For a description of the manuscript, see Wierschin, Handschriften, 30–38.
On this text, see Nothaft, “Ptolemaic Orbs.” The text is extant in 9 mss, to which can be added an excerpt in ms Oxford, Corpus Christi College Library, 144, f. 104r–v (s. xivin). Regarding the teaching of astronomy in twelfth-century schools, see Caiazzo, “Teaching,” 198–202.
Anonymous, Liber de motibus planetarum, ll. 49–53, 75, 132–136, 220–222, ed. Nothaft, “Ptolemaic Orbs,” 184–185, 188, 191.
For reconstructed versions of these diagrams, see Nothaft, “Ptolemaic Orbs,” 187, 192, 196, 199. Diagrams of this general nature are also preserved separately in ms Madrid, Biblioteca nacional de España, 10016, f. 2r (s. xiii).
ms Oxford, Bodleian Library, Digby 47, ff. 2r–8r (s. xiiiex). The other two known witnesses are mss Cambridge, Fitzwilliam Museum, McClean 165, ff. 49v–50v (s. xii4/4); Firenze, Biblioteca Medicea Laurenziana, San Marco 194, ff. 62ra–65rb (s. xiiex/xiiiin).
ms Firenze, Biblioteca Medicea Laurenziana, San Marco 194, 64va–vb: “Hoc enim in Sole vera, quia epiciclo caret et eius excentricus crassitudine. Alii autem planete et epiciclum habent et eorum excentrici crassitudinem … Excentrici enim, ut assignavimus, crassitudinem habent et centrum epicicli in eius medio situm est.”
ms Erfurt, Universitätsbibliothek, Dep. Erf. CA 4o 357, 8v: “Nec pretereundum est quemlibet planetam speram habere spissam et solidam in sui natura que se commetitur secundum sui quantitatem figure firmamenti et est concentralis mundo et eius spissitudo est tanta ut sufficiat continere excentricitatem et semidiametrum epicicli et semidiametrum corporis planete. Unde cum centrum epicicli fuerit in auge excentrici et corpus planete in auge epicicli, tangit corpus planete superiorem superficiem spere. Cum autem centrum epicicli fuerit in oppositione augis excentrici et corpus planete in oppositione augis epicicli, tangit corpus planete inferiorem superficiem spere. Et spera cuiuslibet planete secundum ordinem planetarum contingua est spere alterius” (my translation). See Duhem, Le système, 3: 289–290.
A digital reproduction of the manuscript is available at:
Juste, “ms Paris, Bibliothèque nationale de France, lat. 16200.”
On al-Biṭrūjī’s planetary theory and its reception in Latin Europe, see Goldstein, Al-Biṭrūjī, 1: 3–39; Avi-Yonah, “Ptolemy vs. Al-Bitruji”; Duhem, Le système, 2: 146–156; Lerner, Le monde, 104–110; Shank, “Mechanical Thinking,” 11–12; Samsó, On Both Sides, 530–544.
ms Paris, Bibliothèque nationale de France, lat. 16200, 125va: “Hic dicit Alpetragius quod Ptholomeus dicit hic falsum, quia circuli erraticarum diversos habent polos a zodiaco. Et verum dicit si loquitur de solum circulis eorum. Sed si loquitur de totis spheris eorum, sicut tota sphera Lune est que continet circulum eius declivem deferentem epicyclum et eccentricum eius, tunc non dicit Alpetragius verum.”
Roger Bacon, Opus tertium, c. 102–103, 820–835. An abbreviated version of the same discussion appears in Roger Bacon, De celestibus, pt. 5.14, 437–439. On the biographical background and the date of the Opus tertium, see Hackett, “From Sapientes antiqui.”
See, e.g., Duhem, Le système, 3: 432–437; Hugonnard-Roche, “Problèmes,” 62; Hugonnard-Roche, “Contribution,” 106–108; Grant, Planets, 279–280; Shank, “Rings,” 177–179; Shank, “Mechanical Thinking,” 12–14; Lerner, Le Monde, 115–130; Hasse, “Averroes’ Critique,” 83–84; Malpangotto, Theoricae novae planetarum, 62–63.
See ms Erfurt, Universitätsbibliothek, Dep. Erf. CA 4o 188 (s. xiii2/2), ff. 9vb–34ra. The colophon on f. 34ra reads: “Et sic expliciunt questiones super tractatum de spera in Monte Pessulano. Anno domini 1267o, sexto nonis Septembris, existente Sole in 23o gradu Virginis.” The same date and solar longitude are repeated on f. 56va, at the end of a lemmatic commentary on the same text. Presumably, the calendar date should in each case have read “sexto idus” (8 September), as suggested by the position of the Sun. The existence of this text was previously noted in Grabmann, “Der Einfluss,” 314 (repr. in Grabmann, Mittelalterliches Geistesleben, 2: 361); Thorndike, “Robertus Anglicus,” 468.
ms Erfurt, Universitätsbibliothek, Dep. Erf. CA 4o 188, 16ra–rb: “[I]ntelligas … quod sol in isto materiali circulo sit immobiliter incastratus et insertus sicut gemma in annulo vel cavillam [sic] in rota.” The space intended for a diagram in the upper half of this page has been left empty.
ms Erfurt, Universitätsbibliothek, Dep. Erf. CA 4o 188, 15vb: “Propter quod sequitur positio sexta quorundam modernorum predictas opiniones abicientium et inconvenientia que sequuntur ipsas conantium evitare, cuius positionis primus autor et fictor fuit magister Campanus Lumbardus de civitate Navariensi, qui subtiliter posuit speras omnium planetarum concentricas esse terre et cum hoc simul in ipsis speris per circulos excentricos planetas omnes moveri, sic concordare intendens omnes positiones precedentium, et illorum videlicet qui ponunt speras concentricas terre, et illorum qui posuerunt eas excentricas esse. Supponit autem in positione sua tanquam pro fundamento et radice discontinuationem partium orbium vel sperarum adinvicem infra ipsas et sic speras ipsas secundum substantiam acceptas dividi secundum formam, quod asserit nec inconveniens nec impossibile” (my translation). See also the references to Campanus’s alleged opinion ibid., ff. 29vb, 30rb.
Campanus of Novara, Theorica planetarum iii, ll. 20–28; iv, ll. 295–324 (ed. Benjamin Jr. and Toomer, 144–145, 180–183). On the author, see Paravicini Bagliani, “Un matematico”; Paravicini Bagliani, “Campano da Novara.”
Bernard of Verdun, Tractatus super totam astrologiam 3.3.5, 70–72. See Duhem, Le système, 3: 453–457.
ms Paris, Bibliothèque nationale de France, lat. 7293A, 55r: “Et licet hec omnia sunt spere solide, tamen astrologi cum describunt motus planetarum describunt eos non per orbes sed per circulos lineares ut clarius possunt intelligi.” On this text, see Thorndike, “Notes,” 127; Nothaft, Medieval Latin Christian Texts, 150–151, 617–621; Nothaft, Scandalous Error, 160–161, 246–247.
See Pedersen, “Scriptum.”
John of Sicily, Scriptum super canones Azarchelis, J285, ed. Pedersen, “Scriptum,” pt. 2: 134: “Appello sphaeram planetae non unum solum corpus sphaericum, in quo planeta fixus existat, sed plures orbes ad motum planetae specialiter ordinatos … Oportet autem ad hoc ut apparentia salventur et contra naturalem philosophiam inconvenientia non sequantur, in unoquoque planetarum ad minus 3 orbes sphaericos assignare, quorum unus in concavitate alterius statuatur: ita quod inferior sit concentricus terrae quantum ad superficiem concavam, excentricus autem quantum ad convexam; secundus autem sit excentricus terrae quantum ad utramque superficiem, concentricus tamen superficiei convexae orbis inferioris, ita quod omnino sit super idem centrum, supra quod est orbis inferioris convexa superficies constituta; tertius autem superior orbis sit excentricus terrae ex parte suae concavitatis, sit tamen ex eadem parte concentricus secundo; ex parte vero suae convexitatis sit omnino concentricus terrae … Unde sphaera ex istis orbibus constituta simpliciter est concentrica terrae, sed orbes eam constituentes sunt, quantum ad diversas eorum superficies, diversimode se habentes” (my translation). John’s discussion of the orbicular theory was previously noted by Duhem, Le système, 4: 7–8; Hugonnard-Roche, “Problèmes,” 62–63.
John of Sicily, Scriptum super canones Azarchelis, J285, ed. Pedersen, “Scriptum,” pt. 2: 135: “Huius autem rei figuram sensibilem et exemplar in instrumentis materialibus atque mobilibus ordinavi, in quibus motuum diversitates nostris visibus apparentes experimento sensibili cognoscuntur et condensationis, rarefactionis et vacuitatis inconvenientia devitantur. Huius vero novae positionis imaginationem, quae etsi forsan ab aliis visa est, a nullo tamen de articulate particulariter explicata. Defensionem ab hiis, quae possent obici, praetermitto, quia leviter omnia solvi possunt et alibi, videlicet in theorica planetarum, praecipue locum habent.”
Henry of Friemar the Elder, Quodlibet, q. 6, Utrum in primis operibus Dei sit ponere motus excentricos et epicyclos, ms Città del Vaticano, Biblioteca Apostolica Vaticana, Vat. lat. 1012, ff. 124va–125rb. Excerpts from a differently worded version of the same quaestio (ms Padova, Biblioteca Antoniana, 662, ff. 197r–200v) are printed in Stroick, Heinrich von Friemar, 209–212. On Henry of Friemar and the context of this disputation, see Saak, Augustinian Theology, 347–386; Schabel, “John Duns Scotus.”
On the subject of equatoria, see Poulle, Les instruments.
ms Città del Vaticano, Biblioteca Apostolica Vaticana, Vat. lat. 1012, 125rb: “Tota autem causa erroris qui contingit circa ecentricos et epyciclos est defectus ymaginationis, quia quidam ymaginantur ecentricum esse circulum realem in quo figatur centrum epicicli et similiter quod epiciclus sit circulus realis in cuius figura moveatur corpus planete, quod non est verum, sed uterque est circulus ymaginatus. Est enim ecentricus circulus quidam ymaginatus qui describitur e centro epicicli circa medium spissitudinis orbis deferentis et similiter epyciclus est circulus quidam ymaginatus qui describitur ex motu centri planete in suo orbe, sicut ecentricus describitur ex motu centri epycicli in media spissitudine orbis deferentis. Et sic cum planeta cum orbe et epiciclo in ipso descripto claudatur et infra dyametrum orbis deferentis, nulla sequitur scissio, nec in orbe proprio nec in orbe superiori, ut patet manifeste in instrumentis equationum. Fuerunt autem quidam qui, ut vitarent scissionem predictam, ponebant planetam infra suum epiciclum totaliter, estimantes quod si centrum planete esset in epiciclo et semidyametraliter emineret epiciclo quod sequeretur scissio vel vacui positio. Sed hoc non potest stare, quia secundum hoc numquam possemus salvare quod planeta esset in auge vel in opposito augis nec multas apparentias, quarum ratio sumitur ex hoc quod centrum planete ponitur in circumferentia epicicli, non quod planeta realiter fundetur in epiciclo, cum non sit circulis realis, ut visum est, sed quia centrum planete ex motu ipsius planete in proprio orbe in quo figitur describit epiciclum” (my translation).
Nicholas Trevet, Quodlibet iii, q. 8, Utrum planete moveantur secundum epicyclos, ms Basel, Universitätsbibliothek, B.IV.4, f. 14rb–vb, at f. 14va. On the author and his quodlibeta, see Ehrle, “Nikolaus Trivet”; Friedman, “Dominican Quodlibetal Literature,” 426–429.
ms Basel, Universitätsbibliothek, B.IV.4, 14va: “Est autem eorum ymaginatio talis: ymaginantur epiciclum esse quoddam corpus spericum, cuius dyametrum sit duplum respectu dyametri corporis planete. Ponunt planetam situari sic in epiciclo quod una dyametri extremitas planete sit in centro epicicli et alia in circumferentia epycicli, et ita totum, scilicet epiciclus cum planeta, unum corpus spericum.”
ms Basel, Universitätsbibliothek, B.IV.4, 14vb: “[S]i planete sic essent fixe in epiciclis quod non moverentur motu proprio bene concludit ratio quod, si hec proprie esset vera, aliquando non apparet nobis macule [sic] lune. Sed modo ita est secundum eos quod planeta dum revolvitur ab epiciclo motu proprio revolvitur contra epiciclum, et ideo semper eandem partem habet versus terram et eandem versus celum.” On the idea of the rotating Moon in medieval scholasticism, see Kren, “The Medieval Man,” 225–230; Gabbey, “Innovation,” 115–119; Grant, Planets, 299–302, 463–466.
Peter of England, Quodlibet iii, q. 23, Utrum sint ponendi excentrici et epicycli, ms Città del Vaticano, Biblioteca Apostolica Vaticana, Vat. lat. 932, 216vb–217ra: “Volunt etiam quidam quod luna preter hoc movetur motu girativo super centrum suum proprium, alioquin macula que apparet in luna non semper esset in eadem dispositione quo ad nos, immo illud quod aliquando est superius transponetur ita quod esset inferius … Unde dicitur probabilius quod motus eius super centrum proprium est contra motum epicicli, ita quod qualiter illa macula deberetur transponi per motum epicicli tantum per motum lune proprium in contrarium transponi prohibetur. Et secundum hoc luna habet 5 motus et forte alii quinque planete.” On the author and the date of this quodlibet, see Duba, “Continental Franciscan Quodlibeta,” 572–579.
Albert of Saxony, Quaestiones in Aristotelis De caelo ii, qq. 6–7, 267–285.
Albert of Saxony, Quaestiones in Aristotelis De caelo ii, q. 6, 272: “Secundo modo sphaera vel orbis dicitur unus, quia est unus orbis suppositaliter existens, sive sit concentricus mundo sive sit excentricus; et sic accipitur, cum dicitur quod solis sunt tres orbes, scilicet excentricus deferens solem et duo alii orbes illum includentes, quorum inferior est concentricus mundo quantum ad concavum et excentricus quantum ad convexum, superior autem excentricus quantum ad concavum, et concentricus autem quantum ad convexum, sicut dictum est prius” (my translation).
Johann Widmann of Dinkelsbühl, Utrum tot sunt intelligentie quot sunt celestes spere, ms Melk, Stiftsbibliothek, 958, 466–474, esp. 466–467, 472–474. For an edition and discussion of this text, see Nothaft, “Johann Widmann of Dinkelsbühl.”
Byrne, The Stars, 80–82.
ms Wien, Österreichische Nationalbibliothek, 4907, 354v, cited according to Byrne, The Stars, 81–82: “Nota quod duplex est ecentricus lune; unus est eccentricus simpliciter, scilicet quoad utramque superficiem tam concavam quam convexam et iste est deferens epicicli lune scilicet cui infixus est epiciclus lune ita quod ipsius spissitudo est dyameter epicicli. Alius est ecentricus non simpliciter sed secundum quid scilicet non quoad utramque superficiem sed solum quoad unam suarum superficierum, scilicet aliam concavam aliam convexam et iste est deferens augis. Ex isto notabili sequitur quod luna habet tres ecentricos, unum concentricum mundo quoad superficiem convexam et ecentricum quoad concavam, secundum ecentricum simpliciter, et tertium concentricum quoad superficiem concavam et ecentricum quoad convexam.” The translation is my own.
See the edition in Carmody, ed. Theorica Planetarum, and the discussions of this text in Pedersen, “The Theorica Planetarum-Literature”; Pedersen, “The Origins”; Byrne, “The Mean Distances.”
Pedersen, “The Problem,” 242–243. See also Pedersen, “The Theorica Planetarum,” 64–66, concerning a commentary on the old Theorica planetarum by Taddeo of Parma (1318).
See Nothaft, “An Alfonsine Universe.”
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