During the first fifty years of its printing, the greatest number of Sacrobosco Sphaera editions appeared in Venice, Paris, and Leipzig. Indirect evidence suggests that the Venetian and Parisian copies circulated widely; Leipzig editions, however, primarily served the local market, i.e., university students in Leipzig, Erfurt, and Wittenberg. This paper analyzes fifteen editions of Sacrobosco’s Sphaera issued by three Leipzig printers between 1488 and ca. 1521. These Leipzig Sacroboscos share a common text, set of woodcuts, and mis-en-page that were not much copied by printers beyond Leipzig. The paper also investigates the Leipzig masters who lectured on Sacrobosco during these decades; several became known locally as mathematicians, but most moved to other faculties or left the university. Three of the masters authored commentaries that printers added to their editions. One of these borrowed heavily from a lengthy commentary by the Paduan master, Francesco Capuano, printed 1499 in Venice. Another commentary would be reprinted several times in Cologne, but generally the Leipzig commentaries also remained local in their influence. After Wittenberg printers began issuing Sacroboscos in 1531, no further editions would be printed in Leipzig. The Leipzig Sacroboscos thus illustrate the dynamics of a local university market shaping the early printing history of this introductory textbook.
- Johannes de Sacrobosco
- Tractatus de sphaera
- Local book market
- Scientific commentaries
For their assistance in dating the Leipzig Sacrobosco editions I thank Falk Eisermann, Oliver Duntze and Matteo Valleriani. Michael H. Shank, Razieh Mousavi, Alena Hadravová, Petr Hadrava, Bettina Erlenkamp, Kristin Lippincott, Christoph Mackert, and the other authors in this volume who generously helped me with various bibliographical questions. For hosting me in Berlin as I began work on this paper, I am much obliged to Jürgen Renn, Matteo Valleriani, and Dept. I at the Max-Planck-Institut für Wissenschaftsgeschichte. And I am honored to acknowledge all the librarians who valiantly aided my research during a time of global pandemic.
The early printing of Johannes de Sacrobosco’s (d. ca. 1256) Sphaera appears to follow, geographically, the emergence of printing across Europe. Thirty-six editions of the Sphaera were printed during the incunabula period, from the mid-1450s to 1500. Most of these editions appeared in cities that were the leading centers for the production of incunabula editions (Table 1). Indeed, we notice a roughly linear relationship between the number of Sacrobosco editions printed in a place and the total number of incunabula editions produced there…with several exceptions. Despite robust early printing in Lyon and Augsburg, these places produced no Sacroboscos before 1501; the first Lyon edition appeared in 1564 and no Sacroboscos ever were printed in Augsburg. Inversely, Leipzig ranks second for printing incunabula Sacrobosco editions but only fifth in total incunabula editions. This pattern of early printing raises the question for this study: how did the presence of a local university (lacking in Lyon and Augsburg, but present in Leipzig) shape the production of the earliest printed editions of Sacrobosco’s Sphaera. This elementary text, written early in the thirteenth century, emerged at the same time as the universities; it soon became a standard part of the quadrivial lectures in the arts faculties and has been preserved in hundreds of manuscript copies. Leipzig thus offers an ideal case study for exploring how university masters, early printers, and what we might call “student demand” interacted to create a local market for printed Sacroboscos.
Our analysis will proceed in three steps. We will first examine the fifteen editions printed in Leipzig and identify a set of common features that are found only in these editions, i.e., that did not circulate to editions printed elsewhere. Then, we will consider the Leipzig context in which these features emerged, including university regulations, the masters who lectured on the Sphaera, the three printing shops that issued editions, and the demand for Sphaera editions at the nearby universities in Erfurt and Wittenberg. Finally, we will analyze the three different commentaries on the Sphaera that were printed in Leipzig and authored by three local masters. And we will speculate on why, after 1521, no further editions of Sacrobosco were printed in Leipzig even as the university continued to grow during the sixteenth century, as would printing in Leipzig. We will conclude that Leipzig offered a local university market for Sphaera editions and that Leipzig’s printers successfully filled that niche until more prominent masters and printers in Wittenberg, by 1531, would take over the local market with larger and more complex compilations of material on the Sphaera.
2 The “Leipzig Sacrobosco”
Although issued by three different printers and including commentaries by three different masters, the fifteen known Sphaera editions printed in Leipzig between 1488 and ca. 1521 (Table 2) feature a unique version of the text, a unique set of woodcut illustrations, and a nearly unique format that comprise what I will call the “Leipzig Sacrobosco.” For his Sacrobosco edition, Lynn Thorndike in 1949 collated seventeen manuscripts and an unspecified group of early printed editions (the latter are noted only as “ed” in his apparatus and are not otherwise specified) (Thorndike 1949). The unique features of the Leipzig Sacroboscos do not appear in Thorndike’s edition or in any of the pre-1488 printed editions that I have examined (Sacrobosco 1478, 1480; Sacrobosco et al. 1482, 1485). Apparently, the unique Leipzig elements, created by the initial Leipzig edition of 1488, were copied conscientiously by the subsequent Leipzig editions. Leipzig printers paid little attention to the editions issued by Venetian or other early printers. The Leipzig Sacroboscos also are unique in that they generally do not add other texts (e.g., the medieval Theorica planetarum, Georg von Peurbach’s (1423–1461) Theoricae nova planetarum of 1456, Johannes Regiomontanus’s (1436–1476) Disputationes of 1470) to their editions (Valleriani 2019, 5–7). Only two Leipzig editions, presenting a commentary by Conrad Tockler (1470–1530), include a short text ascribed to Thābit ibn Qurra (826–901) but, according to historian Barbara Obrist, probably compiled in the Latin West during the thirteenth century. Entitled De recte imaginatione spere et circulorum eius diuersorum, this text emphasizes imagined rather than drawn or physical representations of the world. De recte imaginatione had quickly become part of what historian Olaf Pedersen called the “corpus astronomicum,” taught by faculties of arts in European universities.Footnote 2
The unique Leipzig text is defined by particular additions and deletions not found in earlier Sacrobosco copies. For example, in chapter three, discussing the risings and settings of signs, Sacrobosco quoted Ovid’s Ex Pontus, 1.8.28: “Quatuor autumpnos Pleias orta facit.” All the Leipzig editions insert here another phrase from Ex Pontus, 1.2.25: “Cum sumus in ponto cum frigore cumque sagittis,” expanding Ovid’s complaint about his exile.Footnote 4 Later in chapter three, as Sacrobosco explained changing lengths of the days, he wrote: “… quando sol est in signis septentrionalibus; sed econverso, quando sol est in signis australibus.” The Leipzig editions (inadvertently?) omit the second reference to the Sun, “sed est econverso quando est in signis australibus” (Thorndike 1949, 96, 103; Sacrobosco 1488, b8v, c5r). Such small variations presumably do not signal any editorial intention to revise Sacrobosco’s text; but they do suggest that the Leipzig printers worked exclusively with earlier printed Leipzig editions and did not seek to “control” their text against non-Leipzig editions as they printed new editions through 1521.
The unique set of designs for the woodcuts in the Leipzig Sacrobosco is more significant. In her extensive study of the diagrams in thirteenth- and fourteenth-century manuscript copies of the Sphaera, art historian Kathrin Müller found considerable variety in the graphical additions to the text. Her first group of manuscripts has no diagrams. A second group (including the earliest known manuscript copy from c. 1240) offers one diagram, at the only point where Sacrobosco explicitly mentions a figure, “…in presenti figuratione continetur,” depicting Aristotle’s (384–322 BCE) cosmos of nine concentric spheres for the planets, fixed stars and primum mobile (Fig. 1). Dating from the second half of the thirteenth century, a third group inserts three more diagrams (climate zones, epicycle producing stationary points and direct/retrograde motion, and eclipses). Müller’s fourth group adds another fifteen diagrams, with a Cambridge manuscript preserved at the Cambridge University Library (CUL), dated to 1276, providing the earliest copy of this material (CUL, shelfmark Li III 3). Finding the same colors and graphical designs in several late thirteenth-century copies of her fourth group, Müller concluded that an “early standardization of the diagram schema” [Gestaltung] had developed in the manuscripts (Müller 2008, 207–210).
For whatever reasons (cost, lack of knowledge of manuscripts from the fourth group, lack of technical ability to insert woodcuts into the type block?), the earliest printed editions of Sacrobosco include no woodcuts but rather offer large blank spaces in the page, affording readers a place to inscribe their own diagrams (Fig. 1, left). According to bibliographer Jürgen Hamel, woodcuts first appear in two 1478 Venice editions, printed by Franz Renner (d. 1494), who had come from Heilbronn and issued large, fine editions starting in 1471, and Adam von Rottweil (fl. 1470–1500), who had worked with Johannes Gutenberg (1397–1468) and in 1477 began printing in Venice (Hamel 2006, 114; 2014, 73–74). These two Venice editions each present three cuts (concentric spheres, climates, eclipses) of similar size and design; but the cuts differ, suggesting that each printer made his own blocks, one probably copying the other (Fig. 1, right).
As discussed by Catherine Rideau-Kikuchi in this volume, another German printer working in Venice, Erhard Ratdolt (1447–1527), would produce the first Sacrobosco edition with a pictorial apparatus approaching that found in Müller’s fourth group of manuscript witnesses. Earlier a book-binder in Augsburg, Ratdolt specialized in the printing of astronomical, mathematical and “scientific” texts with fine initials and illustrations. The technical innovations in his 1482 edition of Euclid (4th–3rd cent. BCE) and 1483 edition of the Alfonsine Tables have attracted considerable attention from book historians (Baldasso 2009) (Chap. 3). Ratdolt’s first Sacrobosco edition, printed in 1482, contains only four illustrations, featuring a new frontispiece showing an armillary sphere and designs that differ from those in the 1478 Venice editions (Sacrobosco et al. 1482). Ratdolt’s next Sacrobosco edition, printed in 1485, repeats the 1482 frontispiece but massively expands the visual material from three to twenty-four individual woodcuts (Sacrobosco et al. 1485). The three earlier images (concentric spheres, climates, eclipses) are presented in full-page width (10 × 10 cm cuts); the remaining twenty-one cuts range in size from 3.5 × 3.5 cm to 10 × 3.75 cm. Ratdolt’s twenty-four cuts differ, in content and design, from those found in Müller’s fourth group of manuscripts (I use CUL, shelf mark Li III 3 to represent the “standard” manuscript set). Obviously, Ratdolt independently designed the cuts for his 1485 edition.Footnote 5
Ratdolt’s 1485 cuts provided models for the diagrams appearing in two 1488 editions, one printed in Venice by Johann Santritter (fl. 1480–1492) (Sacrobosco et al. 1488), the other by the first Leipzig Sacrobosco printer, Martin Landsberg (Sacrobosco 1488) (Fig. 2). Isabelle Pantin has examined the latter two editions, but she did not notice their reliance on Ratdolt’s edition or the significance of the differences visible in the 1488 cuts.Footnote 6 Table 3 collates the diagrams in these three editions, based on Ratdolt’s twenty-five cuts. Ratdolt’s and Landsberg’s cuts are numbered sequentially; Sanstritter’s follow numeration provided by Pantin. Twenty-one of Ratdolt’s cuts are copied, in content, in Santritter’s edition; about half of these are nearly identical in graphical form. Twenty of Ratdolt’s cuts are copied in content but almost never in form by Landsberg. Landsberg’s designs, we suggest, often sought to expand the explanatory content of the diagrams.
We begin our investigation of Landsberg’s designs by considering the diagrams for the celestial and elemental spheres, the most commonly copied image in the manuscript traditions. Ratdolt’s and Santritter’s cut prominently feature the astrological symbols for the planets and zodiacal signs and illustrate the four elemental spheres. Landsberg’s cut is simpler, naming the planetary spheres in words and depicting neither signs nor elements. Landsberg also uses the same five-pointed mark for planets and fixed stars, depicting only the luminaries differently. In this diagram, placed early in the book, Landsberg appears to be reducing Ratdolt’s content.
Elsewhere, however, Landsberg’s cuts offer viewers more information. The next diagram in the three editions depicts the right and oblique spheres in an orthographic projection (Fig. 3). Ratdolt’s diagram includes only two lines, confusingly marked “horizon obliqua” and “horizon rectus” (terms not found in the text). Santritter created two diagrams, naming the “equator” but otherwise retaining Ratdolt’s design. Landsberg’s cut provides two views of the celestial sphere, marked with the five parallel circles, one for the latitude of zero, the other for some latitude between the equator and pole, imaging the two situations explicitly discussed by Sacrobosco. Landsberg labels the cases “spera recta” and “spera obliqua,” terms from the text. Compared with Ratdolt’s, Landsberg’s cut is less abstract and more elaborate with labels and additional lines.
A similar pattern appears in the most complex images to accompany Sacrobosco’s text, the eclipse diagrams. The manuscripts had offered separate bird’s eye views of solar and lunar eclipses, sizing the circles to show why a lunar eclipse is always visible “everywhere on earth” (actually a lunar eclipse is visible from half the earth’s surface), unlike a solar eclipse visible only along a thin slice of that surface. These diagrams also mark the Moon’s path around the Earth with two circles of similar diameter, intersecting to represent the lunar nodes and attempting to depict, we might say, the tilt of the lunar path out of the plane of the ecliptic (Fig. 4).
In his 1482 cuts, Ratdolt simplified these two images, confusingly placing the intersections of the two circles (lunar nodes?) not in line with the three bodies (Fig. 5).Footnote 8 In the 1485 edition, Ratdolt combined the two images into a single diagram, depicting the Sun twice and the Earth and Moon at roughly the same size. This cut does not label the nodes and presents visual rays from the Sun that do not illustrate the situation at eclipses; indeed, the two lines projecting from the Earth to the Moon on the right seem completely confused to this viewer. Santritter retained two separate diagrams with anthropomorphic images of the luminaries; but he did not depict the visual rays and, to my eye, did not illustrate Sacrobosco’s point about the different visibilities of solar and lunar eclipses on the Earth’s surface. Landsberg’s simpler diagrams illustrate precisely that point. Going beyond the orthographic view, Landsberg uses the “figura” of the eclipse diagram, long described in canons to medieval astronomical tables and found in manuscript eclipse computations, to show what a terrestrial observer sees as the Moon moves through the Earth’s shadow or across the Sun’s surface (right, lower images in Fig. 5). A careful viewer, however, might note that the scales for the lower eclipse diagrams do not match the scales of the upper orthographic views in Landsberg’s cuts. Unlike Ratdolt and Santritter, Landsberg did not show the lunar nodes. Nonetheless, Landsberg’s eclipse cuts add both clarity and detail to Ratdolt’s abstract, flawed design.
Landsberg also included seven cuts that are either new to, or quite independent from, diagrams found in the earlier printed or manuscript traditions. For example, to illustrate Sacrobosco’s discussion of the daily and annual movement of the Sun in chapter three, Ratdolt had designed a cut showing an orthographic view of the celestial sphere on which the Sun’s daily motion, over the course of six months, is depicted (Fig. 6). Sacrobosco had called this motion “parallels, although they are not really circles but spirals,” a description which Ratdolt’s cut (as does Santritter’s) seeks to show with looped lines extending beyond the edge of the sphere (Thorndike 1949, 101 and 133). Landsberg’s cut, entitled “Centrum octoginta paralelli” (center of eighty parallels), completely revises Ratdolt’s design. Employing stereographic projection of the planar astrolabe, Landsberg schematically depicted an astrolabe plate and rete, with the latter reduced to the off-center ecliptic divided into the zodiacal signs (Cancer and Sagittarius are labeled). Although the text speaks of 182 “circles of natural days” that are traced by the Sun’s daily motion through the sky over the six months between summer and winter solstices, the diagram displays only eleven such circles. The pole, around which these circles are centered, is also prominently labeled. The astrolabe’s horizon curve, however, is not shown; hence, Sacrobosco’s discussion of how the Sun’s annual motion gives rise to changing lengths of day and night is only implicit Landsberg’s diagram. This topic, however, is ignored in Ratdolt’s design.
Similarly, Ratdolt had illustrated Sacrobosco’s discussion of the solar theory with a diagram showing an eccentric circle for the Sun. Two leaves later, now in Peurbach’s Theoricae novae planetarum that he issued along with the Sphaera, Ratdolt illustrated Peurbach’s solar theory with another cut showing the same theorica but embodied in physical realizations of orbs that Peurbach (following Ibn al-Haytham (965–1040)) had described (Fig. 7). Interestingly, Landsberg used the Peurbach design in chapter four of his Sacrobosco edition to illustrate the solar theory; but for the lunar theory, Landsberg presented Ratdolt’s design of circles, not the Peurbachian orbs. Neither Landsberg nor any other Leipzig printer would issue an edition of Peurbach’s Theoricae novae planetarum, first printed in 1474 by Regiomontanus.
In chapter three, Sacrobosco discussed the appearance of the Sun, over the course of the year, for dwellers in various climates (or geographical latitudes) of the Earth (Fig. 8). Landsberg added a unique illustration, showing the circles on the celestial sphere (pole, equator, ecliptic, tropics, and Arctic Circle) and the zenith and horizon for six latitudes between the equator and the pole. Each of these six panels is numbered but the text nowhere refers to these numbers. Likewise, the horizon (bottom line of each panel) is not labeled, which might make it difficult for untrained eyes to understand the diagrams. Presumably, the woodcut was designed to be explained orally in a university classroom. Once again, Landsberg’s diagram is more detailed than the sparse, abstract designs found in Ratdolt’s edition.
Leipzig’s most prolific incunabula printer, Konrad Kachelofen, issued only two, nearly identical, Sacrobosco editions, both in 1489 (Sacrobosco 1489a, b). He used the same blocks in both editions and their designs consistently replicate those in Landsberg’s 1488 edition. A “Leipzig look” for Sacrobosco’s textbook had emerged already by 1489.
Landsberg’s second and third editions (with Wenzel Faber’s commentary) issued in 1494 and 1495, respectively, (Sacrobosco 1494, 1495), feature a new set of woodcuts, slightly enlarging the set of his first edition by expanding the six panels of cut 19 (Fig. 8) into three separate cuts, each with two panels, and adding one new diagram (Fig. 9). Not found in the standard manuscript images or in Ratdolt’s early editions, this latter image illustrates Sacrobosco’s very brief mention, in chapter one, of the motion of the eighth sphere backward against the sphere of the “last heaven” by “one degree in a hundred years” (Ptolemy’s (b. 100) theory of precession). Sacrobosco offered no geometrical explanation for this motion; Landsberg’s new woodcut, however, shows two small circles on the ecliptic, near the first points of Aries and Libra, a mechanical scheme usually attributed to Thābit and variously understood by medieval astronomers (Neugebauer 1962; Dobrzycki 2010). Presumably, the Leipzig lecturers had to explain this complex diagram to the students (see below) for Landsberg’s 1494 edition offers no commentary.
Landsberg’s 1494 edition also modified or added content to several of his earlier designs. First, he redesigned the frontispiece, removing the banderole (“Corpus spericum”) and the text identifying the major circles on the celestial sphere and replacing the figure of Atlas, supporting the sphere on his back, with two elegantly draped angels embracing the sphere in their outstretched arms (Fig. 10). This “Christianized” design would appear in all subsequent Leipzig frontispieces (Hamel 2006, 119). Second, Landsberg returned to Ratdolt’s design for Euclid’s and Theodosius’s (347–395) definitions of the sphere (Ratdolt 2 and 3 in Table 3). He removed the labels on the “zodiacal circle” diagram but added cartographic content to the “five zones” and the “climates” diagrams. Third, he reconfigured the “circles of natural days” (Fig. 6). Replacing the orthographic and stereographic projections, respectively, of Ratdolt’s and Landsberg’s earlier images, the revised design represents Sacrobosco’s “spirals” with a bird’s eye view of the sphere from a vantage point about halfway between the lower pole and the plane of the equator (Fig. 11; see below for Faber’s commentary on this diagram). I do not recall ever seeing such a design in medieval illustrations of the sphere!
The third Leipzig printer of Sacrobosco, Wolfgang Stöckel, issued his first edition in 1498 (Sacrobosco 1498). Its twenty-eight cuts carefully copy the designs of Landsberg’s second set and are inserted at the same places in the text.Footnote 10 Stöckel’s 1499 (Sacrobosco 1499) and 1503 (Sacrobosco 1503a) editions feature the same woodblocks.Footnote 11 Landsberg also used the same blocks for the eight editions he issued from 1495 to ca. 1521. Interestingly, for his first set of blocks, Landsberg had xylographically reproduced the text in the diagrams. However, for his second set, the text is typeset in the blocks. Abbreviations and placement of the typeset text in the diagrams vary among Landsberg’s later editions, which suggests that he had to rework the blocks from time to time. But he managed to print nine editions with the second set of blocks. Incunabula woodblocks were known to be robust. For example, printing historian Christoph Reske has calculated that the half-page blocks in the Nuremberg Chronicle survived at least ten thousand impressions, the smaller cuts more than 25,000 impressions (Reske 2009, 76). We have no evidence concerning the size of Landsberg’s Sacrobosco print runs. But even if he had printed as many as three-hundred copies per edition, the nine editions would have required his blocks to survive only 2,700 impressions.Footnote 12 Some breakage is noticeable in his later editions; but most of the blocks show little deterioration over the nine editions.
One final feature appears in the “Leipzig Sacrobosco,” namely the leading of their forms or extra space set between the lines of text so that students could add interlinear glosses. Manuscript copies of university texts had long been prepared with wide margins and line spacings to accommodate student annotation. This format, by the 1470s, was taken up by early printers north of the Alps, especially in Leipzig. Printing historian Holgar Nickel has observed that small, leaded editions (twenty leaves or fewer) of classical Latin authors were a “hallmark” of early Leipzig printing.Footnote 13 All fifteen Leipzig Sacroboscos have leaded settings for the main text and compressed settings for the surrounding commentaries when present (Fig. 12). I have not found a similar concentration of this format in other cities where Sacrobosco editions were printed, especially not in Venice. Clearly, the Leipzig printers intended their leaded Sacrobosco treatises for the local university market.Footnote 14
Hence, in text, diagrams, and mis-en-page, the “Leipzig Sacrobosco” remained quite stable over the fifteen editions. And they seem deliberately designed for the university’s arts students, reading the Sphaera under the guidance of a lecturer.Footnote 15 The most significant change in the Leipzig editions, printed between 1488 and ca. 1521, would be the addition of commentaries by Wenzel Faber in 1495 and by Conrad Tockler and Caspar Jacob in 1503. Before analyzing these textual additions, we must consider the context in which the Leipzig Sphaera were produced, a setting quite different from the other leading centers of early printing such as Venice or Paris.
3 The Alma Mater Lipsiensis as a Local Market for the Sphaera
Founded in 1409 by two-thousand German students and masters who had withdrawn from the Bohemian university in Prague, Leipzig’s university, the sixth to be chartered in the Holy Roman Empire, soon established itself among the Central European universities.Footnote 16 The earliest extant statutes, from 1436 (unchanged in the 1471 reforms), show that the new university’s curriculum and organization were quite typical for a fifteenth-century university.Footnote 17 Baccalaureate students were required to study three mathematical topics: the material sphere, arithmetic, and computus. Yet as is well known, university statutes do not always describe university practices. Not until 1502 (after another reform) do lectures on the material sphere, mathematics, arithmetic, music, and theory of the planets (theorica planetarum) regularly appear in the annual reports of Leipzig’s deans (Table 4).
Despite gaps in the faculty records, Leipzig student notebooks provide scattered evidence that lectures on the Sphaera were held in the fifteenth century.Footnote 19 In the early 1440s a student’s list of lectures he had attended to qualify for the baccalaureate examination (cedulae actuum) includes the Sphaera but no other mathematical topics. A similar document, prepared around 1451, lists Sacrobosco as well as John of Murs (1290–1351) on music and arithmetic, the Theorica planetarum, Euclid and Aristotle’s De caelo et mundo. Another list from 1464 includes the Sphaera, arithmetic, and Euclid. Virgilius Wellendorffer’s (1495–1534) lecture notes, copied in 1486, contain a richly illustrated and annotated Sacrobosco with an explicit indication that Master Wenzel Faber had, at the request of several students, decided to resume his lectures on the Sphaera. Although such documentation is sparse, we can assume that Leipzig masters in the fifteenth century had lectured, at least occasionally, on the Sphaera.
These lectures, however, were short and poorly remunerated. Scattered fifteenth-century evidence suggests that Leipzig’s arts faculty would, during a semester, read on Aristotle’s Ethics in 106 lectures, metaphysics and physics (100 lectures each), politics (86), De caelo et mundo (53), Euclid (74), and Johannes Peckham’s (1230–1292) Optics (54). Mathematical subjects received less attention: twenty-two lectures for the Sphaera, twenty for theory of the planets, seventeen for music, twelve for arithmetic. With lecture fees pegged to the number of lectures, it is not surprising that the arts faculty had difficulty convincing its masters to lecture on Sacrobosco. For most of the fifteenth century, Leipzig’s deans assigned elementary lectures by means of a lottery, forcing masters to cover the low-paid subjects like mathematics. Apparently, this practice proved unsatisfactory; in 1499 the faculty reformed its statutes, agreeing to remunerate mathematics lecturers with a fixed salary and room and board, a strategy that helped regularize lectures on these fields, as can be seen in Table 4. However, most of the masters in Table 4 lectured only once or twice on the Sphaera; they were not, it would appear, especially eager to lecture on Sacrobosco, despite the revised university statutes.Footnote 20
Who were these reluctant masters? Several would develop, at the least, local profiles in mathematics. Tockler, author of one of the Sacrobosco commentaries, we shall consider below. Simon Eyssenmann (fl. 1509–1519), who in 1518 served as dean of the arts faculty and rector of the university, authored an arithmetic textbook in 1511, a computus textbook in 1514, six annual German Practica and three Latin Judica Lipsense between 1514–1520. Although these treatises were mostly printed in Leipzig and were linked to the university, versions of his German Practica were also printed in Landshut, Nuremberg, Augsburg, and Lübeck. In 1522, Eyssenmann became Doctor of Medicine in Ingolstadt and eventually a city physician in Kaufbeuren (Swabia). Caspar Börner (1492–1547), who also had studied in Wittenberg with Martin Luther (1483–1546) and Philipp Melanchthon (1497–1560), would spend his life in Leipzig, first as a teacher in the Thomasschule and from 1539 in the arts faculty, energetically advancing its Protestant reform; collecting mathematical instruments, globes, and maps; and correcting Melanchthon’s 1538 edition of Sacrobosco’s Computus (Sacrobosco and Melanchthon 1538). Moritz Steinmetz (d. 1584) also remained in Leipzig until his death, teaching mathematics and botany in the arts faculty, publishing an arithmetic, a Greek and Latin edition of Euclid, a German Practica for 1565, and a historical survey of comets.Footnote 21 Nonetheless, not until Georg Joachim Rheticus (1514–1574) arrived in 1542 (after overseeing the printing of Nicolaus Copernicus’s (1473–1543) De revolutionibus in Nuremberg) would Leipzig’s faculty include a mathematician of wider reputation (Danielson 2006, 103–114; Burmeister 2015, 47–52).
Other Sacrobosco lecturers became known humanists or (anti) reformers. Bartholomaeus Nägele (ca. 1486–1520) was among that shadowy group of Leipzig masters who in 1515–1519 published anonymous, satirical attacks on scholastics and monks (Epistolae obscurorum virorum) that helped to pave the way for Luther’s movement. In the early 1520s, Christoph Schappeler (ca. 1472–1551) preached radical reform in Swabia and co-authored a tract that rallied support for what eventually became the Peasant’s War. Gregor Breitkopf (1472–1529), who lectured for twenty-five years in Leipzig’s theology faculty, published editions of classical authors, but remained Catholic and authored a polemic against the Anabaptists. Henning Feuerhahn (d. 1546), who spent his life in the arts faculty, published new Latin poetry and co-edited anti-Lutheran polemics with Breitkopf.
Christophorus Kanisi (d. 1554) lectured seven times on the Sphaera, as a member of the theology faculty, but did nothing further to distinguish himself. Several Sacrobosco lecturers left the university to practice medicine (Giltzheim, Aurifaber). The remaining masters left Leipzig and disappeared from the historical record (Baumgärtner, Sekler, Sibart, Christanni, Schlautiz, Richter, Lincke). Lecturers on Sacrobosco, during the first half of the sixteenth century in Leipzig, did not tend to become leading stars in the university’s firmament.
A final bit of evidence about Sacrobosco at the university comes from public lecture notices. As is well known, medieval universities had, since their origins, publicly announced official news and lectures by hanging manuscript broadsides at designated locations (“das schwarze Brett” in German areas) in their towns. With the advent of printing, masters commissioned printed broadsides to announce their lectures. Survival rates for such ephemeral materials are, of course, quite random. For Leipzig, the few surviving announcements are mostly for humanistic lectures, starting in the 1460s for manuscript broadsides, in the 1490s for printed sheets. In 1506, the faculty formalized this practice in their statutes: “Notices of lectures by any faculty that are to be presented for fees in a public hall, should be printed and posted in many public places both inside and outside the city before the semester begins.” Leipzig’s only extant announcement for a mathematical lecture is for Sacrobosco (Fig. 13). The public lecture, in the winter semester of 1506–1507, would be held at the eleventh hour in a university hall. Sacrobosco’s text was available from the Leipzig printer, Martin Landsberg, who also printed the announcement. The lecturer, Conrad Tockler, attached this printed notice to his personal copy of the 1499 Venice edition of Sacrobosco, noting below the printed text that he had offered the lectures to sixty-four auditors, despite an outbreak of plague in Leipzig (only 118 students had matriculated that semester at the university).Footnote 22
Into this market of sporadic lectures, unenthusiastic lecturers, confessional strife, and even plague, the three Leipzig printers issued fifteen editions of Sacrobosco’s Sphaera. Martin Landsberg, who printed the earliest edition in 1488, would become Leipzig’s most prolific incunabula printer (about 480 editions); after 1500, he printed another 430 editions before his death in 1523. Originally from Würzburg, Landsberg had matriculated at the Leipzig University in 1472, earned a BA in 1475, and by 1485 began issuing imprints without dates or printer marks. His earliest extant edition is a German calendar (GW M15996). In the same year, he began printing annual calendars and astrological prognostications authored by the Leipzig master, Wenzel Faber, who would become the most widely published calendar maker of the incunabula period. Landsberg quickly established himself as the leading Leipzig printer of classical texts for the university lecturers (he lived and printed directly across the street from the university buildings); he also printed many contemporary authors and after 1518 became Leipzig’s leading printer of both Reformed and anti-Reform titles (Geldner 1968–1970, Vol. 1, 245–246; Claus 1973, 108–109; Reske 2007, 515; Lehmstedt 2019, 96–105). The Sacrobosco thus represented a very small portion of Landsberg’s massive production.
The next two Leipzig editions, both dated to 1489, were printed by Landsberg’s rival, Konrad Kachelofen. As noted above, Kachelofen (who had not matriculated at a university) copied the number and design of Landsberg’s woodcuts and placed them identically within the text (but he abbreviated the text and broke the pages differently). Kachelofen printed in Leipzig from 1484 until 1517. He used more than a dozen type sets and issued a wide range of titles, including humanistic university texts, but only about half as many editions of annual almanacs and practica as did Landsberg (Geldner 1968–1970, 241–244; Reske 2007, 514–515; Lehmstedt 2019, 85–94). In 1488, Wenzel Faber, together with Landsberg, provoked a public feud with another local calendar-maker, Paulus Eck (ca. 1440–ca. 1509) and his printer Kachelofen, resulting in dueling broadsides, accusations of failed astrological predictions, and indications of a rising (Bohemian) professor publicly ridiculing a (Bavarian) student who dared to publish annual almanacs. Perhaps this public attack deterred Kachelofen from printing further mathematical titles for the university; in any case, despite his major investment of twenty-four woodcuts for his 1489 Sacroboscos, Kachelofen apparently never again printed the Sphaera.
The third Leipzig printer to issue Sacroboscos was Wolfgang Stöckel, who had earned a BA in 1490 at the university in Erfurt. In 1495, he matriculated in Leipzig, and later that year married the widow of a Leipzig printer and took over the business. Stöckel printed in Leipzig from 1495 until 1526 when, as a result of financial and political problems, he moved to Dresden where he printed until his death in 1540. In Leipzig, he issued mostly university texts until 1518 when he abruptly shifted his output to reformation tracts. In comparison with Landsberg and Kachelofen, Stöckel printed very few annual almanacs (2) and practica (18). As had Kachelofen, Stöckel copied Landsberg’s woodcuts in number and design, but issued only three Sacrobosco editions, in 1498 without commentary (Sacrobosco 1498), in 1499 with Faber’s commentary (Sacrobosco 1499), and in 1503 with a commentary by the Cistercian monk Caspar Jacob (Sacrobosco 1503a). The latter edition replaces the usual Leipzig title, Opusculum…spericum, with a title I can find in no other Sacrobosco edition: Astronomice sciencie sphericum introductorium.Footnote 23 Although university lectures on the Sphaera occurred nearly every year between 1503 and 1509 (Table 3), no further printed Leipzig editions appeared until Landsberg’s in 1509. For whatever reason, Stöckel, like Kachelhofen, abandoned the Sphaera.Footnote 24 After 1503, Landsberg would remain the sole Leipzig printer of the Sphaera.
Like printers everywhere, Leipzig’s sought to coordinate their selection of titles and print runs with their estimates of market demand. Printers who misjudged the market soon disappeared. Thus, we might speculate on how the fifteen known Leipzig editions of Sacrobosco correlated with the market.Footnote 25 Conceivably, Leipzig printers might have provided texts for not only local students but also for those in nearby Erfurt (roughly one-hundred kilometers from Leipzig) or Wittenberg (sixty kilometers distant), a new university founded in 1502. As can be seen in Fig. 14, Leipzig and Erfurt by 1450 had become relatively large universities, enrolling each year more than four-hundred new students (Fig. 14). Although Erfurt’s matriculations declined by the 1470s, Leipzig’s remained strong until 1520s when the outbreak of the Reformation and the Peasants’ Wars emptied the universities of Central Europe. Interestingly, even though Erfurt printing began in the early 1480s, no edition of Sacrobosco is known from that town; and the first Sacrobosco to be printed in Wittenberg appeared in 1531. We might guess that Leipzig editions served students in all three universities until 1531 when Wittenberg’s printers took over the market (forty-nine editions until 1629) (Chaps. 4 and 5). No Sacrobosco editions were printed in Leipzig after ca. 1521.Footnote 26
As is well known, most students at late medieval universities studied only in the arts faculty; only a small portion completed a BA or MA degree. Summing the data depicted in Fig. 14, we find that about 31,000 students matriculated at the three universities between 1488 and 1531. If we assume that ten percent of these matriculants purchased a printed Sacrobosco, the fifteen Leipzig editions would have needed an average print run of about two-hundred copies to meet this demand. More research would be required to substantiate this estimate. But it does seem plausible that the Leipzig printers could have met the need at the three universities with only fifteen editions over the forty-four years from 1488 until 1531. If fewer local students purchased Sacroboscos, we might guess that some portion of the Leipzig print runs were shipped to other university markets (e.g., Prague, Cracow, or Vienna) or were sold at Leipzig’s annual book fairs. Interestingly, according to Matteo Valleriani’s Sphaera CorpusTracer, no edition is known that was printed in Prague, only one in Vienna (1518), and three in Cracow (1506, 1513, 1522). Not all cities with universities and print shops issued Sacrobosco editions.
The local market for Leipzig’s Sacroboscos becomes more apparent when compared to the international market served by Venetian printers. A rough means to assess distribution of a printed edition is to survey surviving copies. Although sixteenth-century book databases do not yet provide reliable data on survival rates, GW does include numbers that enable comparative, if not definitive, conclusions for the fifteenth century. As can be seen in Table 5, many more Venice Sacroboscos are extant, in libraries scattered across the globe, than are Leipzig Sacroboscos (Table 5). Most of the Leipzig fewer editions are held in German, Austrian, or Polish libraries, with several in Uppsala (spoils from the Thirty Years War) and seven in London.
These details about the Leipzig arts faculty and its teaching of the quadrivium in the late fifteenth and early sixteenth centuries suggest that the Leipzig printers, in issuing fifteen Sacrobosco editions from 1488 until ca. 1521, primarily served the local market, including the nearby universities in Erfurt and Wittenberg. These editions offered the Sphaera as a stand-alone text, not combined with other elementary astronomical textbooks such as the Theorica planetarum or Sacrobosco’s Computus or with modern works by Peurbach or Regiomontanus. It appears as if Leipzig’s rather undistinguished lecturers desired low-cost imprints that offered their students Sacrobosco’s text and little more. For further clues about how the text was used by Leipzig’s masters, we turn finally to the commentaries.
4 The Leipzig Sacrobosco Commentaries
In the previous sections, we have suggested that the fifteen Leipzig Sacrobosco editions should be regarded as a local phenomenon, with Leipzig printers and masters with largely local reputations serving local students. However, might the three commentaries, printed in the Leipzig editions, have attracted wider attention and brought the Leipzig Sacrobosco into interplay with other printers and masters across Europe?
We first introduce our commentators. Wenzel Faber, from Budweis in Bohemia, would author the first Sacrobosco commentary to be published in Leipzig. He had matriculated at the university in 1475, earning a BA in 1477, an MA in 1479, and a Bachelor of Medicine in 1488. He was a member of the small Fürstenkolleg from 1483–1488, the large Fürstenkolleg from 1488 to 1508 (in these institutions, he received a regular salary); he served as rector in 1488, and as dean in 1489. The initial editions of Faber’s multi-leaved annual prognostications (Latin) or Practica (German) were printed by Leipzig’s first printer, Marcus Brandis (b. ca. 1455), from 1482–1485. But after Landsberg began printing, his shop issued essentially all of Faber’s annual Practica, prognostications and broadside almanacs, more than 60 editions between 1488 and 1515.Footnote 28 If, as noted above, Faber had “resumed” lectures on the Sphaera in 1486, it seems quite likely that he had worked with the printer of his calendars, Landsberg, to produce the first Leipzig edition of Sacrobosco in 1488.
Our second commentator, Conrad Tockler—whose writings recently have been studied by Matteo Valleriani and Nana Citron—published a wider pallet of works than Faber, yet probably was not as well known. Born in Nuremberg, another major printing center, Tockler matriculated in Leipzig in 1493. In 1495, he received the BA, in 1502, the MA. From 1502 until 1510, Tockler lectured on the quadrivium (music, Sphaera, Theorica planetarum, optics, and Euclid) nearly every semester. In 1509, he became Bachelor of Medicine, in 1512 doctor of medicine. Apparently, he spent the remainder of his life in the medical faculty, but university records do not document his lectures there.Footnote 29
Tockler worked closely with local printers to issue textbooks for Leipzig’s arts students: Marsilius Ficinus’s (1433–1499) De sole (Ficinus and Tockler 1502) with the printer Stockel; John of Murs’s Arithmeticae communis (Muris and Tockler 1503), and Tockler’s commentary thereupon as a separate imprint (Tockler 1503), both printed by Landsberg. Editions of Peter of Cracow’s (1430–1474) Computus novus (Kremer 2007), printed in 1507 and 1511 by Landsberg, include a one-page astrological text attributed to al-Battani (858–929)—De ortu quatuor triplicitatum secundum Conradum Noricum—that Tockler presumably copied from the 1483 editio princeps.Footnote 30 In 1511, Landsberg printed two short texts authored by Tockler, canons for using tables and circular diagrams (neither given in the imprints) for simple calendrical and computistic operations. Tockler wrote commentaries on other quadrivial texts, including Peurbach’s Theorica novae planetarum that remained in manuscript. Finally, Tockler, like Faber, published annual astrological calendars and almanacs for an extra-university audience (twenty editions from 1504 to 1515). Most were printed in Leipzig, but several Nuremberg printers issued editions, including several in Czech for distribution in Bohemia.Footnote 31 All of Tockler’s annual calendars are traditional for the genre. Indeed, as Valleriani and Citron have emphasized, most of Tockler’s editions are quite conventional for a late medieval lecturer on the quadrivium who was steeped in astrological medicine.
A final Leipzig Sacrobosco commentary, appearing in a single edition printed in 1503 by Stöckel, was authored by Caspar Jacob, a monk from the Cistercian monastery in Grünhain (about sixty kilometers south of Leipzig) (Sacrobosco 1503a). Shortly after the founding of Leipzig’s university, the Cistercians had established a “Bernard College” there for their monks; similar colleges had been set up at universities across Europe, from Paris (1246), to Prague (1366), Cracow (1416), Oxford (1437), Erfurt (1443), Rostock (1444), and Greifswald (1487).Footnote 32 By providing living quarters supervised by the abbot of a nearby monastery, the Bernard colleges sought to enable monks to follow the Cistercian Rule in the non-cloistered setting of the university. Despite these colleges, and despite Pope Benedict XII’s (1285–1342) bull of 1335 (Fulgens sicut stella) requiring houses of his order to send some brothers to universities, the Cistercians of the fourteenth and fifteenth centuries were not known for their embrace of academic study, especially of the arts curriculum. In Leipzig, about four-hundred Cistercians had matriculated before the closure of Bernard College in 1536, after the upheavals of the Reformation. Most of these monks attended during the years from 1480 to 1520. They heard lectures on the Bible and Peter Lombard’s (1096–1160) Sentences but rarely finished a baccalaureate; only a very few became masters in the theology faculty. In 1488, however, the Cistercian masters did receive the privilege to join the arts faculty. However, despite such activity, Caspar Jacob’s Sacrobosco commentary is the only example I have found of a Leipzig Cistercian interested in the quadrivium.Footnote 33 And it is one of the few known examples of a Cistercian monk, in the fifteenth or sixteenth centuries, authoring a non-theological university text.
Jacob dedicated his commentary to Father Peter Tumner (Tümpner), ordinary from the Cistercian Altzella house about eighty kilometers east of Leipzig and “provisor” (instructor) at the Bernard College. Although Jacob describes Tumner as a master of art and philosophy and a bachelor of theology, the latter does not appear in Leipzig’s matriculation records and I have found no traces of Tumner in standard bio-bibliographical reference works.Footnote 34 Jacob likewise does not appear in the Leipzig matriculations; indeed, he appears only once in the university records, listed in 1501 as a “determinator” (bachelor) of the Bernard College now recognized as a master by the arts faculty.Footnote 35 He does not appear among the masters who lectured on the Sphaera (Table 4 above); however, the 1503 printing of his edition with commentary suggests that he was teaching the Sphaera, perhaps privately within Bernard’s College.Footnote 36 His commentary is preserved only in the 1503 Sacrobosco edition, itself extant in a single, lightly annotated copy.
Faber’s commentary was the first to appear in Leipzig, issued by Landsberg in 1495. At several points, Faber referred to 1491 as “our time;” apparently, he wrote the commentary several years before Landsberg printed it (Sacrobosco 1495, B3v, H1v). Appropriate for the university context we described above, Faber’s commentary is very “pedagogical” in form and content. Although occasionally his remarks extend over several pages, most of Faber’s forty-seven interventions are short glosses, directly tied to a passage in Sacrobosco. Much of the commentary is a kind of reading guide, identifying larger topics in Sacrobosco’s text, numbering points made by the earlier author, and explicating some technical terms.Footnote 37 Faber’s commentary is much simpler and more straight forward than the larger, more expository commentaries of, for example, Jacques Lefèvre d’Étaples (1450–1536) of 1495 (Chap. 2) and Pedro Sánchez Ciruelo (1470–1554) of 1498 in Paris (Chap. 13), and Francesco Capuano (b. 1450) of 1499 in Venice—editions that comprise the earliest generation of printed Sacrobosco commentaries.Footnote 38
Occasionally, however, Faber did offer additional materials or “suitably correct” (bene correctum) Sacrobosco (Sacrobosco 1495, H8r). Invoking Aristotle, Physics I—one should move from the general to the specific—Faber began with a lengthy introduction, defining astronomy and defending astrology by citing a host of medieval authors, going beyond Sacrobosco’s rather sparing invocations of Ptolemy and Alfraganus (al-Farghānī) (d. 861). After Ptolemy, Faber mentioned Isidore of Seville (560–636), Albert the Great (d. 1280), Albumasar (Abu Ma’shar) (787–886), Pierre d’Ailly (1351–1420), Abraham ibn Ezra (1089–1187), Alcabitius (al-Qabisi) (d. 867), Haly Abenragel (d. 1040), and Leopold of Austria (fl. 1300). To undergird his distinction of theoretical and practical astronomy, Faber referred to Thābit, Peurbach, John Hispalensis (John of Seville) (1100–1180), Campanus of Novara (1220–1296), Almeon (al-Mamun)Footnote 39 and the Alfonsine Tables. By parading such a train of witnesses, Faber sought to elevate the status of the Sphaera in Leipzig’s arts faculty. Seven benefits result, Faber concluded, from reading Sacrobosco’s “short and easy” work: one learns about God by following the Creator’s footsteps; one better understands other books on natural philosophy, such as De caelo or the Meteorologica; one becomes acquainted with the poets discussed by Sacrobosco (Virgil (70–19 BCE), Ovid (b. 43), Lucan (39–65)); one learns to understand the Alfonsine Tables, eclipse predictions, and the motions of the planetary spheres; this prepares the mind to study other sciences; and one becomes worthy of being called a philosopher (citing Boethius (d. 524)) (Sacrobosco 1495, A2r–A4r).
Faber also enriched Sacrobosco by adding or expanding literary references. In considerable detail, he recited Greek myths on the origins of constellations such as Taurus, Sagittarius, the Pleiades, and the Corona borealis, referencing the classical sources. He summarized the astrological qualities of the twelve zodiacal signs and their triplicities. He explained the meaning of the term “pole” in the Christian liturgical chant for the Feast of the Ascension (Iam Christus ascendit polum). Citing Macrobius (370–430 BCE), he explained that the city of Syrene lies directly on the Tropic of Cancer because the Sun casts no shadows there at summer solstice. Glossing Sacrobosco’s final sentence about Dionysius the Areopagite (5th–6th cent.) and the solar eclipse during Christ’s Passion, Faber provided details about the topography of Athens, and confusingly conflated the early Christian saint and the sixth-century Neoplatonist philosopher (Corrigan and Harrington 2019). Faber’s commentary took Sacrobosco far beyond the worlds of medieval mathematics or natural philosophy.
Faber also imported some astronomical and natural philosophical content to Sacrobosco’s thin text, usually borrowing from other widely circulating late medieval textbooks. For example, at the woodcut depicting Aristotle’s cosmos of concentric spheres (Fig. 1), Faber referred to unnamed “philosophers” who disagree on the relative roles of Aristotle’s primum mobile and God in causing celestial motions. Likewise, philosophers demand uniform motions in the heavens, while astronomers “say that it is irregular, sometimes fast, sometimes slow,” arguing that regular motion on an eccentric is seen, from the earth, as irregular against the concentric ecliptic circle. Faber inserted quantitative information on the relative sizes of stars in their six magnitudes, data he could have found in the recently printed edition of Leopold of Austria’s Compilatio de astrorum scientia, a textbook composed roughly at the same time as Sacrobosco’s. Several folios later, Faber listed the planetary distances in terrestrial radii, also compiled by Leopold.Footnote 40
Faber took his readers fastidiously through Eratosthenes’ (276–194 BCE) computation of the circumference of the Earth, giving all the intermediate values, and showing how to use Sacrobosco’s rule for deriving the diameter from the circumference of a circle: subtract the twenty-second part from the circumference and divide the remainder by three (Sacrobosco 1495, C2r–C3r). After discussing Sacrobosco’s summary of the seven climates on the earth’s surface, Faber inserted a “Tabula climatum” that lists twenty-four climates, with the longest days ranging from twelve to twenty-four hours, at half-hour intervals. With its peculiar set of names for the climates and enigmatic quantitative values, the source of this table remains a mystery.Footnote 41 And at several points, Faber instructed his readers in practical astronomy. He described how to inscribe a local meridian line using a gnomon, how to measure the altitude of the pole with a quadrant or astrolabe, and how to find the length of a day with a vague reference to a globe or armillary sphere. Did he expect his Leipzig students to carry out hands-on exercises with brass instruments?Footnote 42
Only a handful of times did Faber explicitly correct or update Sacrobosco. This author, Faber explained, had followed Ptolemy and al-Battani in giving the eighth sphere a single motion (precession). Thābit had added two small circles (Fig. 9) to the ecliptic to move the eighth sphere. More recently, King Alfonso X of Castile (1221–1284) had given the eighth sphere two motions, one of “access and recess” (the small circles rotating once in seven-thousand years), the other completing its course in 49,000 years, motions that in Ptolemy’s time “had not yet been discovered” (Sacrobosco 1495, A6r–v, B3r–v, H2v–H3r). In other words, Faber here endorsed the scheme for precession plus trepidation of the Parisian Alfonsine Tables, developed in Paris around 1320 and used widely across Europe by the fifteenth century. Not surprisingly, Faber had used these tables (or the ephemerides of Regiomontanus based on those tables) for making all his annual almanacs and prognostications. Criticizing Sacrobosco’s assertion that all the planets travel in a band within six degrees of the ecliptic, Faber obtusely described Ptolemy’s geometrical models for planetary latitudes and concluded that Venus can reach a maximal latitude of 7;30°, which requires Sacrobosco’s band around the ecliptic to be widened. The value 7;30, not found in Ptolemaic latitude tables, is an erroneous value that appears in the widely copied Tables of 1322 by John of Lignères (14th cent.) and the 1483 editio princeps of the Parisian Alfonsine Tables (given as the maximal latitude for Mars, not Venus!).Footnote 43
Faber criticized Sacrobosco on the philosophical status of geometrical models for the celestial bodies, a topic not centrally addressed, however, in the commentary. Concerning the daily motion of the Sun across the sky, Sacrobosco had written:
…the Sun, moving [over the course of the year] from the first point of Capricorn through Aries to the first point of Cancer with the [daily] sweep of the firmament, describes 182 parallels, to which parallels, although they are not really circles but spirals [spire], since there is no sensible error in this, no violence is done if they are called ‘circles’ (Thorndike 1949, 133).
Most of the early printed editions, including all from Leipzig, render the term “spere” rather than “spire.”Footnote 44 Presumably unaware of the typographic problem, Faber adds a term for “spiral,” describing what we might call the continuous line visible in both Ratdolt’s 1485 and Landsberg’s 1494 diagrams (see Figs. 6 and 11):
Note about the text: when the author says “circles,” he speaks improperly, because a circle, when it is drawn, that is, proceeding from some point, the circumference is terminated at the same point from which the circumference of the same circle began. The circles in question here, however, are not terminated at the same point but are carried around in spirals [circumferuntur girative ita], so that all “circles,” improperly so-called, endure as one line, etc. Therefore, he calls them much more appropriately “spheres” [referring to the misprinted ‘spere’].Footnote 45
Faber here seems to be instructing readers how to understand the diagrams, not the three-dimensionality of the cosmos or of philosophers’ models. Later in the commentary, where Landsberg inserted a diagram for the Sun’s motion that is very similar to one in Peurbach’s Theorica novae planetarum, (Fig. 7), Faber again criticized Sacrobosco for referring only to “circles.” Peurbach, emphasizing the three dimensionality of the theorica, had famously opened his tract with the phrase “sol habet tres orbes,” a language that Faber did not accept, writing rather that “sol triplicem habet motum” (Peurbach 1474, [A1]r, Sacrobosco 1488, H2v). But Faber also commented that the Moon and planets move around the deferent, which is an “orb with a certain thickness (in se spissitudinem)” in whose “concavity” moves not a circle but a “small sphere” (sperula) called the epicycle. Faber’s language here clearly mirrors Peurbach’s. However, the equant, Faber continued, is “correctly called a circle or circumference” since it is “only an imaginary eccentric circle along which the center of the epicycle moves uniformly because it [moves] irregularly relative to the center of the deferent.”Footnote 46 Faber’s theorica were both physical and imaginary.
Finally, we note that Faber opened his remarks on the planetary theorica (chapter four) with an encomium to the Sun. All planets move irregularly with respect to the first movable (primi mobilis); hence, “the Sun is the king among the other planets because its motion determines the conditions that are necessary for the irregularities of the planets’ motion.” Faber did not specify here what “conditions” create which “irregularities,” merely noting that all the planets’ apogees process around the poles of the zodiac. He did not move to the language of heliocentrism, De revolutionibus Bk 1, 10: “…as though seated on a royal throne, the Sun governs (gubernat) the family of planets revolving around it.”Footnote 47 But his commentary did expand Sacrobosco’s rather terse description of the planetary theorica.
The second Leipzig commentary on Sacrobosco was authored by Tockler. Since this work has been recently analyzed by Matteo Valleriani and Nana Citron, I need here only note several places where Tockler’s treatment differs interestingly from Faber’s (Valleriani and Citron 2020, 120–127). First and most obviously, Tockler provided much more astrological content, both medical and otherwise, for his readers. He often referred explicitly to Ptolemy’s Liber quadripartitus and a group of practical astrological texts that had been printed together in Venice in 1493.Footnote 48 He quoted classic medieval astrological texts by Albumasar and Leopold of Austria, both of which had recently been printed by Ratdolt (Albumasar 1489; Leopold of Austria 1489). Tockler’s students would have been introduced to the latest published works on practical astrology.
Unlike Faber, Tockler introduced his students to some of the mathematical details required to compute horoscopes and planetary positions with the Parisian Alfonsine Tables (Venetian editions had been printed in 1483 and 1492). The brief, incomplete samples of astronomical tables inserted into his commentary do not allow any actual computation, but they do introduce the genre.Footnote 49 Tockler’s recomputation of Erastothenes’ determination of the radius of the Earth, however, is filled with typographical and/or computational errors and would have confused his readers or forced them to fix the numbers in the margin, as was the case in a copy now in Munich.Footnote 50 Tockler indicated that the obliquity of the ecliptic is changing (from Ptolemy’s 23; 51 to Almeon’s 23;33 and now in “our time” to 23;28), but did not inform his readers that the latter value had just appeared in the editio princeps of Regiomontanus’s Epitome (Sacrobosco et al. 1503, C6r; Regiomontanus 1496, b1r). He also nicely summarized Peurbach’s physical description of the solar theorica, quoting (unlike Faber) Peurbach’s phrase “sol habet tres orbes” but did not name the source or elaborate Peurbach’s theorica for the other planets.Footnote 51 The second edition (Sacrobosco et al. 1509) of the commentary includes a lengthy text “recently added and diligently revised” by Tockler, giving instructions for constructing a “material sphere” of wood and metal to represent the celestial bodies with ten concentric rings, a kind of armillary sphere.Footnote 52 Tockler did not, however, integrate his presentation of this material sphere with Peurbach’s physical models.
The third Leipzig commentary, prepared by, and for, Cistercian monks, offers a quite different reading, emphasizing natural philosophy and contemplation of the “eternal governor” of the world. Sacrobosco’s text becomes the site for discussion of natural causes, motion, the composition and disposition of celestial bodies, the elements, generation and corruption, the certitude of natural versus mathematical knowledge, and, as Jacob entitled his introduction, “the dignity of the science of astronomy.” Readers might guess that Jacob enjoyed access to a well-stocked library as the commentary refers to many standard texts in the university arts curriculum. At one point, he cited one of the earliest published Sphaera commentaries by Francisco Capuano di Manfredonia, printed in 1499 by Simon Bevilacqua (1450–1518) in Venice.Footnote 53 A quick check reveals that Jacob took most of his commentary, verbatim, from that Paduan master and lecturer! The Cistercian commentary thus represents a transalpine circulation of knowledge, a dependency that, to the best of my knowledge, has not previously been recognized by bibliographers or historians of Sacrobosco.
A large part of Jacob’s introduction, “De dignitate astronomice scientie,” is lifted directly from Capuano’s “Prologus.” Three-quarters of the subsequent sixty glosses are copied, in full or part, from the opening sentences of the sections into which Capuano had divided his commentary. Often Jacob added his own comments to Capuano’s. On nearly every folio, Capuano referenced the Ptolemaic textbook of thirty chapters by al-Farghānī (also frequently mentioned by Sacrobosco); he also quoted the standard university texts by Aristotle (De caelo et mundo, Physica, De motu animalium, Metaphysica, De generatione et corruptione), Averroes’s (1126–1198) commentaries on these texts, Ptolemy’s Almagest I and the Centiloquium, Albert the Great, the Theorica planetarum, and more sparingly, Euclid, Theodosius, and Haly Abenragel’s De judiciis astrorum, an astrological compendium. These works hence appear in Jacob’s commentary.
But Jacob also introduced new texts, most of which had been printed over the past two decades. Among classical authors, he cited Aristotle’s Meteorologica and Analytica posteriora, Ptolemy’s Cosmographia, Proclus’s (412–485) Sphaera, Julius Firmicus’s (4th cent.) Mathesis, Manilius’s (1st cent. BCE) Astronomica (quoted in length several times). His medieval sources include Albumasar’s Introductorium in astronomiam and Flores astrologiae, Avicenna’s Canon, the Parisian Alfonsine Tables, Campanus’s Theorica planetarum (a text that had not been printed), and Regiomontanus.Footnote 54 And in his introduction, Jacob quoted from the patristics, Augustine’s (354–430) Soliloquia and John of Damascus’s (675–749) sermons.
Recently, Michael H. Shank has argued that Capuano’s Sacrobosco commentary, with its extensive mingling of astronomical and physical themes and detailed arguments against a two-fold motion of the Earth (diurnal and annual), may have provided a foil against which Copernicus directed his heliocentric theory. Most of the provocative passages analyzed by Shank, quoting the final 1518 version of Capuano’s commentary, do not appear in the 1499 version used by Jacob. Nonetheless, Jacob followed Capuano in taking a physical approach to astronomy. He emphasized that spheres must be imagined as “solid” and “dense” (A5r). He quoted Capuano on the terrestrial elements air and water participating in circular motions not proper to them, due to the drag (raptus) of the neighboring lunar orb.Footnote 55 Going beyond Capuano, he discussed Albert the Great’s distinction, in De meteoris, between two types of elemental fire below the Moon, and quoted from Manilius’s Astronomica I, 141–170, on the places of the four elements around the Earth (Sacrobosco 1503a, B4r–B5r; Magnus 1651, 2:5; Manilius and Manilius 1977).
Unlike Capuano, Jacob mentioned several times the “tabulas Alfonsi.” In describing Alfonsine precession, Jacob suggested that one must “imagine” two motions, one of 1;28° in two-hundred years in the order of the signs (or a complete revolution in 49,000 years), the other of two “small circles” at the beginning of Aries and Libra (B1v–B2r) completing their revolution in seven-thousand years. Jacob contrasted these motions to Ptolemy’s single motion of precession (1° in one-hundred years), urging readers to choose “the recent more thorough investigation of the motion of the spheres” (Sacrobosco 1503a, B1v–B2r, B6v–C1r). In a table, he lifted from the Sacrobosco commentary by Jacques Lefèvre d’Étaples (also in the 1499 compendium), Jacob listed some of the mean motions from the Alfonsine Tables, to a precision of sexagesimal fourths.Footnote 56 He did not, however, instruct his readers on how to compute quantitative planetary positions. Instead, he followed Capuano in describing the planetary theorica. Each planet has orbs for its deferent and epicycle; however, the equant is an “imaginary circle” so that the deferent is “not moved equally and uniformly around its center” (Sacrobosco 1499, l2v–l3r; 1503a, K4v–K5r). Despite their emphasis on a physical astronomy, neither Capuano nor Jacob offered their readers a consistent language for describing the Ptolemaic planetary theorica.Footnote 57
Hence, Leipzig’s masters had prepared three rather different Sacrobosco commentaries for their students. The earliest, by Faber, offers a “humanistic” reading with its attention to classical literary works and the semantics of technical terms. Tockler’s is more “practical,” emphasizing tools for the working astronomer/astrologer, albeit jumbled together without a clear focus and not providing enough details to, say, cast or interpret a horoscope. The Cistercian Jacob silently presented an abridged summary of the massive 1499 Paduan commentary by Francesco Capuano, citing many classic university texts on the natural philosophy of the heavens and earth but also introducing the recently printed Alfonsine Tables.
The commentaries by Tockler and Jacob were never reprinted. Faber’s would appear, between 1501 and 1508, in seven editions printed in Cologne by Heinrich Quentell (d. 1501) and heirs (Sacrobosco 1500a, b, 1501, 1503b, c, 1505, 1508). Like Landsberg, Quentell printed primarily for the local university market, which may have prompted him to turn to an early university printing center like Leipzig for his material. As far as I know, Quentell and heirs were also the only printers to copy the Leipzig Sacrobosco in leading the text and reproducing the designs of all the woodcuts. Apart from this resonance in Cologne, the Leipzig Sacrobosco and its three commentaries did not circulate beyond Saxony.
Leipzig offers a case study of the early printing of Sacrobosco in a local university setting. As noted above, over the first fifty years (1472–1521) of printing the Sphaera, three cities had dominated: Venice with nineteen editions, Paris with seventeen and Leipzig with fifteen editions. Cologne follows with seven editions. Paris had a university, but its printers, like those in Venice, appear to have issued their editions for an international as well as local market. Although we have speculated that Leipzig editions may have been acquired by students in the nearby university towns of Erfurt and Wittenberg, it seems clear that the local market was the primary force shaping the production of Leipzig Sacroboscos from 1488 until ca. 1521. After that date, no further Leipzig editions would be printed; by 1531, the production of central European Sphaera editions moved north to printers in Wittenberg and to Melanchthon’s powerful influence.
For their local market, Leipzig’s printers and masters created what we have called the “Leipzig Sacrobosco,” an edition comprised of idiosyncratic elements that do not appear in editions printed elsewhere. These include a particular version of Sacrobosco’s text, a pedagogically inflected set of diagrams to accompany the text, leading of the print block so that readers could add interlinear annotations, and a reluctance to issue an edition containing works beyond the Sacrobosco. The Leipzig Sacrobosco was a slim quarto codex, apparently designed for elementary lectures on the Sphaera and little more.
We have, however, identified several examples where content from the Leipzig Sacrobosco did circulate beyond the local. Jacob structured his 1503 commentary on the more comprehensive commentary of the Paduan master, Francesco Capuano, printed in 1499 in Venice. Faber’s commentary, printed five times in Leipzig by 1521, was also issued in Cologne. And the short text by ps.-Thābit that Tockler had added to his 1503 commentary, was issued again in a 1518 edition. But beyond these incidents, the Leipzig Sacrobosco did not become enmeshed in the network of texts, paratexts, authors, printers, and publishers that would characterize the later printing history of Sacrobosco’s Sphaera stretching into the sixteenth and seventeenth centuries (Valleriani et al. 2019; Pantin 2020) (Chap. 10).
Digital repositories: Sphaera CorpusTracer; Gesamtkatalog der Wiegendrucke (henceforth GW).
(Carmody 1956, 118–119; Thorndike and Kibre 1963, col. 924; Pedersen 1978, 319; Rashed 2009; Hasse 2016, 405–406). (Carmody 1960, 118–119, 140–144) describes this text, extant in nearly 100 manuscripts, as “Arabic unknown. Definitions and instructions in elementary astronomy, facts, and terminology.” He judges Tockler’s edition to have “no value” as a source for establishing the text, which he edits. The text was printed once more, in 1518, inserted at the end of the imprint as a lone quire and not found in all copies. See (Ps. Ptolemy et al. 1518, unfoliated sheet after colophon; Hamel 2014, 95–96).
Martin Landsberg’s printer marks in column 2 were taken from (Hamel 2014, 142–143), extant copies were identified from GW and “Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des 16. Jahrhunderts” (henceforth VD16).
Ovid’s full sentence reads: Hic me pugnantem cum frigore cumque sagittis/cumque meo fato quarta fatigat hiems (Tissol 2014, 48 and 34).
Ratdolt’s cuts often reappear in his editions of other texts. See, for example, (Leopold of Austria 1489).
(Pantin 2020, 270–272): Pantin did note that Santritter made four large and significant additions of text to his edition; I shall here ignore the woodcuts Santritter created for these additions, material that he did not take from Ratdolt.
Cuts denoted by bold font are very similar in form to Ratdolt’s.
No eclipse can occur when the Moon is 90° from its nodes, as depicted in Ratdolt’s 1482 cut.
Did Leipzig students notice this fundamental error, rather ironic for a book on the Sphaera? Misplaced zodiacal signs on woodcuts of the Sphaera are not uncommon. See (Regiomontanus 1496: a3v).
The collation of the editions differs, however. Landsberg 1494 is AG6, Stöckel 1498 is AE6FG4.
Interestingly the 1499 and 1503 editions rotate the “circles of natural days” block by 180 degrees.
Estimating print runs in the early decades of printing remains extremely difficult. See (Eisermann 2017, 178).
Using GW’s definition of editions “mit Durchschuss,” I find that twenty percent of Leipzig’s 1500 incunabula editions were leaded, far more than in other major printing centers such as Venice (0.3 percent of 4,300 editions), Paris (3 percent of 3,875 editions), Cologne (3 percent of 1,750 editions), Lyon (0.8 percent of 1,600 editions) or Augsburg (0.2 percent of 1,375 editions). Some surviving copies of these leaded textbooks are filled with student annotations. Historian Jürgen Leonhardt has even found examples of several copies of the same edition filled with identical marginalia, suggesting their original owners took dictation from the same lecturer (Nickel 1989, 135; Leonhardt 2004).
For examples of classroom dictation, recorded in interlinear and marginal glosses in humanistic texts issued in leaded format by Leipzig printers, see (Bräuer et al. 2008).
Note, however, that most of the surviving copies I have examined are clean, not annotated by early owners. This may suggest that sixteenth-century bibliophiles preferred unannotated books for their collections, or that Leipzig students were less than assiduous in reading Sacrobosco.
The first wave of imperial universities included Prague (founded 1348), Cracow (1364), Vienna (1365), Heidelberg (1386), Cologne (1388), Erfurt (1392), Rostock (1419), and Leuven (1425). Leipzig did not acquire its law faculty until 1457 (Bünz 2008a, 13–15).
Given Leipzig’s tepid response to “Renaissance humanism” and the Reformation before 1542, historians have debated the extent to which continuities or disruptions characterize its history from the via antiqua of the early fifteenth century to the via moderna of later centuries. Cf. (Rothe 1961; Döring 1990; Häuser 2009–2010, Vol. 1). For a useful overview of university curricular statutes around 1400 (note that Ptolemy’s Almagest appears only once, in the Prague statutes), see (Lorenz 1985, 223).
(Erler 1895–1902: passim). I find nothing on the Sphaera in the lists of lectures for 1527 and 1528 recorded in UBL, Ms 1470, 181r–184v.
(Zarncke 1861, 455–456; Helssig 1909, 36–37, 53–61; Schmidt-Thieme 2002, 196; Bünz 2008a, 27). In 1521, the Wittenberg arts faculty had established two chairs for mathematics; not until 1542 would Leipzig, as part of its reform under Philipp Melanchthon’s influence, create similar chairs, naming Georg Joachim Rheticus as mathematice maiores and Balthasar Klein as mathematice minoris. These professors, however, apparently did not lecture on the Sphaera. See (Erler 1895–1902, Vol. 2, 669; Stübel 1879, 548; Burmeister 2015, 292).
Only one of Landsberg’s editions has a non-standard title; his 1510 edition with no commentary is entitled Textus spere materialis, echoing the title frequently announced for the university lectures (Sacrobosco 1510).
Stöckel did print several other university mathematical texts, an arithmetic in 1505 and 1507, and a computus in 1515. See VD16 A 1875, A 1878, S 2366.
I have not examined extant copies of Leipzig Sacroboscos for evidence of early ownership or provenance.
For an overview of early astronomical imprints for university lecturers, see (Zinner 1964, 44–47).
Data from (Erler 1895–1902, Vol. 1, xc–xcvii).
(Valleriani and Citron 2020): Three manuscript codices, written and collected by Tockler, are known. UBL, Ms 1605, ÖNB 5274 and ÖNB 5280 contain texts on quadrivial topics (including Peurbach’s Theorica nova planetarum), astronomical instruments, sundials, and one astrological miscellany, but nothing on medicine.
Leipzig printers Landsberg, Stöckel, and Johannes Thanner had printed editions of Peter’s text in 1487, 1499, 1504 and 1506. Clearly the Computus cracoviensis accompanied university lectures on this topic. Cf. (Nallino 1977, Vol. 1, xxviii; Thorndike and Kibre 1963, col. 1449). For bibliographies of Tockler’s printed works, see (Schmidt-Thieme 2002; Valleriani and Citron 2020, 135–136). Editio princeps of the Ficinus had appeared in Florence in 1493 (GW 9880), of the al-Battani in Venice in 1493 (GW M36394). Tockler’s edition of John of Murs’s arithmetic may be its editio princeps: see GW M2570020 (undated) and VD16 T157 (Vienna, 1515).
For the broadside Czech almanacs, printed by Hieronymus Höltzel in Nuremberg, see NLCR, Teplá 503 (fragment, for 1507); Teplá 505s (fragment, for 1510) (Boldan 2008).
Of the 370 medieval English manuscripts of Cistercian provenance, only a handful contain content related to the trivium and quadrivium (including copies of Sacrobosco’s Sphaera). See (Bell 1989, 83; Fitzpatrick 2010, 1 and 10). For the historiography of Cistercian ambivalence toward university study, see (Schneider 1999).
In 1472, a Caspar Carnificis de Grunenhayn did matriculate, whom Erler suggested may have been our Caspar Jacobi de Grunhayn (Erler 1895–1902, Vol. 1, 287 and 282, Vol. 3, 378–379).
A 1514 inventory of the Altzella library, then called a biblioteca publica, includes—in addition to scholastic texts of theology, church history, and liturgy—significant numbers of humanistic and contemporary texts. Astronomical works include De celo et mundo, astrological classics (Albumasar, Centiloquium), the Theoerica planetarum and the Alfonsine Tables, both manuscript and the 1483 editio princeps. See ThULB, MNs. App. 22 A, esp. 22r–24r; (Palmer 1998; Mackert 2008).
For example, Faber explained terms such as acute and obtuse angles, archetype, isoperimeter, cosimeter, homogeneity, diameter, pole, solstice, cosmicus, autonomastice, chronicus, chronicle, climate, and natural hours, often referring to Greek roots.
(Sacrobosco 1495, A7r, B2v; Leopold of Austria 1489, a8v). These cosmic dimensions, ultimately derived from Ptolemy’s Planetary hypotheses, circulated widely in medieval Arabic and Latin texts, albeit marred by canonical sets of scribal errors. Faber’s numbers follow exactly the peculiar values found in the 1489 editio princeps of Leopold, which makes it highly likely that our commentator used that edition (Goldstein 1967, 57; Swerdlow 1968, 130–131, 174–175; Helden 1985, 27, 34–35).
(Hadravová and Hadrava 2020, 283) indicate that Faber’s table does not match any of the more than sixty tables of places they have found in manuscripts dating from the thirteenth to the sixteenth centuries. The computation of latitudes from these day lengths are very erratically computed for an obliquity of about 23;30°. The column headed “Stadia latitutinis climatum,” displaying very irregular first differences, I do not understand.
A study of annotations in copies of editions of Faber’s commentary might shed light on this question.
Ratdolt’s 1482 edition gives “spere,” his 1485 edition corrects to “spire.” Most editions after 1500 give “spere.” Note that an autograph by the Leipzig student, Virgil Wellendörffer, copied ca. 1486, gives “spere.” UBL, Ms 1470, 420v.
“Nota circa litteram: cum dicitur circuli, autor improprie loquitur, quia circulus, cum describitur procedendo videlicet ab aliquo puncto terminatur circumferencia in ipsum punctum, a quo circumferencia circuli eiusdem est inchoata. Circuli autem, de quibus hic est ad propositum, non terminantur in idem punctum, sed circumferuntur girative ita, ut omnes circuli improprie dicti manent una linea et cetera. Ideo vocat eas speras magis proprie loquendo” (Sacrobosco 1495, F2r).
“Item alius ex circulis est equans qui proprie circulus vel circumferentia nominatur et est eccentricus circulus solum imaginatus super quo motus centri epicycli regulariter mouetur nam super centro defferentis irregulariter circumfertur” (Sacrobosco 1495, H4r).
Tockler's tables include a table of planetary periods and mean motions (B1v); of right and oblique ascensions of signs (D6v, E1v); of half-day lengths for the latitude of Leipzig (said to be 51°, but the data are for 50°, E2r); of day lengths for latitudes from the equator to the Tropic of Cancer, at intervals of 15 min (doubling the entries in Faber’s similar table! F5r–v); and a table the positions of the solar apogee from 1500 to 1556 at four-year intervals (G1v) as well as another for the planetary apogees in 1503 and 1504 (G2v), both computed from the Parisian Alfonsine Tables.
BSB, Res/2 A.lat.a. 199#Beibd. 5, D2v. The second edition of Tockler’s commentary corrects some of these errors; see (Sacrobosco et al. 1509, B6v).
(Sacrobosco et al. 1503, F6v). For Tockler’s lengthy and apparently original commentary on Peurbach, see ÖNB Ms 5274, ff. 57r–120v.
(Sacrobosco et al. 1499) includes Sacrobosco’s text with surrounding commentary by Cecco d’Ascoli, separate commentaries by Francisco Capuano (e1r–l5v or 41 leaves) and Jacques Lefèvre d’Étaples (l5v–o6r or 20 leaves), and Peurbach’s Theorica novae planetarum surrounded by Capuano’s commentary (p1r–9–3r or 62 leaves). According to (Shank 2009, 295) Capuano’s was “perhaps the longest” commentary on Sacrobosco until Christopher Clavius’s at the end of the sixteenth century.
Jacob associated no specific text with Regiomontanus, referring to his and the Alfonsine Tables’ presentation of a two-fold motion for the eighth sphere (precession plus trepidation). Perhaps Jacob meant here Peurbach’s Theorica novum planetarum, printed by Regiomontanus in 1474, which does offer a complex theorica for the two-fold motion. See (Sacrobosco 1503a, B1v). Note that, in the final version of his commentary, Capuano also linked the Alfonsine Tables and Regiomontanus to the theorica for the eighth sphere. See (Ps. Ptolemy et al. 1518, f. 25va).
(Sacrobosco 1503a, C1r; 1499, m3r). D’Étaples had listed the values to sexagesimal sevenths.
For a recent study of medieval texts on “imagination” and the sphere, see (Obrist 2018).
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Ficinus, Marsilius, and K. Tockler. 1502. Preclari oratoris et philosophi Marsili Ficini Libellus de Sole. Leipzig: Wolfgang Stöckel.
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Ps. Ptolemy, Campanus da Novara, Pierre d’Ailly, Cecco d’Ascoli, Robert Grosseteste, Theodosius of Bithynia, Michael Scot, Joannes Regiomontanus, Jacques Lefèvre d’Étaples and Francesco Capuano. 1518. Sphera cum commentis in hoc volumine contentis. videlicet. Cichi Esculani cum textu / Expositio Joannis Baptiste Capuani in eandem / Jacobi Fabri Stapulensis / Theodosij de Speris / Michaelis Scoti / Quaestiones Reverendissimi domini Petri de Aliaco etc. / Roberti Linchontensis Compendium / Tractatus de Sphera solida / Tractatus de Sphera Campani / Tractatus de computo maiori eiusdem / Disputatio Joannis de monte regio / Textus Theorice cum expositione Joannis Baptiste Capuani / Ptolemeus de Speculis. Venice: Heirs of Ottaviano Scoto I. https://hdl.handle.net/21.11103/sphaera.101057.
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Sacrobosco, Johannes de. 1489b. Iohannis de sacro busto spericum opusculum unacum utilissimis figuris textum declarantibus. Leipzig: Konrad Kachelofen. https://hdl.handle.net/21.11103/sphaera.100266.
Sacrobosco, Johannes de. 1494. Opusculum Iohannis de Sacro Busto spericum. cum figuris optimis et nouis textum in se. sine ambiguitate declarantibus. Leipzig: Martin Landsberg. https://hdl.handle.net/21.11103/sphaera.100271.
Sacrobosco, Johannes de. 1495. Opusculum Johannis de sacro busto spericum cum notabili commento atque figuris textum declarantibus utilissimis. Leipzig: Martin Landsberg. https://hdl.handle.net/21.11103/sphaera.100886.
Sacrobosco, Johannes de. 1498. Opusculum Johannis de sacro busto spericum. cum figuris optimis et novis textum in se sine ambiguitate declarantibus. Leipzig: Wolfgang Stöckel. https://hdl.handle.net/21.11103/sphaera.100887.
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Sacrobosco, Johannes de. 1500b. Opusculum Iohannis de sacro busto sphericum cum notabili commento atque figuris textum declarantibus utilissimis. Cologne: Heinrich Quentell. https://hdl.handle.net/21.11103/sphaera.100890.
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Sacrobosco, Johannes de. 1503b. Opus sphericum magistri Ioannis de Sacrobustho natione Anglici. figuris verissime exculptis et interpretatione familiari ad commoditatem desiderantium iucundissima Artis Astronomice callere principia pulcherrime et iterata recognitione illustratum. Cologne: Heinrich Quentell. https://hdl.handle.net/21.11103/sphaera.100894.
Sacrobosco, Johannes de. 1503c. Opus sphericum magistri Ioannis de Sacro busto natione angli figuris verissime exculptis et interpretatione familiari commoditatem desiderantium iucundissima Artis Astronomice callere principia pulcherrime et iterata recognitione illustratum. Cologne: Heinrich Quentell. https://hdl.handle.net/21.11103/sphaera.100024.
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Kremer, R.L. (2022). Printing Sacrobosco in Leipzig, 1488–ca. 1521: Local Markets and University Publishing. In: Valleriani, M., Ottone, A. (eds) Publishing Sacrobosco’s De sphaera in Early Modern Europe. Springer, Cham. https://doi.org/10.1007/978-3-030-86600-6_12
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