Borrowers and Innovators in the History of Printing Sacrobosco: The Case of the In-Octavo Tradition

Abstract

The Sacrobosco editions constitute a textual tradition wherein innovation owed to the interaction of two types of actors: borrowers, responsible for chains of related editions, and innovators, who wrote relatively original commentaries. This can be observed in the “in-octavo tradition,” a series of editions printed in several European towns, which began with Apianus’s 1526 Sphaera and endured until the seventeenth century. Different kinds of innovation were produced in it (concerning the layout, the illustration, and different kinds of textual additions). This successful attempt at standardization produced a kind of manual that always retained an essential part of its original features while remaining capable of evolution. This evolution was due to close cooperation between the publishers and mathematicians, and to the fact that the former, with a few exceptions, kept control over the process, and combined innovation with the artful practice of reusing borrowed material.

1 Introduction

The advent of print culture greatly facilitated the building of textual traditions. The great number of manuscripts of Johannes de Sacrobosco’s (died ca. 1256) Sphaera were copied in codices containing variable sets of texts—with or without illustrations, with or without different kinds of commentary, and with numerous variants on the original text itself. Many of these manuscripts were copied from earlier ones, so it is possible to reconstruct certain lines of transmission, but a stemma would be impossible to achieve. Confronted with “legions” of manuscripts, Lynn Thorndike contented himself with collating twenty significant manuscripts and inventorying the principal commentaries (Thorndike 1949). With the printed editions, in contrast, it is possible to make a census of all those still in existence and to study their interrelations.¹ Very few of them were completely unrelated to the others, as their authors, editors, and publishers were more or less aware of the other editions available on the market. Thus, the entire body of Sacrobosco editions, with its different branches—some of which eventually became trunks of their own²—can be studied as a textual tradition. In this frame, we can observe more precisely how innovations occurred. I thus intend to focus on the interaction between two types of actors that contributed to the transmission of the Sacrobosco tradition: borrowers, responsible for long chains of related (if not identical) editions, and innovators, who chose to write commentaries that were, up to a certain point, original, and as a consequence signed their contributions personally.

2 The Dialectic of Tradition and Innovation: The In-Octavo Editions

In the case of the Sacrobosco editions, borrowers and innovators worked together in close collaboration. This is probably linked to the fact that booksellers were, as a rule, particularly involved in the publication of the treatises of the sphere, and that they understood the art of combining innovations with well-tried materials as crucial to commercial success. These booksellers had to respond to the specific demands of the teachers of mathematics (as well as to the vaguer demands of a larger clientele), as they depended on these teachers for achieving the mathematical part of the work; but they kept much more control over the whole process than in the case of more sophisticated scientific works. In some instances (Oronce Finé (1494–1555), Peter Apian (1495–1552)), the mathematicians were also competent in book design, book printing, and even book selling, which contributed to blurring the distinction between the roles.

Quite often, the more innovative writers of commentaries tended to bury the original text under a considerable amount of new data and arguments, or even to depart from the original pattern, so that their claims for full authorship prevailed over their linkage to the tradition. That was the case with Oronce Finé (Chap. 8), Francesco Maurolico (1494–1575),³ and many others, notably the authors of oversized treatises intended as summae of cosmological knowledge rather than simple textbooks, which deeply transformed the field around 1570. These works were elaborated mostly for the use of teachers of astronomy, but they also originated from the desire to assert the mastery of Catholic mathematicians over the field of cosmology, which was then dominated by Lutherans.⁴ Erasmus Oswald Schreckenfuchs (1511–1579), who published his commentary in 1569 (Schreckenfuchs 1569),⁵ taught at the Catholic University of Freiburg im Breisgau and dedicated his work to Jacobus Curtius, Canon of the Cathedral of Constance, a patron and benefactor of the university; Christophorus Clavius (1538–1612), as is well known, published his Sphaera (first edition 1570) (Clavius 1570) to provide a summa of the orthodox cosmological doctrine for the use of Jesuit colleges.⁶

However, we can observe at least one long series of editions in which borrowing, copying, and imitating carried as much weight as innovating. This series, which I shall call the “in-octavo tradition,” began with Apianus’s 1526 edition and endured until the middle of the seventeenth century, though it dwindled down in the last decades of the sixteenth century due to the emergence of successful competing models of treatises on the Sphaera. Francesco Giuntini (1523–1590) was its last significant contributor, that is if we set aside the 1626 edition by Franco Burgersdijk (1590–1635), which revived the “in-octavo tradition” in extremis (Chap. 11). But Giuntini soon abandoned it to write two more original treatises on the Sphaera under his own name. This is a strong indicator that the tradition could not integrate highly idiosyncratic projects.

I shall describe the development of the “in-octavo tradition” both through time and space (since several printing centers in Europe were involved), and try to analyze the different kinds of innovation that were produced in it. These innovations concerned the commentary, the illustration, and the layout and editing (including the formulation of titles). It is often tough to determine whom exactly they ought to be attributed to, but the following inquest should at least improve our understanding of the type of actors involved, and of their principal aims and motives.

3 The Predecessors: The Venetian Incunabula and the Leipzig Editions

The Sphaera was probably first printed in Venice in 1472 or earlier (Sacrobosco ca. 1472a);⁷ the first dated edition appeared in Ferrara in 1472 (Sacrobosco 1472b). These first editions were without commentaries and had no printed diagrams, but some blank spaces (two in the Venice edition, three in the Ferrara edition) allowed the insertion of manuscript drawings. Other editions followed, and from 1478 onwards, some printed figures were added.⁸ The complete set of the ‘Venetian Sacrobosco diagrams’ first appeared in the revised edition printed by Johannes Santritter (before 1460–after 1498) in 1488. This Santritter 1488 edition originated a tradition. It was copied by other Venetian printers and book-sellers, notably Ottaviano Scoto (ca. 1444–ca. 1499) and Melchior Sessa (active 1505–1555).⁹

The Venetian editions, from the 1488 Santritter edition onwards, contained significant corrections to the original text and at least four important additions: a description of the armillary sphere, a preliminary treatise of geometry, an excursus on the constellations at the end of chapter II, and a large note concerning domification (the construction of the figura caelestis for the horoscopes) in chapter III. The books were small quartos,¹⁰ of which the Sphaera occupied around forty pages, followed by two other texts: Johannes Regiomontanus’s (1436–1476) Disputationes contra Cremonensia deliramenta and Georg von Peuerbach’s (1423–1461) Theoricae novae planetarum.¹¹ The long-line layout was dark and dense, and the white spaces quasi-inexistent. Some detached subtitles and, above all, numerous images helped the readers to find their way through the text. These images were small and purely descriptive (lettered geometrical diagrams were avoided). Some of them derived from a long manuscript tradition.

Indeed, a significant minority of the manuscripts of the Sphaera had been illustrated,¹² and a kind of iconographical tradition had even been established as early are the second half of the thirteenth century. The diagrams were always related to the same parts of the text, that is, mainly to the first and fourth chapters, and to a lesser extent the third chapter. Some of them had very ancient sources and had been transmitted through the manuscript traditions of late Antiquity texts, notably Calcidius’s In Timaeum (fourth cent.) and Macrobius’s In somnium Scipionis (first quarter of the fifth cent.), of which the earliest surviving manuscripts are from the ninth century.¹³

In the following list, we have underlined the diagrams for which prototypes can be traced back to the thirteenth and fourteenth centuries (or even earlier). Of course, for each type of diagram, there existed a quantity of variants. Further research on the fifteenth century manuscripts of the Sphaera would be necessary to identify the sources of the diagrams in the first illustrated editions of the Sphaera. This list is the brief census of the diagrams that illustrated the text of Sacrobosco in the Venetian incunabula, from the Santritter 1488 edition onwards (Table 9.1).

Table 9.1 The diagrams in the Venetian editions from 1488. (NB: The diagrams that had ancient models are underlined)

Fig. 9.1

Quod Terra sit rotunda (Table 9.1, n 9). From (Sacrobosco 1488). Deutsches Museum, München/Public Domain Mark

Even before the turn of the century, other types of treatises on the Sphaera appeared in which Sacrobosco’s text was accompanied by commentaries, sometimes collected in massive in-folio volumes (Sacrobosco 1495b, 1498, 1499a, b). Other diagrams were conceived for these publications, often more purely geometrical than in the series above described, and new elements were added, notably samples of astronomical tables. At the same time, however, the idea of providing the students with handy textbooks was carried forward. This intention was most apparent in a series of tracts printed in Leipzig starting in 1486 (Sacrobosco 1486, ca. 1487, [1489], and so on). The volumes were small quartos, and they contained no other text than the Sphaera, except for some of these editions which included a commentary by Wenceslaus Faber from Budweis (died in 1518) (Sacrobosco [ca. 1495a], 1499a, b, 1500, 1501a, b, 1503a, 1505, 1508). The Sphaera commented by Conrad Tockler (1470–1530) (Chap. 5) was published by the same printer in Leipzig, in the same format and with the same figures (Sacrobosco 1503b, 1509).

The layout of the Leipzig quartos was quite different from that of the Venetian incunabula. Large interlinear spacing facilitated note-taking. The text was divided by pilcrows, but there were no detached subtitles (other than the titles of see Chapter II, III and IV of Tractatus de Sphaera by Sacrobosco). The diagrams (which were revised and augmented around 1494) illustrated almost the same topics as those of the Venetian editions, but they were different in style; they were often best suited to give the reader a simple but concrete understanding of the basic cosmological phenomena. For instance, the revised iconography provided what is probably the first attempt, in any version of the Sphaera, to include a map in the diagram of the terrestrial zones (Asia, Africa, and Europa are crudely delineated in the northern habitable zone). Besides, some diagrams had no counterparts in the Venetian editions, like a series of seven diagrams in the third chapter that showed the variation of the horizon (and its consequences) for people living at different latitudes (Fig. 9.3) (Table 9.5).

4 The Founder of the Tradition: Petrus Apianus (1526)

The new orientation towards pedagogical clarity, cosmographical realism, and interest in a more practical understanding of astronomy was accentuated in the edition printed by Petrus Apianus in Ingolstadt in 1526 (Sacrobosco 1526), which founded the in-octavo tradition. Apianus was then still at the beginning of his career. He had recently moved to Ingolstadt from Landshut where he had already published at least one world map, astrological practica, a book on a new kind of sundial (Apianus 1524a), and what was to become (after its revision by Gemma Frisius (1508–1555)) a best-seller, the Cosmographicus liber (1524), a manual based on Ptolemy’s (second century) geographical knowledge that also contained abundant up-to-date information about land surveying, map projections, instrument making, and navigation (Apianus 1524b).¹⁴ Moreover, Apianus’s bias towards practicality showed itself in the way the book was printed: it was lavishly illustrated and contained volvelles (wheel charts) (Vanden Broecke 2000, 130–50). This kind of paper instrument, already used in the Middle Ages, had been introduced in printed books by Regiomontanus, followed by other mathematicians, instrument makers, and designers of astronomical books like Lazarus Behaim and Johann Stoeffler (1452–1531) (Regiomontanus (1472–1474?); Stoeffler 1514; Gingerich 1993, 63–74; Bennett 1998, 195–222; Rhodes and Sawday 2001; Kremer 2011; Schmidt 2011; Stijnman and Upper 2014).

This background must be kept in mind to better understand the new orientation around practicality given to the Sacrobosco printed tradition by Apianus’s edition, which at first sight is a much less innovative book than the Cosmographicus liber. Indeed, Apianus refers to this earlier work in the Ad lectorem of his 1526 Sphaera. He adds that this new edition of the Sphaera has been conceived “because of the numerous correspondences that exist between geography and astronomy.”¹⁵ Indeed, if young students acquired a precise knowledge of the sphere and its circles via Sacrobosco, they would understand thoroughly the measures of Earth and heaven.¹⁶

The Apianus edition contained only the text of the Sphaera, slightly revised, without additions, notes, or commentary, and exhibited thorough editorial work. The layout was airier, using some paragraphs with first-line indents and blank interlinear spaces at the end of the chapters and of the sections in chapters. These chapters and sections had titles and subtitles printed in capital letters, and their set, more complete than in the Venetian incunabula (Table 9.2), better helped the reader in moving through the succession of topics in the text, and in grasping the logical organization of the treatise.

Table 9.2 Titles and subtitles in the Venetian editions from 1488 and in the edition of Apianus (1526)

However, the main improvement lay in the illustration. The diagrams of the Apianus edition bore an evident link of continuity to those of its Venetian and Leipzig predecessors in that they concerned the same topics, but they had all been redrawn. Several of these new diagrams were inspired by diagrams already present in the Venetian (Fig. 9.2) as well as the Leipzig editions (Table 9.5), but Apianus had found new visual solutions whenever the models at his disposal lacked clarity or relevance, or when they perpetuated out-of-date representations. An improved mastery of three-dimensional images provided better readability.

Fig. 9.2

Quod Terra sit rotunda. From (Sacrobosco 1526, A6r). State Library Regensburg--999/Philos.1325, urn:nbn:de:bvb:12-bsb11110162-1

For instance, his figure of the elementary and celestial spheres (Table 9.1, No. 3) showed ten celestial spheres (instead of nine) according to the standard opinion of the astronomers at the beginning of the sixteenth century: it corresponded to the model adopted in the Alphonsine Tables and explained in Peuerbach’s Theoricae novae planetarum (of which Apianus was to publish an edition in 1528). Thus, in Apianus’s edition, the figure was more up to date than the text, which remained true to the original version and listed only nine celestial spheres.¹⁷ Furthermore, in this diagram, like in that of the four elements (Table 9.1, No. 5), the sphere of earth was no longer included into the sphere of water, for earth and water formed one single sphere, according to the new representation of the terraqueous globe.¹⁸ Such a representation was then still quite rare among Sphaera editions, for the printers reused the same woodcuts from edition to edition. It had first appeared in the edition supervised by Oronce Finé and printed in Paris by Vincent Quignon (active 1514–1557) for Regnault Chaudière (active 1509–1554) in 1516.¹⁹

More generally, the images were better distributed throughout all parts of the text (Table 9.5), and Apianus managed to replace diagrams that were not intelligible without the aid of the text with figures that made sense by themselves. To begin with, instead of the ambiguous diagram showing “The revolution of heaven” (Table 9.1, No. 6), there appeared the image of a celestial globe, the horizon of which separated the diurnal from the nocturnal sky (Sacrobosco 1526, A4v).

Indeed, Apianus created a coherent visual language with which his reader could become familiar, as the diagrams often constituted series. For instance, in chapter III, the figure of the “circles of natural days” (Table 9.1, No. 21) is followed by a series of eight diagrams that show what happens to the respective length of night and day (and to related phenomena) around the year under different latitudes (that is, different horizons).²⁰

Fig. 9.3

Opusculum spericum cum figuris optimis et novis. When the zenith is between the Equator and the Tropic of Cancer (first diagram), and on the Tropic of Cancer (second diagram). From (Sacrobosco 1494). Courtesy of the John Carter Brown Library

Fig. 9.4

When the zenith is on the Arctic Circle (first diagram), and between the Arctic Circle and the North Pole (second diagram). From (Sacrobosco. 1526, D1r). State Library Regensburg--999/Philos.1325, urn:nbn:de:bvb:12-bsb11110162-1

Fig. 9.5

De divisione climatum. From (Sacrobosco 1526, D2v). State Library Regensburg--999/Philos.1325, urn:nbn:de:bvb:12-bsb11110162-1

Fig. 9.6

De divisione climatum. From (Sacrobosco 1538, F4r). Bavarian State Library Munich—Astr.u. 154, urn:nbn:de:bvb:12-bsb00020992-1

Fig. 9.7

Unmounted volvelle. From (Sacrobosco 1538, B8r). Bavarian State Library Munich—Astr.u. 154, urn:nbn:de:bvb:12-bsb00020992-1

Fig. 9.8

Mounted volvelle. From (Sacrobosco 1543b, B8r). Staats- und Stadtbibliothek Augsburg—Math 745, urn:nbn:de:bvb:12-bsb11267683-6

The figure of the “circles of natural days” (Apianus 1526, C1r), which inaugurates the series, shows the sphere of the sun, a small Earth at its center, the oblique track of the ecliptic, and the tight quasi-parallel (in fact spiral) circles that symbolize the path of the sun, day after day, as it follows the diurnal revolution of the heavens while progressing along the ecliptic of its own proper motion.

The next diagram (Apianus 1526, C1r) shows that in the “right sphere,” that is at the equator, the horizon passes through the poles of the world and always divides the “circles of the days” into equal parts, so that nights are equal to days, whatever the position of the sun. The ecliptic and the earth are no longer visible, but we recognize the sphere and the band of solar spiral circles (“circles of the days”). These circles, drawn like lines, are vertically positioned, perpendicular to the line of the horizon (dividing night and day). Three of them are more heavily marked: the middle one (the path of the sun at the equinox that corresponds to the axis of the horizon) and those at both extremities (the solar path at the summer and winter solstices). At the right and left extremities of the horizon line, small stars symbolize the north and south poles: the plan of the horizon coincides with that of the axis of the world. The band of the “circles of the days” is divided by twelve lines (portions of meridians), parallel to the horizon and equally spaced. They are numbered and symbolize the perfect equality of all diurnal and nocturnal hours, whatever the season, in the right sphere (sphaera recta).

In the seven next diagrams, the basic elements are the same, but the respective positions of the horizon (with its axis), the axis of the world, and the “circles of the days” vary, as the text describes what happens to people “whose zenith is” at different latitudes (Fig. 9.4). Thanks to the consistency of the visual language, the principle of the variation of the duration of day and night (and of the direction and length of shadows) is easier to grasp. Apianus’s effort towards transforming the traditional Sphaera into a modern manual capable of transmitting useful and applicable cosmological knowledge ended there, but this effort was to be pursued by followers and imitators.

5 The Model Perfected: The Wittenberg Editions

Apianus’s Sphaera was never exactly copied, but the model it provided was soon imitated and improved. The University of Wittenberg, founded in 1502, was then at a critical juncture in its reformation process. The disorders provoked by radical reformers like Thomas Müntzer (ca. 1489–1525) and the Zwickau Prophets, notably the 1525 Peasant War, had convinced Martin Luther (1483–1546) and Philipp Melanchthon (1497–1560) of the necessity of founding a strong educational system in order to spread the teaching of moral philosophy, physics, the arts of language, and mathematical disciplines (Kusukawa 1995). The elaboration of new programs at Wittenberg and the publication of manuals, meant to be circulated in Germany and even throughout Europe, were the focus of this scheme.²¹

The publication of a new edition of the Sphaera took place in a still more particular context. Melanchthon, who was the professor of Greek at Wittenberg, was a strong advocate of mathematics. He thought it provided key knowledge for reading ancient texts, history, and geography. He furthermore grew more and more convinced that the attentive study of celestial signs was a Christian duty, as it helped to pursue a better understanding of God’s providential governance. He expressed this conviction in a well-argued apology of astronomy and astrology addressed to Simon Grynaeus (1493–1541) and appended as a preface to the new edition of Sacrobosco prepared for the beginning of the 1531–1532 academic year (Sacrobosco 1531).²² This letter to Grynaeus was written in August 1531 while Melanchthon was observing the return of Halley’s comet, which made a deep impression on him (Kusukawa 1995, 124–34).

This momentous preface was instrumental in the success of the book,²³ whose other attractive features were borrowed from the Apianus edition. The Wittenberg editor imitated Apianus’s airy layout, his clear subtitles, and his use of paragraphs. He even added several new paragraphs and introduced many interlinear blank spaces.²⁴ He suppressed a few diagrams²⁵ and copied the rest of them, either closely (in almost all cases) or more freely, to improve their clarity.²⁶ In only one case, he followed another model.²⁷

But the important thing was that the Wittenberg edition set a dynamic process in motion. The printers of the Sphaera had always worked for the universities that provided their first market. But in this case, the association and the cooperation were still closer. The regular reprinting of the Wittenberg Sphaera over decades shows that the printers had a monopoly on the production of textbooks for the University of Wittenberg and for other Lutheran universities, and that they were supposed to adapt this production to any change in the syllabus, with the aid and under the supervision of the professors. That was probably a good business model, and the large quantity of books produced year after year allowed the ‘Wittenberg Sacrobosco’ to be widely known and influential, even outside Germany: already in 1532, the Venetian bookseller Melchior Sessa copied the Wittenberg edition instead of reproducing one of the versions of the Sphaera that had been regularly printed in Venice since 1472 (Sacrobosco 1532).²⁸ Moreover, the low commercial risk and the easy access to teachers of mathematics created the favorable conditions for a smooth evolution. Moderate additions were progressively introduced, and two significant revisions took place before 1545.

In the 1531 edition, the additions were limited to four mnemonic Latin verses on the cosmic, acronychal, and heliacal risings and settings (Mane vehit supra terram tibi cosmicus ortus…), and to an extract of Regiomontanus’s Epitome (III, 21) on “the double cause of the inequality of natural days” (Dies naturales duplici causa inaequales esse) (Sacrobosco 1531, F2r–F3r). The 1534 and 1536 Wittenberg editions (Sacrobosco 1534a, 1536) followed the 1531 edition line to line, but the next edition, in 1538, was carefully revised, with important changes in the layout and the subtitles, the addition of several notes,²⁹ and even some corrections to the text. Furthermore, at the end of the book, an extract from Alfraganus (Sacrobosco 1538, G6v–G8r)³⁰ followed the one from Regiomontanus. However, the more obvious additions concerned the diagrams, notably with the introduction of four volvelles.³¹ This imitation of the device used in Apianus’s 1524 Cosmographia signaled the moderate but significant tendency towards practicality (at least as far as pedagogical methods were concerned) that was to characterize the Wittenberg treatises on the Sphaera. The volvelles were all the more useful as pedagogical tools in that their movable parts, printed on a folded sheet at the end of the volume, had to be cut out and assembled by the reader. Besides, they were true paper instruments, meant to complement certain demonstrations or to show some of the elementary procedures of astronomical calculation. For instance, the second volvelle bears this caption:

Instrument by which the roundness of Earth according to latitude [that is, from south to north] is proven, and by which all that the author says in the third chapter about the natural days is very easily understood.³²

The underlying diagram (Fig. 9.7) shows a graduated circle (a meridian), the axis of the world, the southern star Canopus, “Helice” (that is Ursa Major), and the quasi-parallel circles (more exactly, spiral) that describe the daily motion of the sun as it progresses along the zodiac, from one tropic to the other. These circles are divided into equal portions by twelve numbered arcs (which are portions of meridians). The lines of the climes above the arctic circle are also drawn. The movable part of the volvelle is a half-disk, bearing the words “HORIZON” and “NULLA DIES SINE LINEA” (“Not a day without writing a line”), a proverb taken from Pliny (23–79) (Natural history, XXXV, 84), which is an admonition against laziness. This half-disk is meant to recover the part of the hemisphere under the horizon; a kind of paper alidade, showing the zenith, is attached to it (Fig. 9.8).

The next edition, in 1540, strictly followed the 1538 edition, with only one (probably accidental) change: the letter of Melanchthon was dated August 1540 (Sacrobosco 1540, A8v).³³ Then, in 1543, a new revision occurred leading to significant additions: in Chapter III of Tractatus de Sphaera by Sacrobosco, an “Annotatio” on the three causes of the inequalities of natural days (with a new diagram) (Sacrobosco 1543b, E2r), two more marginal notes on the climes (Sacrobosco 1543b, F4v, F5r), and a “Table of the maximal lengths of the natural days in every latitude between the arctic circle and the pole.”³⁴ Aside from this, the extract from Alfraganus at the end of the book was replaced by a brief treatise on the “Poetical risings of the stars” (De ortu poetico), which provided all the information needed to inventory and to interpret the astronomical passages in classical texts. The De ortu poetico was accompanied by two astronomical tables printed on two folded sheets (Sacrobosco 1543b, G3v–I7v).³⁵

Thus, thanks to the Wittenberg editions, the series of small treatises that derived from the edition of Apianus fully became a tradition: the transmission of the model, always clearly recognizable, was kept alive by its ability to evolve, unjeopardized by changes and additions.

6 The Development of the In-Octavo Tradition

The success of the Wittenberg Sphaera launched a long-lasting movement. During the rest of the century, about seventy editions following the same model, more or less improved and with different sets of additions, were printed in several European towns. It will be clearest to present the progress and ramification of this tradition in tabular form (Table 9.3).

Table 9.3 The in-octavo tradition 1526–1601^a

In the first column, the editions that were used as models are listed, for they introduced major innovations that were adopted by later editions. Each of these editions is identified by the initial letter of the town where it was printed, followed by a number. For instance, “W3” (for “Wittenberg 3”) means the third model of edition (with a particular set of texts and of diagrams) that was published in Wittenberg. The relationship between this model and its predecessors is briefly indicated in underlined notes. If the model-edition in question was reproduced in the same town without significant changes, the dates of the editions are given below (and the names of the booksellers if they were different from the editors of the preceding editions).

In the second column, the editions that copied a model are described according to the same principles. They are placed in front of the model they copied, and the variants they could introduce are briefly indicated in underlined notes. The editions that showed significant variants but were not copied, or that transmitted limited variants but not a whole model (notably Paris 2–5 and Cologne 2), are in this second column.

In the third column, publications are mentioned that were linked to the Sacrobosco editions, but were outside the “in-octavo tradition” proper.

This tabular presentation shows that the development of the tradition was not chronologically linear. For instance, the tracts published in Venice by the Sessa firm until 1601 (V1 and V2) reproduced (with nonessential variants) a model conceived in Wittenberg in 1531 (W1); whereas in the same town, the Scoto firm published, from 1569 to 1586, a Sphaera (V3) that followed a 1556 Parisian model (P6).

It also shows that the rhythm of the innovations was rather rapid up to 1556, at which point it slowed down, and that the initiative of the innovations passed from town to town.

Thirdly, the analysis of these progressively introduced changes suggests that it would be quite misleading to make a sharp distinction between innovations and borrowed material: in the in-octavo tradition, the innovation process was largely a braiding process in which old and new materials, either produced inside the tradition or borrowed from outside, were closely interlocked. All these indications will be examined further, as they bring us back to the initial question: what kinds of actors were mostly responsible for the changes?

7 Publishers Versus Mathematicians

My point is that the evolution of the in-octavo tradition was the result of close cooperation between the publishers and the mathematicians, but also that the former, with a few exceptions, kept control over the process, which accounts for the longevity of this tradition.

7.1 The Shift from Town to Town

As we have seen, in the in-octavo tradition, the power to innovate passed from town to town. Almost each time, the existence of close cooperation between mathematicians and publishers figures as an important factor. At first (between 1531 and 1543), the most creative publishers were in Wittenberg; afterward in Paris. Between 1564 and 1582, the main feature of the editorial landscape was a kind of rivalry between Lyons and Antwerp, while Cologne also entered the game.

In the cases of Wittenberg and Paris, the main causes of the shifts are apparent. Apianus, the founder of the tradition, was simultaneously a printer and a mathematician, but he did not work in association with a university, and his interest in astronomical textbooks (the Sphaera in 1526 and Peuerbach’s Theoricae novae in 1528) soon dwindled, as he embarked on a career at the imperial court. Then, around 1530, the reform of the university of Wittenberg experienced a significant turning point, as we have seen. Melanchthon supervised an editorial program that produced several innovative textbooks, notably in astronomy, written or edited by the professors and printed at the university print shop. The Wittenberg innovations, which did so much to give the in-octavo tradition its identity, were thus an exception in that their principal initiator was neither a mathematician nor a bookseller, but the reformer of the university syllabuses. However, when his efforts in this field had borne fruit, Melanchthon turned his attention to other priorities, such as the reform of the teaching of philosophy (the first version of his Initia doctrinae physicae was to appear in 1549). Moreover, the Wittenberg mathematicians, notably Kaspar Peucer (1525–1602), went on to publish alternative models of astronomical textbooks (Peucer 1550), and the publication of successive editions of the Sphaera, which remained in use, became simple routine work.

Paris had become one of the main centers of the European book trade during the first decades of the sixteenth century. It had benefited from the importance of its university and from the decline of Venice, which had been the center of the book world in the fifteenth century, but was now handicapped by a succession of political and economic crises. Major proponents of mathematical humanism were then teaching in Paris, notably Jacques Lefèvre d’Étaples (ca. 1450–1536) (Chap. 2) and his disciples, and in the next generation Oronce Finé (Chap. 8). These scholars were convinced of the necessity of spreading their ideas through the publication of innovative books, and could rely on their relationship with different interconnected milieus to do so: the Art Faculty and the Parisian colleges, the humanists engaged in pedagogical reform, the courtly circles that supported the foundation of the Collège royal, and prestigious printers able to assert themselves in the European market, namely Henri I Estienne (active 1502–1520) and Simon de Colines (active 1520–1546). Then, towards the end of the 1540s, less distinguished booksellers decided to widen the range of mathematical books offered on the market in order to attract new customers: Jean Loys, Guillaume Richard, and above all Guillaume Cavellat.³⁶ Their first targets were students, and they eagerly copied the pocket-sized textbook published in Wittenberg. They could furthermore count upon the cooperation of teachers who were willing to revise the annotation while preparing their own lectures: from 1545 to 1556, five editions of the Sphaera (P2 to P6) were published in Paris with significant additions and changes.

The move to Lyons (Ly1) was short-lived and probably mainly due to the initiative of the astrologer Francesco Giuntini, who wished, as we shall see, to affirm his mastery of all astronomical knowledge, starting with the Sphaera. At first, the in-octavo tradition probably appealed to him as an easy way to enter the field. But he abandoned it as soon as he saw that it offered too narrow a framework and did not permit him to expand his ambitions.

Antwerp was a “commercial megapolis” (Pettegree 2010, 250), and each time a kind of book proved successful, Antwerp booksellers often tried to enter its market. Until 1561, Jean Richard had on several occasions published two variants of the Wittenberg editions (A1 and A2). In 1566, in association with the heirs of Arnold I Birckmann (died 1542), he published, with some suppressions, a copy of Ly1 (A3). Then, in 1573, another Antwerp bookseller, Jean Bellere (1526–1595), issued a new edition (A4) that combined A3 and the Paris 1556 edition (P6). Finally, in 1582 (A5), the same Bellere still added Albertus Hero’s (1549–1589) notes that had been printed in Cologne the preceding year (C2). This practice of combining borrowed material, which needed little mathematical expertise, can barely be called innovation. In any case, these attempts were not successful, as the in-octavo tradition was already declining.

The Cholinus firm in Cologne resorted to similar practices: it first followed a Parisian model (C1); then it freshened it up by adding some modest scholia written by Albertus Hero (C2). The masterpiece was achieved by Goswin Cholinus (active 1588–1610) in 1601 (C3): he published a new version of the Sphaera emendata that looked like a patchwork of diverse material, for an anonymous mathematician³⁷ had added to Elie Vinet’s (1509–1587) and Hero’s scholia several extracts from Clavius’s commentary, some new notes (under the heading “Commentarius”), and even one scholium of Giuntini, one extract from Peuerbach’s Theoricae, and two new (but not original) diagrams.

7.2 Editorial Policies and Clustered Publications

For printers and booksellers, the publication of the Sphaera was as a rule part of a larger editorial program that included printing several mathematical and cosmological textbooks. Thus, as we have seen, Peter Apian began by editing a Cosmographicus liber in 1524, even before he settled as a printer in Ingolstadt. In 1529, he published a modified version of the Cosmographiae introductio of Mathias Ringmann (1482–1511) and Joannes Waldseemüller (ca. 1470–ca. 1521) (Ringmann and Waldseemüller 1529). He published the Sphaera in 1526, then Peuerbach’s Theoricae novae planetarum in 1528, according to the same editorial principles (Peuerbach 1528). The printers of the university of Wittenberg imitated first Apianus’s Sphaera (1531), then Apianus’s Theoricae novae (1535); both editions were copied by Melchior Sessa the elder in Venice, in 1532 (the Sphaera) and 1534 (the Theoricae).

In 1538, the Wittenberg editors adopted the coupling of the Sphaera and Sacrobosco’s De anni ratione, alias Computus ecclesiasticus, which was largely imitated by printers outside Germany, either in one volume or two separate editions. Other works, partly complementary to the Sphaera, partly redundant with it, were published in parallel by the same firms, such as Hartmann Beyer’s (1516–1577) Quaestiones novae in sphaeram, an adaption of the Sphaera, first printed in Frankfurt (1549), then reproduced in Wittenberg (1550) and in Paris (1551) (Beyer 1549, 1550, 1551). From around 1550 on, as we have seen, the Wittenberg publishers continued to print regularly the 1543 model of the Sphaera, but they minimized the impact of obsolescence by printing, in parallel, the works of the actual professors in mathematics, Kaspar Peucer and Sebastianus Theodoricus (Sebastian Dietrich) (died in 1574) (Theodoricus 1563, 1564).³⁸

The Parisian bookseller Guillaume Cavellat, active from 1549 to 1575, had in his catalogue a remarkable set of mathematical and astronomical textbooks (Pantin and Renouard 1986; Pantin 1988). He seems to have been keen to find new titles in this field. He was also responsible for important changes in the Sacrobosco in-octavo tradition, notably the adjunction of Pierio Valeriano’s (1477–1558) Compendium in Sphaeram. Numerous similar examples—too many to enumerate—show that the publication of the Sphaera has to be evaluated in the context of booksellers’s editorial policies.

7.3 Anonymity Versus Signature

Until the first publications of Elie Vinet’s Scholia (Paris, 1551, P5), the changes and additions to the text and the illustration were always anonymous, with the noticeable exception of Apianus’s founding work. For instance, there were some scholia in W2 and W3, and P1, P2, P3, and P4 added new ones, but their authors did not sign their names.

The case of the Wittenberg editions is interesting. They were published under the authority of Melanchthon, who wrote the preface, but certainly did not supervise the editorial work. For W2 (1538) and W3 (1543), this work may probably—at least partially—be ascribed to Georg Joachim Rheticus (1514–1574), then titular of the chair of lesser mathematics in Wittenberg, before and after his momentous stay with Nicolaus Copernicus (1473–1543) in Frombork.³⁹ In any case, Melanchthon remained the inspiration for the evolution of the Wittenberg treatises on the Sphaera. The addition, in W3, of the small anonymous treatise De ortu poetico, which gives technical explanations on heliacal, acronycal, and cosmical risings and settings followed by a number of poetical quotations with commentary, corresponded exactly to Melanchthon’s conception of what ought to be the lectio poetarum (Ben-Tov 2009). Thus, in Wittenberg, the anonymity of the editors and commentators responded to a conscious policy: all publications displayed the pedagogical views of the university, under the authority of Melanchthon. However, the adaptions later published in Wittenberg by Kaspar Peucer and Sebastianus Theodoricus (Sebastian Dietrich) bore the name of their authors.

Indeed, in the second part of the century there came a change. As a probable result of a more competitive situation, the publishers now obviously recognized that signatures added value to their editions. A signature, often strengthened by a dedication,⁴⁰ highlighted the novelty of an edition and could warrant the request for a privilege. In March 1550, Guillaume Cavellat obtained a royal privilege for the printing of the Sphaera, which expired in March 1555. In France, as a rule, it was impossible to obtain a second privilege for the same work without demonstrating that the edition had been significantly improved, as the criterion of newness had been, since the origins of the system, essential in the granting of privileges (Armstrong 1990, 92–99).⁴¹ Cavellat successfully applied for a privilege for the Sphaera Joan. De Sacro Bosco emendata cum scholiis Eliae Vineti.⁴² The heirs of Giacomo Giunta (1487–1546) in Lyons also obtained a royal privilege for the treatise of the sphere “corrigé et augmenté par maistre François Junctini professeur en Mathematique.”⁴³

When no author was available, a bookseller could write the dedication himself and obtain a privilege. That was the case with Jan Waen (active 1545–ca. 1565), who dedicated to Hieronymus Ruffaut (died 1563), abbot of Saint-Vaast in Arras, a reprint of W2 (and A1), but without Melanchthon’s preface, under an imperial privilege (A2 & L1, 1547).⁴⁴ Thus, the decision for signature or for anonymity responded to editorial policies and commercial strategies. It was for the bookseller to decide which signatures were worth displaying. On the title page of the Cologne 1601 edition (C3), there is only one new name (in addition to those of Sacrobosco, Vinet, Hero,⁴⁵ Pierio Valeriano, and Pedro Nunez): that of Clavius. The Cholinus were the printers of the Jesuits in Cologne and used their emblem as their mark. The names of Giuntini and Peuerbach appear inside the volume, but not that of the author of the new “commentarii,” who probably also supervised the organization of the new textual patchwork—unless we identify him as Thomas Abel, who discreetly signed his name under a poem at the end of the introductory part of the book.

7.4 The Large Range of Innovations and the Importance of the mise en texte

Innovation in the in-octavo tradition concerned a large range of elements. The additions, substitutions, and corrections in the scholia were viewed as fundamental—that is why the names of Elie Vinet, Francesco Giuntini, and even the modest Albertus Hero were displayed on the title-pages. So were the improvements in the illustration (as we shall see below).

The text itself was frequently submitted to revision. The corrections were superficial and only meant to improve the clarity of the style. At first, they were mainly due to the fact that nobody held the original author in particular respect. But, with the Parisian editions, a ‘humanist turn’ progressively occurred. The title of the 1545 edition printed by Jean Loys (P2) already boasted that the text was “more correct, thanks to the diligent collation of manuscript and printed exemplars” (ex diligenti manuscriptorum impressorumque codicum collatione castigatior), and this evolution lead to the production in 1555/1556 of a Sphaera emendata (P6) that enjoyed great success: until the end of the century, all the new editions (and their imitations) retained this phrase at the beginning of their titles.

Indeed, the titles played a role in the innovation process: there never was a new model of edition without a new title—in turn faithfully copied in the imitations of this model. The new titles always advertised the innovations: the scholia and the improvement in the text, as we have seen,⁴⁶ but also the changes in the illustration⁴⁷ and other additions: “addita est praefatio…Philippi Mel. ad Simonem Grynaeum” (W1), later “Cum praefatione…” (W2) and “Praemissa praefatione…” (P1); “with a small treatise of the same author entitled the Comput” (“Ejusdem autoris libellus, cujus titulus est Computus…,” W2); “and other materials printed to please the students” (“et alia quaedam in studiosorum gratiam edita,” W3). On V2’s title-page appear the words: “with some additions that help to explain what is told in the Sphaera” (“Addita sunt quaedam ad explanationem eorum quae in Sphaera dicuntur facentia”), which means that the preface of Melanchthon has been replaced by a short treatise of elementary geometry. The addition, in P4, of Valeriano’s Compendium in Sphaeram is also advertised, as is that of Pedro Nunez’s Annotatio in P6. Even the new marginalia and the index introduced in the 1564 Giuntini edition (Ly1) are signaled: “Cum annotationibus in margine, et indice rerum et locorum memorabilium.”

This highlighting of the index and the marginalia shows that what the French historians of the book analyze as the elements of the “mise en texte” and “mise en livre” (Martin and Vezin 1990; Martin 2000) was viewed as an integral part of the innovation process. For instance, the Apianus and the Wittenberg editions had no running titles, and their pages were unnumbered. Guillaume Cavellat, in 1550 (P4), was the first to number the folios and add running titles.

As we have seen, the editors of the in-octavo editions, from the beginning, improved the clarity of the divisions of the text, using more subtitles, interlinear blanks, and other typographical devices. In this respect, W1 had already made progress in comparison to I1. Then W2 changed the wording of the subtitles (some of them became short summaries) and introduced a hierarchy between them to mark more clearly the logical structure of the text. For instance, in the last part of Chap. 2 (Table 9.4).

Table 9.4 The subtitles of the last part of chap. I in W1 and W2

From 1545 (P2) on, the Parisian editions adopted an important innovation: the four chapters became four books, each divided into numbered chapters. However, this tendency to modernize the Sphaera was checked by the humanist turn operated by Elie Vinet. In 1551 (P5), the Sphaera returned to the original division into four chapters.

7.5 The Illustration: Scientific and Commercial Issues

From 1526 to 1538, the principal innovations concerned the illustration (Tables 9.5 and 9.6). Apianus and the anonymous editor or editors of Wittenberg did all the work, and the result was deemed so satisfactory that their successors simply copied their set of diagrams. Only Franco Burgersdijk, in 1626, was to undertake a complete reworking of the illustration (Chap. 11).

Table 9.5 The diagrams from the Venetian incunabula to the Apianus edition^a

Table 9.6 From the Apianus edition to the Wittenberg editions^a

The creation of the complete set of diagrams that illustrated the in-octavo Sphaeras from 1538 to 1620 was progressive. Its authors borrowed from their predecessors (the Venetian incunabula, the Leipzig quartos, and above all the Apianus edition), but also from books outside this strict tradition. Thus, the editor of W2 (1538) borrowed fifteen diagrams from Oronce Finé’s Protomathesis, published in Paris in 1532. As a result, some figures of a type that had previously been excluded from the tradition were introduced into it: four true geometrical diagrams meant to explain the ascensions of the signs (in Chapter III of Tractatus de Sphaera by Sacrobosco). However, as we have seen, the more striking innovation of W2 was the arrival of four volvelles, of which the different parts were printed on folded sheets bound at the end of the volume—the reader had simply to cut the parts and assemble them.

If we set aside a few additions that were not retained for long in the tradition, the iconography of the in-octavo editions was thus conceived between 1526 and 1538, with a strong dynamic of innovation. It was the main contribution of the German mathematicians to this tradition, and their work in that field was so well received by the public that a certain commercial logic cemented this contribution’s place in future publication. The typical set of diagrams and volvelles of the in-octavo tradition was such a success that to modify it was out of the question. It could even be used as an identifying trademark.

The main reason why iconographical innovation ceased at an early stage in the in-octavo tradition was thus probably commercial. Such immobility could have represented a detrimental shortcoming, as it was indicative of a lack of serious mathematical work on the text: the invention of new diagrams was bound to happen as soon as mathematicians worked on a text and made commentary. However, this did not happen in this case, thanks to the particular character of Sacrobosco’s short introduction to cosmology, whose large and enduring success was due to its completeness, the clarity of its style, but also its avoidance of all mathematical complexities. The Sphaera was more descriptive—even narrative—than demonstrative. As Thorndike has observed, it achieved a happy compromise between the literary tradition, derived notably from Macrobius’s Commentarii in somnium Scipionis, and a then (in 1220) recent and more scientific approach to cosmology, permitted by the first translations of Arabic astronomers. Rival manuals composed at around the same time, such as those of Robert Grosseteste and John Peckham, were far less successful, although they were more up-to-date, probably because they were too dryly technical and mathematical and less elegantly written, and because they suppressed the quotations of classical poets (Thorndike 1949, 21). Indeed, technicity was not banned altogether, as it subsisted in largely diffused commentaries very soon to be associated with Sacrobosco’s Sphaera, like the one attributed to Michael Scot that was composed in the first half of the thirteenth century.

Thus, from the beginning up to the Renaissance, the successful formula was the association of a short, clear, and elegant treatise with commentaries that could afford further information. In the in-octavo tradition, as soon as the Sphaera was provided with a set of clear, precise, pedagogical, and (if possible) self-explanatory diagrams, the effort turned elsewhere. The editors made improvements of a different kind. They wrote pedagogical or erudite notes—notably to rectify some blunders owing to Sacrobosco’s lack of humanist training, and to explain the meaning of a few Greek words.⁴⁸ And they also resorted to additions: the addition of a few modest tables inside the commentary,⁴⁹ and above all the addition of other texts to complement the Sphaera.⁵⁰

8 The Limits of the Tradition: The Case of Francesco Giuntini

This cumulative process had its limits. The control of the publishers over the evolution of this tradition fostered innovation to a certain degree; but it could also hinder it. The iconography, as we have seen, consisted of a fixed set of diagrams; the additions were welcome, but only if they could fit into the handy format of the in-octavo textbook; the original contributions of skilled commentators were sought-after, provided that they let the model remain recognizable. The ideal new edition in the in-octavo tradition was an improved item that continued on the lines of previous editions. The case of Francesco Giuntini shows that more ambitious projects were bound to leave this framework.

Francesco Giuntini, a Florentine by birth, had been a Carmelite priest and a doctor of theology. His assiduous practice of astrology and, above all, his Protestant sympathies led him into trouble. In 1561, he went to Lyons as a religious exile, publicly renounced his heresy, and entered a new career as a mathematician and astrologer with the support of the Italian colony in Lyons. After a time, he won the patronage of royal officers and even began to aim higher.⁵¹ His first commentary on Sacrobosco was published in 1564, when he was still at the beginning of this successful second career (Sacrobosco 1564a). It fit into the framework of the in-octavo tradition, which likely appeared to him a good medium to widen his fame outside the Lyons circles. The presence of Melanchthon’s preface in praise of astrology (which had to be printed without the name of its author) probably appealed to him as well (Sacrobosco 1564a, 3r–7v).

In the dedication of the work to Thomas de Gadagne (ca. 1539–1594), lord of Bellegarde, Giuntini states that Filippo Tinghi (died 1580), a Florentine printer and bookseller settled in Lyons, has asked him to emendate the Sphaera and add some “very brief notes” (“brevissimis notis”) to explain the difficult passages, a demand which he has eagerly answered out of his zeal for promoting such a universally useful science as astronomy (Sacrobosco 1564a, 2r–v). Indeed, the “very brief notes” were to consist of innumerable marginalia, abundant scholia (even lengthier than Vinet’s, and printed in bigger type), and long technical appendices, which concerned the method of determining the polar altitude at any location in the northern hemisphere,⁵² the method of determining longitudes,⁵³ the method of determining the duration of natural days at different latitudes,⁵⁴ and instructions for the calendar (Sacrobosco 1564a, 143–46). The Giuntini edition thus brought into the in-octavo tradition a noticeable amount of material borrowed from other types of treatises on the Sphaera—adaptions or huge commentaries in which the original text was buried. Whereas the standard in-octavo model included only two modest tables, as we have seen, Giuntini added a series of tables (none of them original), which transformed the original textbook into an introduction to astronomical practice and calculation.⁵⁵

A table of the measures of the earth (perimeter, diameter etc.) in different units of measurement (leagues, miles, etc.).⁵⁶

A table to compare the measures of the obliquity of the ecliptic by Ptolemy, Albategnius, etc. until Johannes Werner. (Sacrobosco 1564a, 41–42)

A table of the cosmic and chronic risings and settings of the twelve zodiacal signs. (59)

Two tables of the astronomical risings and settings of the zodiacal signs under the right sphere, measured in arcs of the equator, and in hours and minutes. (66–67)

A table of the astronomical risings and settings of the zodiacal signs under the oblique sphere, measured in arcs of the equator and calculated for each of the eight climes. (70–71)

For the determination of latitudes (first appendix), a table of the true position (verus locus) of the sun at midday for each day of the year according to the Prutenic Tables⁵⁷ (119–20), a table of the equation of the sun⁵⁸ (123), and a table of the declination of the sun. (125)

A table of the longitudes and latitudes of the principal towns of the world (130–36)

For the determination of the length of natural days, a table of the semi-diurnal arcs and of the latitudes of the sun at midday under different latitudes. (139–42)

Two calendar tables. (243, 246)

Giuntini was not satisfied with this first work on the Sphaera and he planned more ambitious publications, both to attract the attention of more important patrons and to advance the project he took most to heart: asserting the complete legitimacy of astrology as an integral part of the science of the stars, and as the science of Providence, perfectly compatible with the Catholic faith, even under the new Tridentine rules.⁵⁹ In 1573, he dedicated to Catherine de’Medici (1519–1589), the queen mother, the first version of his Speculum astrologiae (Lyons: Filippo Tinghi), which contained a series of astrological treatises and new astronomical tables (Tabulae resolutae). Then he published a two-volume commentary on the Sphaera in 1577–1578, which rivaled that of Clavius, though it was far less methodical and much more digressive (Giuntini 1577–1578).⁶⁰ Its most exceptional feature was the space it devoted to astrological and theological questions. The content of the former commentary was immersed into this new one, which still retained the typical diagrams conceived in Wittenberg (mixed with new ones), and even the in-octavo format, but, all the same, no longer belonged to the tradition founded by Apianus. The same year (1578), Filippo Tinghi published a new edition of the Sphaera emendata (Ly2). The scholia added in 1564 had been removed from it, replaced by a short treatise of elementary geometry. Giuntini’s commentary and the in-octavo tradition had parted company for good.

9 Conclusion

In this paper, I focused on a kind of collective authorship, which was responsible for the development of a long-running tradition that developed from 1526 until the seventeenth century. I chose the privileged example of the in-octavo tradition to provide an interesting point of view on the means, the ways, and even the rhythm of innovation in the Sacrobosco field. This tradition was a successful attempt at standardization, producing a kind of manual that was able to retain, for over half a century, an essential core of original features even as it continued to evolve. This success proves the efficiency of a commercial model. The never-relenting interest in this particular model of Sphaera among a succession of booksellers in several European countries was certainly a motor for innovation: it would not have been possible to perpetually reprint the same book without drying up the market. It was necessary to innovate, at least to a certain extent, to gain enough new customers. But on the other hand, the constraints of the tradition, the obligation to retain the model, and the weight of trade imperatives imposed a limit on innovation, which, at the end, made decline inescapable. Between Giuntini’s intervention and Burgersdijk’s late attempt at reviving the tradition in 1626 (Chap. 11), no significant innovation occurred: the Wittenberg 1538 (W2) and the Paris 1555/1556 (P6) models were still printed, either in a repetitive manner (in Paris and Venice), or with different attempts at refreshment (in Antwerp and Cologne). In the second part of the sixteenth century, the concurrence of numerous new types of tracts on the Sphaera had marginalized the type studied in this paper.

In spite of the importance of the German mathematicians who conceived a remarkable set of cosmological pedagogical diagrams (following Melanchthon’s educational plan), and in spite of the patient work of annotation achieved by a succession of professors (notably Elie Vinet), the actors who did most to support first the dynamic of the tradition, then its longevity, were probably the printers and booksellers: they did not write commentaries, but in many cases⁶¹ they acted as intermediaries between the authors and the public, and they managed to keep control over the process. Innovation, as they conceived it, was a braiding process: it was often achieved through the artful combination of diverse borrowed material. In this way and in this specific instance, the printers and booksellers were largely responsible for blurring the distinction between borrowers and innovators.