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*

8 In 1478, Franciscus Renner from Heilbronn and Adam Burkardt from Rottweil printed in Venice two different editions with three diagrams (the elementary and celestial spheres; the climes; the solar and lunar eclipses). In 1482, still in Venice, Erhard Ratdolt published a new edition that added a fourth figure (an armillary sphere). In 1485, Ratdolt released another edition with twenty-two small new diagrams and some improvements to the existing diagrams.

9The Santritter edition was used as a model for the editions printed in Venice by [Bonetus Locatellus] for Octavianus Scotus, 4th of October 1490, for Melchior Sessa, 3rd of December 1501 and 3rd of December 1513, and by Jacobus Pentius for Sessa, 24th of December 1519.

10The dimension of the small quarto page is about 180 × 140 mm (145 × 115 mm for the printed text).

11Regiomontanus's and Peuerbach's texts do not begin on the recto of the first folio of a quire, which indicates that they were not meant to be sold or bound separately.

12Only seven of the twenty manuscripts described by Thorndike (see Footnote 1) are with diagrams and only five of these seven have what could be considered as a 'complete set.'

(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).

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).

13Late Ancient diagrams concern the concentric spheres of the world (see Chapter I of *Tractatus de Sphaera* by Sacrobosco), the terrestrial and celestial zones, the climes (see Chapter II of *Tractatus de Sphaera* by Sacrobosco), the *figura retrogradationis* (showing how the movement of the planet on its epicycle produces, as observed from the earth, cycles of direct motion, station, and retrograde motion), and the lunar and solar eclipses (see Chapter IV of *Tractatus de Sphaera* by Sacrobosco). On this iconographic tradition, see notably (Obrist 2004; Müller 2008).

zodiac with respect to the axis of the world is not correct.

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

270

#### **Table 9.1** (continued)

a Concerning the diagram that shows the spheres of the elements and the celestial orbs, there is a discrepancy between the diagram, which corresponds to the original text of Sacrobosco (according to which the sphere is divided into nine celestial spheres), and the revised text of the Santritter edition and its followers that lists ten celestial spheres (Chap. 5).

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

#### **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.

14On Apianus, see (Röttel 1995).

15 (Sacrobosco 1526, A1v):"…cum Geographia plurimum comercii habeat cum Astronomia…."

16 (Sacrobosco 1526, A1v):"…visum est mihi haud inutile fore, si ingenuis adolescentibus primum omnium Astronomiae rudimenta praelegerem, Sphaeram IANI de Sacrobusto accuratissime interpretarer. Futurum tandem existimans ut ex sphaerae circulorumque ejus attenta cognitione, spaciorum terrae coelique absoluta notitia proveniret."

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

a The subtitles marked with an asterisk correspond to a long addition on the visible constellations of the eighth sphere and their correspondence with those of the ninth and tenth spheres. b The first two subtitles «Quorum zenith est» are in the flow of the text.

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.

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

17The discrepancy in Apianus's work is the reverse of that in the Venetian editions, which modernized the text and kept the traditional figures.

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

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).

18The change concerning the representation of the spheres of water and earth was a consequence of the navigation of Amerigo Vespucci along the east coast of Brazil in 1501, which proved that the southern hemisphere was not immersed in water. Joachim Vadianus was probably the first to infer that the earth constituted one single sphere with the water, from which it "partly emerged," doing so in a letter to Rudolf Agricola that was published for the first time in Wien in 1515. See (Randles 1980, 44–48; Grant 1994, 635–37).

19 In the (Chaudière 1516) edition (and in the 1519, 1524, and 1527 re-editions), the terraqueous globe is represented in the diagram of the four elements (a2v), but not in the diagram of the elementary and celestial spheres (a2r). In the *Sphaera* printed in Wien in 1518 by Johann Singriener for Lucas Alantsee, the terraqueous globe, with a map drawn on it, figures in the diagram of the elementary and celestial spheres (a3r, a6v).

20This part of chapter 3, entitled "on the variation of phenomena according to latitude," is not illustrated in the Venetian editions; in the Leipzig editions, it is illustrated with seven diagrams, which have only remote links to Apianus's diagrams (Fig. 9.3).

 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

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.

**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

#### **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

21On the amazing transformation of the modest town of Wittenberg into one of the largest book production centers in Germany, thanks to the publication of religious pamphlets, in the first place, but also of educational manuals, see (Pettegree 2010, 91–106).

22On Melanchthon's vision of astrology, see notably (Caroti 1986; Müller-Jahncke 1998).

23On the success of Melanchthon's letter, see (Pantin 1987).

24The description of the colures (see Chapter II of *Tractatus de Sphaera* by Sacrobosco) in the Apianus edition (B2v), for instance, does not use a paragraph to separate the general description from what concerns each colure; it uses two asterisks instead ("…∗∗ Colurus igitur distinguens solsticia…"). The Wittenberg 1531 edition (C3v) adds a paragraph and an interlinear blank, and it also keeps the asterisks (probably because their meaning was no longer understood). A second example: the beginning of the section on the natural days ("Ex praedictis etiam patet quod dies naturales. Est enim dies naturalis…") is only marked by an intralinear blank (before "Ex praedictis") in the Apianus edition (B8v). In the Wittenberg edition (D3v), a new paragraph, made more visible by an interlinear blank, begins at "Est enim dies." As a consequence of this airier layout, the text of the Wittenberg 1531 edition is printed on forty-three folios (instead of thirty-one in the Apianus edition).

25The diagrams on the effect of refraction, supposed to enlarge the image of the stars near the horizon, were suppressed.

(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,

26Examples of improved diagrams include two figures of the terrestrial zones in Apianus's edition: the first one is a crude geometrical diagram; in the second one, a kind of map covers all the space between the polar circles. In the Wittenberg 1531 edition, there is only one larger and more precise geometrical diagram, with the name of the zones inscribed.

27The image of the lathe that illustrates the definition of the sphere (Sacrobosco 1531, B1v) is closer to the diagram introduced by Jacques Lefevre d'Étaples in Parisian treatises on the *Sphaera* (Chap. 2).

28For a general view of the development of the in-octavo tradition, see the next sections.

29For instance: (Sacrobosco 1538, B1v): a note on Euclid's definition, which is quoted in Greek and translated; (D4v): a marginal note on 'CHRONICUS:' "Pro Chronico legendum [in Greek:] *akronuchos…*," with a quotation in Greek from Proclus's commentary on Hesiod; (F2v): a marginal note on the evaluation of the width of the first climate: "Unui gradui latitudinis, tribuuntur hoc loco 56. Milliaria et duae tertiae unius. Est enim hic locus omnino fere ex Alfragano desumptus."

30The text "De ortu et occasu Planetarum, et occultationibus eorum de sub radiis solis. Diff. xxiv" is taken from the edition printed in Nuremberg in 1537, with Regiomontanus's *Oratio habita Patavii in praelectione Alfragani* and a preface by Melanchthon: *Rudimenta astronomica Alfragani. Item Albategni…de motu stellarum*.

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 quasiparallel 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 halfdisk 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

31On the probable author of the revision of the 1538 Wittenberg edition, Georg Joachim Rheticus, and on the changes to the illustration and the subtitles, see *infra*.

32 (Sacrobosco 1538, B8r): "Instrumentum quo et rotunditas terrae secondum latitudinem probatur, et facillime omnia ea., quae autor in tertio capite de diebus artificialibus tradit dijudicantur."

33The change to the date of the preface was probably a mistake that originated in the printer's shop (because of the habit of making the date of the preface match with that of the printing). In the next Wittenberg editions (1543, 1545a, and so on) the initial date (1531) was restored. However, the error was transmitted to Paris and Antwerp editions (Table 9.3).

34 (Sacrobosco 1543b, F1v–F2r): "Tabula maximorum dierum naturalium ad singulas elevationes poli habitantium a circulo arctico usque ad polum arcticum."

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).

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

35The tables are referred to in G7v ("Huc pertinet Tabula continens ingressum Solis in XII signa Zodiaci") and G8r ("Huc referatur Tabula quae habet gradus eclipticae cum quibus stellae insigniores olim oriebantur et occidebant"). They have disappeared from most copies.

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.

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

#### **Table 9.3** (continued)

#### **Table 9.3** (continued)

a In this table, only true editions are listed. In some towns, particularly in Paris, the practice of reissuing earlier editions with a new date on the title was quite common. As the products of this practice ("separate issues" in English, "émissions" in French) had strictly no impact on tradition, they are not taken into account to prevent skewing the statistics. Editions posterior to 1601 are not listed here.

b 1542 is the date at the colophon; 1543 is the date on the title page.

c The 1540 Wittenberg edition copies line for line W2, with one exception: all marginal notes are inserted into the text, and the preface is dated 1540 (instead of 1531).

d 1555 on the "achevé d'imprimer;" 1556 on the title-page.

e 1557. Two reissues with the date modified: 1558, 1559.

f 1564. Reissue with the date modified: 1567.

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 inoctavo 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.

36On Cavellat's career, see (Pantin and Renouard 1986).

37This anonymous editor of the Cholinus edition was perhaps Thomas Abel, a physician and professor of mathematics, who wrote a poem "De hoc libro sphaerico emendato," printed between Hero's 1581 dedication and the beginning of the *Sphaera*.

#### *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.

38Theodoricus's adaptions of the *Sphaera* were reprinted in Wittenberg in 1567, 1570, 1573, 1578, and 1583.

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

39The 1538 edition (W2) adds an edition of the *De anni ratione*, with a preface by Melanchthon addressed to A.P. Gasser. This preface states that the editorial work for the *De anni ratione* was done by Caspar Borner, but that the idea for the addition was Rheticus's. The intervention of Rheticus in W2 is thus documented. In a letter to Paul Eber (1 March 1562), Rheticus affirmed that he had "prepared the *Sphaera* and *Computus* for the press" in 1550 and complained of having been miserly paid (then, the W3 model was firmly installed in Wittenberg and the supervisor's work was routine). From the summer of 1542 on, Rheticus no longer taught in Wittenberg, but before that date the supervision of the printing of mathematical textbooks had been part of his job (Rosen 1970, 1974).

40Vinet wrote a dedication to Johannes Tacitus (P4), and Francesco Giuntini one to Thomas de Guadagne (L1). Even Albertus Hero wrote a dedication to Paulus Kuechovius (C2), though the few *scholia* he added to those of his predecessors were quite small indeed.

41A great change occurred in the French book-privilege system in February 1566, when the ordinance of Moulins (art. 78) stipulated that it was henceforth mandatory to publish under royal privilege. However, this still concerned "nouveaux livres." See (Saugrain 1744, 357–58).

42This privilege was first used in P6 (1555/1556). It is worth noting that Vinet's *scholia* had first been printed by Cavellat in 1551 (P5) under the first privilege. But P6 was *emendata* and added, for the first time, Pedro Nuñes's *Annotatio in extrema verba capitis de climatibus* translated by Vinet.

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.

43Privilege of Ly1.

44 Imperial privileges could be granted to "republication as well as new publication, although in most cases even republication was claimed to be an improved and enlarged version of the first edition" (Maclean 2012, 140). On imperial privileges and their use in the Netherlands, see (Gompel 2011, 61–64). There, as in France, in the first part of the sixteenth century, book-privileges were mainly meant to protect the commercial interests of the beneficiaries; afterwards, they became mainly instruments of censorship.

45Vinet's and Hero's dedications are printed at the beginning of the volume, in addition to Melanchthon's letter, now an anonymous preface.

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

46The anonymous *scholia* of P3 were mentioned in the title too: "with notes that throw much light on somewhat obscure passages" ("cum annotationibus, quae locis aliquot obscuris magnam lucem afferunt")*.*

47W2: "with new figures that explain the risings [of the zodiacal signs]" ("et novis quibusdam typis, qui ortus indicant"), echoed in P1 by "with the addition and illustration of numerous new figures" ("Plurimis novis typis auctus et illustratus").

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).

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

**Table 9.5** The diagrams from the Venetian incunabula to the Apianus editiona

**Table 9.5** (continued)

a In this table all diagrams indicating an imitation or an influence are underlined. They are described with "similar to" if the imitation is obvious or with "linked to" if the imitation is less complete b For more details, see (Table 9.1)

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

48The Paris editors were particularly keen on this point. For instance, the Wittenberg 1538 editor (W2) already tells, in a sober marginal note (D4v), that in Sacrobosco's text "chronicus ortus" means "achronichos," referring to Proclus's commentary on Hesiod, whereas the 1545 Paris editor

**Table 9.6** From the Apianus edition to the Wittenberg editionsa

**Table 9.6** (continued)

a In this table as in (Table 9.5) the diagrams copied from other editions (or inspired by them) are underlined. The new diagrams in W2 are in bold

b P2 (Paris, 1545b) adds two crude and completely redundant diagrams. The first one (in a note on Euclid's definition of the sphere) remains in the Paris editions until P5 (1551), the second one (on the solar eclipse) until P6 (1555/1556)

**Fig. 9.5** *De divisione climatum*. From (Sacrobosco 1526, D2v). State Library Regensburg--999/ Philos.1325, urn:nbn:de:bvb:12 bsb11110162-1

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 inoctavo tradition was an improved item that continued on the lines of previous

(P2) expands on this topic in a long note ("Corrupta scriptura…" D5r). Then Elie Vinet, in 1551 (P5), writes a new version of the note with more erudite details (34r). The 1550 Paris editor (P4) adds some notes on difficult words, like "Archetypus" (B7r) and "Diaphanum" (B8r).

49 In W3, the table of the longest natural days for all degrees of latitude between the arctic circle and the pole appeared (Sacrobosco. 1543b, F1v–F2r), and in P2 a table of the climes (Sacrobosco. 1545b, F3v). The first massive addition of tables occurred thanks to Giuntini, but never to appear again in further editions (see *infra*).

50For a general view of additions, see (Table 9.3).

**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

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

51On Giuntini's career, see (Ernst 2001; Pantin 2013).

52 (Sacrobosco 1564a, 117–27): "Quomodo altitudo poli Aquilonaris et aequatoris sit investiganda."

53 (Sacrobosco 1564a, 128–29): "Quomodo Astrologi invenerunt locorum longitudines."

54 (Sacrobosco 1564a, 136–42): "De quantitate diei et noctis, ortu et occasu Solis."

55The tendency to transform the original textbook into an introduction to astronomical practice and calculation, already present in Lefevre's and Finé's work on the *Sphaera* (Chaps. 2 and 8), had been reinforced in many adaptions and 'hypercommentaries' of Sacrobosco, notably those of (Schreckenfuchs 1569) and (Clavius 1570).

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

56 (Sacrobosco 1564a, 30): "Tabula quantitatis terrae secundum Ptolemaeum et experientiam."

57On Giuntini's reliance on Erasmus Reinhold's "Copernican tables," though he had otherwise no Copernican sympathies, see (Omodeo 2014, 136–39; Proverbio 1997).

58The equation of the sun (*aequatio Solis*) is the arc of the ecliptic between the true position (*verus locus*) of the sun, determined by a line issued from the center of the world and passing through the center of the body of the planet, and its mean position (*medius motus*) determined by a line issued from the center of the world and parallel to a line issued from the center of the eccentric deferent of the Sun and passing through the center of the body of the planet. All these notions are part of the knowledge taught in the *Theoricae planetarum*.

59Although the Council of Trent had hardened the control of the practice of astrology, Giuntini felt confident that he could promote this practice by using the same arguments as those developed by Melanchthon. On Giuntini's astrology, see (Thorndike 1941, 129–33; Pantin 2013).

60One volume of Giuntini's work is dated 1577, the other one 1578, but both were issued together. This commentary was reprinted in 1583 as part as the second in-folio volume of the much enlarged new version of the *Speculum astrologiae* (Lyons: Filippo Tinghi).

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.

61Not in all cases printers acted as intermediaries: as we have seen, in Wittenberg, the printers followed the instructions of the university.

#### **References**

#### *Editions of Sacrobosco's Sphere Anterior to the In-Octavo Tradition*

———. 1508. *Opus sphericum…figuris verissime exculptis et interpretatione familiari…illustratum*, comm. Wenceslas Faber von Budweis. Cologne: Heirs of Heinrich Quentell. http://hdl. handle.net/21.11103/sphaera.100183.

———. 1509. *Textus Spere materialis…cum lectura Magistri Conradi Norici*, comm. Conrad Tockler. Leipzig: Martin Landsberg. http://hdl.handle.net/21.11103/sphaera.101042.

———. 1513. *Sphaera mundi*. Venice: Melchior Sessa. http://hdl.handle.net/21.11103/ sphaera.101023.

———. 1516. *Mundialis sphere opusculum*. Paris: Vincent Quignon for Regnault Chaudière. http://hdl.handle.net/21.11103/sphaera.100991.

———. 1518. *Opusculum de sphaera*. Wien: Johann Singriener for Lucas Alantsee. http://hdl. handle.net/21.11103/sphaera.100883.

———. 1519. *Sphaera mundi*. Venice: Jacobus Pentius for Melchior Sessa. http://hdl.handle. net/21.11103/sphaera.100992.

#### *Editions in the In-Octavo Tradition (1526–1601)*

———. 1526 **[I1]**. *Sphaera…per Petrum Apianum accuratissima diligentia denuo recognita ac emendata*. Ingolstadt: Petrus Apianus. http://hdl.handle.net/21.11103/sphaera.100070.

———. 1531 **[W1]**. *Liber de sphaera. Addita est praefatio in eundem librum Phlippi Melanchthonis ad Simonem Gryneum*. Wittenberg: Joseph Klug. http://hdl.handle.net/21.11103/ sphaera.100138.

———. 1532 **[V1]**. *Liber de sphaera.* Venise: G.A. Nicolini da Sabio for Melchior Sessa. http:// hdl.handle.net/21.11103/sphaera.100118.

———. 1534a. *Liber de sphera.* Wittenberg: Joseph Klug. http://hdl.handle.net/21.11103/ sphaera.100085.

———. 1534b. *Liber de sphaera.* Venice: G.A. Nicolini da Sabbio for Melchior Sessa. http://hdl. handle.net/21.11103/sphaera.100179.

———. 1536. *Liber de sphaera.* Wittenberg: Joseph Klug. http://hdl.handle.net/21.11103/ sphaera.101008.

———. 1537a. *Liber de sphaera.* Venice: Maffeo Pasini and Francesco Bindoni. http://hdl.handle. net/21.11103/sphaera.101059.

———. 1537b. *Liber de sphaera.* Venice: Giovanni Antonio Nicolini da Sabbio for Melchior Sessa. http://hdl.handle.net/21.11103/sphaera.101060.

———. 1538 **[W2]**. *Libellus de sphaera*. Wittenberg: Joseph Klug. http://hdl.handle.net/21.11103/ sphaera.101106.

———. 1540. *Libellus de sphaera*. Wittenberg: Joseph Klug. http://hdl.handle.net/21.11103/ sphaera.101025.

———. 1541a. *Liber…de sphaera. Addita est praefation in eundem librum Philippi Mel. Ad Simonem Grineum*. Venice: Francesco Bindoni and Maffeo Pasini. http://hdl.handle. net/21.11103/sphaera.100140.

———. 1541b. *Liber…de sphaera. Addita est praefatio in eundem librum Philippi Mel. Ad Simonem Grineum*. Venice: Giovanni Antonio Nicolini da Sabbio for Melchior Sessa. http:// hdl.handle.net/21.11103/sphaera.100144.

———. 1542/1543 **[P1]**. *De sphaera liber. Plurimis novis typis auctus*. Paris: Jean Loys. http:// hdl.handle.net/21.11103/sphaera.101027.

———. 1543a **[A1]**. *Libellus de sphaera*. Antwerp: Jean Richard. http://hdl.handle.net/21.11103/ sphaera.100180.

———. 1543b **[W3]**. *Libellus de sphaera*. Wittenberg: Peter Seitz. http://hdl.handle.net/21.11103/ sphaera.101029.

———. 1545a. *Libellus de sphaera*. Wittenberg: Veit Kreutzer. http://hdl.handle.net/21.11103/ sphaera.100818.

———. 1545b **[P2]**. *Sphaera typis auctior, quam antehac, atque ex diligenti manu scriptorum impressorumque codicum collatione castigatior*. Paris: Jean Loys and Guillaume Richard. http://hdl.handle.net/21.11103/sphaera.101054.

———. 1545c. *Liber de sphaera*. Venice: Giovanni Antonio Nicolini da Sabbio for Melchior Sessa. http://hdl.handle.net/21.11103/sphaera.100145.

———. 1546. *La Sphere…traduicte de latin en langue francoyse*, transl. Martin de Perer. Paris: Jean Loys. http://hdl.handle.net/21.11103/sphaera.101030.

———. 1547 **[A2 & L1]**. *Sphaera*. Antwerp and Louvain: Martinus Nutius for Jean Richard and Jan Waen. http://hdl.handle.net/21.11103/sphaera.100917 [A2]. http://hdl.handle. net/21.11103/sphaera.100125 [L1].

———. 1550b. *Libellus de sphaera*. Wittenberg: Johann Krafft. http://hdl.handle.net/21.11103/ sphaera.100157.

———. 1550c **[P4]**. *Sphaera typis auctior, quam antehac…cum annotationibus*. Paris: Guillaume Cavellat. http://hdl.handle.net/21.11103/sphaera.100952.

———. 1551a. *Sphaera*. Antwerp: Jean Richard. http://hdl.handle.net/21.11103/sphaera.100161.

———. 1563. *Libellus de sphaera*. Wittenberg: Johann Krafft. http://hdl.handle.net/21.11103/ sphaera.101070.

———. 1564a [Ly1]. *Sphaera…emendata cum additionibus in margine…nunc recenter compertis et collectis a Francisco Junctino Florentino sacrae theologiae doctore*, comm. Elie Vinet and Francesco Giuntini. Lyons: Symphorien Barbier for Filippo Tinghi and the heirs of Giunta. http://hdl.handle.net/21.11103/sphaera.101071. Reissue with the date 1567. http://hdl.handle. net/21.11103/sphaera.101111.

———. 1564b. *Sphaera emendata*, comm. Elie Vinet. Paris: Guillaume Cavellat. http://hdl.handle. net/21.11103/sphaera.100110.

———. 1564c. *Sphaera. Addita sunt quaedam….* Venice: Francesco Rampazetto. http://hdl.handle.net/21.11103/sphaera.100165.

———. 1566a **[C1]**. *Sphaera emendata*, comm. Elie Vinet. Cologne: Maternus Cholinus. http:// hdl.handle.net/21.11103/sphaera.101076.

———. 1566b **[A3]**. *Sphaera emendata cum additionibus in margine*, comm. Elie Vinet and Francesco Giuntini. Antwerp: Jean Richard and the heirs of Arnold Birckmann. http://hdl. handle.net/21.11103/sphaera.101114. http://hdl.handle.net/21.11103/sphaera.101115.

———. 1568. *Libellus de sphaera*. Wittenberg: Johann Krafft. http://hdl.handle.net/21.11103/ sphaera.101112.

———. 1569a **[P7]**. *Sphaera emendata*, comm. Elie Vinet. Paris: Guillaume Cavellat and Jérôme de Marnef. http://hdl.handle.net/21.11103/sphaera.100240.

———. 1572b. *Sphaera emendata*, comm. Elie Vinet. Paris: Guillaume Cavellat and Jérôme de Marnef. http://hdl.handle.net/21.11103/sphaera.100268.

———. 1577a. *Sphaera. Addita sunt quaedam….* Venice: heirs of Melchior Sessa. http://hdl.handle.net/21.11103/sphaera.100478.

———. 1594a. *Sphaera emendata*, comm. Elie Vinet and Albertus Hero. Cologne: Goswin Cholinus. http://hdl.handle.net/21.11103/sphaera.100656.

———. 1601c **[C3]**. *Sphaera emendata, aucta, et illustrata…nunc accessere R.P. Christoph. Clavii breves commentarii*, comm. Elie Vinet, Albertus Hero and Christoph Clavius, ed. Thomas Abel [?]. Cologne: Goswin Cholinus. http://hdl.handle.net/21.11103/sphaera.100327.

#### *Large Commentaries on the Sphere*

#### *'Adaptions' of the Sphere and Other Cosmological and Astronomical Books*

Dietrich, Sebastian, see Theodoricus.

——— (Sebastian Dietrich). 1564. *Novae quaestiones sphaerae, hoc est, de circulis coelestibus, et primo mobile*. Wittenberg: Johann Krafft. http://hdl.handle.net/21.11103/sphaera.101072.

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# **Chapter 10 André do Avelar and the Teaching of Sacrobosco's** *Sphaera* **at the University of Coimbra**

**Roberto de Andrade Martins**

**Abstract** André do Avelar was the mathematics professor of University of Coimbra from 1592 to 1616. During his lifetime he published two astronomical works: a popular vernacular book called *Reportorio dos tempos* (1585) and *Sphaerae vtrivsque tabella* (1593). Avelar's *Sphaera*, composed for use at the university, was the only Latin version of Sacrobosco's work ever published in Portugal. Avelar's book was inspired by Sacrobosco's work and followed it closely, but it might be regarded as a new work, because he changed the wording and the order of presentation of the topics, added new information and several tables. After his retirement, Avelar was accused of Jewish beliefs and practices, and was condemned by the Inquisition in 1620, dying in prison. This paper analyzes Avelar's life, his work at the University of Coimbra, the content and role of his *Sphaera*, his career, and his trial by the Inquisition.

#### **1 Introduction**1

All over Europe, the *Tractatus de sphaera* by Johannes de Sacrobosco (died ca. 1256) remained the most widely known astronomical textbook for centuries. Four versions of Sacrobosco's *Sphaera* were published in Portugal in the sixteenth century. Three of them were in Portuguese, and only one in Latin (do Avelar 1593) (Fig. 10.1).

The title page of the Latin version contains some biographical information about the author, André do Avelar (1546–ca. 1623): born in Lisbon (*Olysipo*, in Latin), he was a Master of Arts and Philosophy (to be exact, in theology), and at the time of

R. de Andrade Martins (\*) FESB, Bragança Paulista, Brazil

UNIFESP, São Paulo, Brazil

GHTC-USP, São Paulo, Brazil e-mail<EMAIL_ADDRESS>
1The author is grateful for the support provided by the Brazilian National Council for Scientific and Technological Development (CNPq). The author is also grateful to Charlie Zaharoff for his careful revision of the paper.

**Fig. 10.1** Title page of André do Avelar's commentary on the *Sphaera*. From (do Avelar 1593, fol. 1). Courtesy of the Biblioteca Universidad de Sevilla

the book's publication he was a professor of mathematics at the University of Coimbra. As one can see on the title page, the work was published with the permission of the Inquisition. The elliptical emblem contains the expression "Flectimur sed non frangimur" (we are bent, but not broken), meant to exhibit a proud and defiant attitude in the face of adversity. Here, on the very first page of the book, we find the main topics to be addressed in the following paper: a Latin commentary on the *Sphaera*; its author's biography; the teaching of the *Sphaera* at the University of Coimbra; and the involvement of the author in the Inquisition.

## **2 Pedro Nuñes and the** *Sphaera* **at the University of Coimbra**

The first Portuguese university was created in Lisbon in 1290 (Rodrigues 2006). During the fourteenth century it moved to Coimbra, then back to Lisbon, back again to Coimbra, and once more to Lisbon (1377), where it remained until 1537, when it

was permanently relocated to Coimbra by King João III (1502–1557). Only after this final move was the university endowed with its earliest chair of mathematics, which was first occupied by Pedro Nuñes (1502–1578) in 1544 (da Fonseca 2001; da Fonseca 2004).

The Society of Jesus was officially approved by Pope Paul III (1468–1549) in 1540. In the same year, two Jesuits arrived in Portugal to begin their religious and educational work. Their first school in Portugal was the Colégio de Jesus in Coimbra, founded in 1542. The Colégio do Espírito Santo began its activities in Évora in 1551, and it officially became the second Portuguese university in 1559 (Dias et al. 2012, 117). No other university was created in Portugal until the twentieth century.

Pedro Nuñes studied medicine at the universities of Salamanca and Lisbon, obtaining his title in 1525. During his medical studies he became deeply involved with mathematics and astronomy, and in Portugal he obtained the position of "Royal Cosmographer" in 1529 (da Fonseca 2004). From 1531 onwards, he was the tutor of two of the younger brothers of King João III: Luís, Duke of Beja (1506–1555), and Fernando, Duke of Guarda (1507–1534). Later on, he also taught the prince and future king Dom Sebastião (1554–1578). Some noblemen also benefited from Nuñes's teachings during this period, including Dom João de Castro (1500–1548), who became famous for his navigations and was later viceroy of Portuguese India.

In 1537, Nuñes published his first book, containing a Portuguese translation of the *Sphaera* with commentary as well as a partial translation of Georg Peuerbach's (1423–1461) *Theorica planetarum* and other tracts (Nuñes 1537). It was dedicated by his author to Prince Luís. This was not the first Portugese translation of Sacrobosco; another one, by an anonymous translator, had been published twice before 1520 (Bensaude 1912; de Albuquerque 1965) (Chap. 7).

It is clear that Nuñes's translation was not intended to be nor ultimately used as an academic textbook, because the statutes of the university prescribed the exclusive use of Latin as the official idiom for teaching (Leite 1963, 314). The language and content of Pedro Nuñes's first book show that his envisioned audience included people associated with navigation (pilots and cosmographers). That is what the author himself stated in the preface of his book:

Having seen that the treatise on the *Sphaera* and the theory of the Sun and the Moon, and also the first book on the Geography of Ptolemy, contain those principles that must belong to any person who wants to know something about Cosmography, I translated them into our language so that those who do not know Latin would not be deprived of them. (Nuñes 1537, 5)

Nuñes had taught philosophy at Lisbon University (1531–1533), and became its initial professor of mathematics after it was moved to Coimbra (da Fonseca 2001; da Fonseca 2004). He certainly used Sacrobosco and Peuerbach as the basis of his astronomical teaching. Another of his books was possibly produced for the use of his students: *Astronomici introdvctorii de spaera epitome* (Nuñes 1940, vol. 1, 244–67). It is a very short version (twelve pages) of the first three books of the *Sphaera*. There is only one known copy of this book and it lacks the title page; for that reason, its place of publication, publisher, and date are uncertain. Some historians (including Joaquim Bensaúde) claim that it was written before the translation of the *Sphaera*; others (such as Rodolfo Guimarães) suppose that it was composed

later (Nuñes 1940, vol. 1, 329–33). It is doubtful that it could be of any use outside the academic environment. Hence, I think that it was composed for use at the university, probably after 1544. This book was published only once in the sixteenth century and was not reproduced in Nuñes's *Opera* (printed in 1566, 1573, and 1592), although that work contained his comments on Peuerbach's *Theorica planetarum*.

In 1547, Nuñes was appointed as the first "cosmógrafo-mor" (high cosmographer) of the Portuguese kingdom, holding that position until his death in 1578 (da Mota 1976, 54). The duties of the high cosmographer during this period are not well known. The oldest official regulations about the *cosmógrafo-mor* were established in 1559, but they are unknown; only the directives of 1592 survived. Those were established under Spanish rule, and might have been widely different from their predecessors.

Pedro Nuñes taught mathematics only from 1544 to 1557, with frequent calls by the king to Lisbon. In 1557, he took a leave and moved to Lisbon for 4 years, possibly because of the needs of his position as high cosmographer. He retired from the university in 1562, shortly after his return to Coimbra (da Fonseca 2004). It is odd that his chair was not assigned to any other professor for three decades. Mathematics had been a relevant part of the Liberal Arts curriculum in all European universities since the Middle Ages, and it was also required for the study of medicine because of its astrological components. It is known that there were temporary teachers of mathematics in some periods after Nuñes's retirement; but the chair remained vacant until 1592.

#### **3 Mathematics at the** *Colégio das Artes* **of Coimbra**

The extended absence of a mathematics professor at the University of Coimbra can be explained, however, by the fact that this discipline was taught at another institution. In 1542, King Dom João III also founded the *Real Colégio das Artes e Humanidades* (Royal School of Arts and Humanities), a preparatory school in Coimbra, which was attached to the university. Its aim was providing the prerequisite studies for the main university courses. It was created as a general college for grammar, rhetoric, poetry, logic, philosophy, mathematics, Greek, and Hebraic. Its faculty numbered sixteen, one of them a professor of mathematics (Teixeira 1899, 4–5).

Its activities began in 1547 under the direction of André de Gouveia (1497–1548), who had formerly been the dean of the University of Paris. André de Gouveia brought from France several outstanding teachers and the school soon gained prominence (Hopkins 2016, 165). One of the foreign teachers brought by Gouveia to Coimbra was Élie Vinet (1509–1587), who became a friend of Pedro Nuñes and helped to disseminate his works abroad. In 1555, Dom João III decided to hand the direction of the *Colégio das Artes* to the Company of Jesus (Dias et al. 2012, 118).

Several archival documents of the 1550s refer to the professor of mathematics (Teixeira 1899, 282, 305, 403, 407), although there is no information about who occupied the chair. The directive of the *Colégio das Artes* was contained in the 1559 statutes of the University of Coimbra, which ascertained that the students of arts should have lessons on arithmetic, geometry and perspective during the third term of the second year, and during the third term of the third year they should read the *Sphaera* (Leite 1963, 317–18). Perhaps the subjects that were lectured on were not so different from the curriculum taught at other Jesuit schools. Jerónimo Nadal (1507–1580) wrote the statutes of the Jesuit School of Mesine and included the following mathematical topics in the study of philosophy: some books of Euclid (died 285 BCE), practical arithmetic, the *Sphaera* or the cosmography of Oronce Fine (1494–1555), the astrolabe of Johannes Stoeffler (1452–1531), and the astronomy of Georg von Peuerbach (1423–1461). In 1552, Nadal proposed a general plan of study for all Jesuit schools, including a more complete program of mathematics, adding to the previous list the study of the theory of music and perspective; all the students of philosophy should study mathematics for 3 years (Fuentes 2012, 136–37). Baltasar Torres (1518–1561), the first professor of mathematics at the *Collegio Romano*, wrote two poposals for the teaching of mathematics at the Jesuit schools that were similar to those of Nadal (Fuentes 2012, 139). It is unlikely, however, that the teaching of mathematics at the *Colégio das Artes* was so complete. Nadal himself visited the school of Coimbra and complained in his report that only the students in their second and third years received lectures on mathematics, which lasted only half an hour each day (Fuentes 2012, 141).

Christophorus Clavius (1538–1612), one of the most famous mathematicians of late sixteenth century, studied at the *Colégio das Artes*. When he was 16 years old, he entered the Society of Jesus in Rome, and the next year he was sent to Coimbra, where he remained as a student from 1556 to 1560. It is unlikely that he was ever a student of Pedro Nuñes, and we do not know who could have been his mathematics professor at the Jesuit college, so he was probably a self-taught mathematician (Lattis 1994, 14–15; Baldini 1998, 214). In 1561, he went back to Rome, and in 1563, he began teaching mathematics at the *Collegio Romano*.

Sometimes the philosophy teachers of the *Colégio das Artes* provided their students with the necessary mathematical and astronomical knowledge by introducing the study of the *Sphaerae* in their courses on natural philosophy, between the lessons on Aristotle's (384–322 BCE) *Physica* and the study of his *De Coelo* (Baldini 1998, 205). Some manuscripts of such mixed lectures are extant, the earliest one from 1570, written by the Jesuit "Ioannis Gomesii Bracharensis," that is, João Gomes of Braga—an otherwise unknown philosophy teacher at Coimbra. A similar manuscript by another Jesuit priest, Luís de Cerqueira (ca. 1552–1614), who taught philosophy at Coimbra from 1581 to 1585, is also preserved, as are analogous manuscripts by three Jesuits teaching at Évora in the decade of 1580 (Baldini 1998, 235).

Philosophy, not mathematics, was the main focus of the professors of the *Colégio das Artes*. From 1592 to 1606, they published the eight volumes of the famous *Cursus Conimbricensis*, containing the best commentaries on Aristotle produced at that time. These underwent several editions and were used throughout Europe (Casalini 2017).

It seems that the first Portuguese Jesuit mathematician was João Delgado (1553–1612). He joined the Jesuit order in 1574 and 2 years later was sent to Rome to study at the Collegio Romano, where he learned mathematics under Clavius. He remained there for 9 years and returned to Portugal in 1585 (Leitão 2008, 46). He intended to go to Brazil as a missionary,2 but for unknown reasons he remained in Coimbra, where he taught mathematics from 1586 to 1589. The manuscripts of his lessons corresponding to 1586/7 and 1587/9 have been preserved (Baldini 1998, 229). From that time onwards, the influence of Clavius in Portugal was remarkable (Carolino 2006).

In 1590, Delgado began to teach mathematics at the Colégio de Santo Antão in Lisbon. This Jesuit school had begun its activities in 1553 and it was initially dedicated to the teaching of Latin, Greek, rhetoric, ethics, and religion. Mathematics was taught there occasionally, but at the end of 1573, the cardinal Dom Henrique asked the Jesuits to include in their curriculum the study of subjects related to navigation. The agreement was only fulfilled many years later, under the Spanish domain. João Delgado became the first mathematics teacher of Santo Antão, starting in 1590 with the *aula da esfera* (lessons on the sphere) (Leitão 2008). He was sometimes substituted by another priest, Francisco da Costa (1567–1604). Several manuscripts of Delgado's courses have been preserved, some of them on astronomy (especially Sacrobosco and Peuerbach), but also including astrology (Silva and Ferreira 2008, 103–08). The manuscripts of Francisco da Costa that have been preserved show that he lectured on geography and hydrography—that is, the science of navigation (Silva and Ferreira 2008, 113–20). The mathematician Christoph Grienberger (1564–1636), who had also studied under Clavius, also taught at the Colégio de Santo Antão in the period 1599–1602, returning afterwards to Rome. Hence, from 1590 onwards, the Jesuit Colégio de Santo Antão in Lisbon became an outstanding center for the study of mathematics, and especially astronomy (Leitão 2008).

#### **4 André Do Avelar's** *Reportorio dos tempos*

After the disappearance or death of King Sebastian I (1554–1578) during the battle of Alcácer Quibir, his great-uncle, Cardinal Henry (1512–1580), assumed the throne. His death led to a succession crisis, and the Portuguese crown was seized by the Spanish king Phelippe II (1527–1598). He was called Phelippe I in Portugal, where he was king from 1581 to his death. During his reign, the University of Coimbra received new statutes.

They were signed by the king in 1591, with immediate effect. This decree declared as vacant the mathematics chair and established the *modus operandi* for the election of a new professor (called "lente," or reader). The new statutes of the

2 Jesuit priests sent to distant places as missionaries were required to study mathematics (astronomy, geography, cartography etc.). For more information, see (Baldini 1998, 196–203).

university required that candidates for the chair of mathematics should read two lessons, one about Euclid and the other on the theory of the planets (Universidade de Coimbra 1593, fol. 77r).

There was only one candidate for the job: André do Avelar. In January 1592, he was examined and presented his lectures, and the selection commission decided to bestow him the chair of mathematics, because there was no other candidate ("opositor," that is, opponent) and because he was "one of the greatest men in this science" (Almeida 1967, 47–48). The university Dean ("Reitor"), who played a part in the decision, was Dom Fernão Martins Mascarenhas (1548–1628); he later became the General Inquisitor of Portugal in 1616 (Martins 2011).

Who was André do Avelar at this time? The documentation of his selection only states his name (penned as "Andre dauellar"), that he was poor (so that the university would have to pay his taxes) and a "foreigner" (probably meaning that he was not from Coimbra). Also, the selecting commission knew that he was knowledgeable in mathematics (de Almeida 1967, 47–48).

Very little is known about his life previous to his entrance into the University of Coimbra.3 Most of the available biographical information about him comes from the documents of the Inquisition.4 He was born in Lisbon in 1546 to a family of converted Jews ("cristãos-novos," or New Christians). His father was called Galás do Avelar, and his mother was Violante Fernandes. He had four brothers and three sisters. He studied in Salamanca and Valladolid, obtaining the degree of Master of Arts; he also studied theology. He married Luiza de Faria, and they had six children, three sons, and three daughters (Baião 1919, 134–35).

We have no information about his way of living before he became professor of the University of Coimbra, and at that time he was 45 years old. There is, however, a relevant event in this period: in 1585, he published his first book (Fig. 10.2), called *Reportorio dos tempos*—an untranslatable title; it means something along the lines of a repertory or collection of information concerning time.

This is a peculiar work, belonging to a category of books on astronomy, calendars, and astrology, which became common in Spain and Portugal from the late fifteenth to the early seventeenth century (da Costa 2007, 75–79). They usually received the names *Chronographia* or *Reportorio dos tempos* (or *Reportorio de los tiempos*, in Spanish). They were different from the almanacs found all over Europe in several respects. They were large books (sometimes with a few hundred pages), not cheap and disposable items; they were intended to function as general nontechnical treatises of permanent significance. They were always written in vernacular in order to reach a wide public. The oldest example was Andrés de Li's *Reportorio de los tiempos*, published in Zaragoza in 1495. This small work was printed several times in Spain and in Portugal, where it was translated and improved by Valentim

3There is only one publication describing Avelar's life (de Almeida 1967) and, although it transcribes relevant documents, it is very sketchy and does not deal with Avelar's religious involvement and the Inquisition process.

4Avelar presented his biographical information to the Inquisition on March 23, 1620 (Braga 1892– 1902, vol. 2, 603–04; Baião 1919, 134–35).

**Fig. 10.2** Title page of André do Avelar's first book, *Reportorio dos Tempos*. Notice that it contains an emblem very similar to the one that was published in his *Sphaera*, in 1593. From (da Costa 2007)

Fernandes (died ca. 1518). It inspired successively larger works with similar titles and content, the most famous being Jerónimo de Chaves's (1523–1574) *Chronographia o reportorio de los tiempos.* The last known works of this type were composed in Portugal by Manuel de Figueiredo (1568–1630) and in Spain by Rodrigo Zamorano (1542–1620).

This highly popular class of works represents a nice example of a blend combining various approaches and interests (Cardoso and Martins 2018). Its chronological part included information required by priests to calculate the religious calendar and the correlation between the hours of each weekday and the planets, according to astrologers; it described the division of day and night in natural and artificial hours; the heavenly spheres, and the astrological influence of each planet; the Zodiac was described both from the point of view of its influence on the sublunary world and

regarding the details of the sun's motion along the ecliptic, and the duration of the days and nights. This kind of work included a fairly detailed description of the universe and its parts, of the heavenly circles and their terrestrial counterparts, introducing the zones and climes. The religious calendar, with the names of Catholic saints connected to each day, was combined with recommendations concerning what should be done or avoided in each lunar phase, for each month. A considerable part of the book was devoted to astrological medicine, explaining the four humors and temperaments, and the astronomical choice of treatments according to the temperament and the configuration of the heavens. Eclipses were described both as purely astronomical phenomena, providing tables of their occurrences, and as astrological causes of storms, wars, and other calamities. The treatises dealt with the influence of the moon on the weather and on crops, and they sometimes presented information concerning navigation and tides.

The encyclopedic character of works of this kind shows that it was not aimed at a particular public with a specific interest—indeed, any person of that time could profit from reading some part of the book. This circumstance probably explains the wide circulation and popularity of those works.

André do Avelar's *Reportorio dos tempos* was not an exception; it was typical for that kind of literature. As with many other works of this type, it drew heavily from earlier *Reportorios* without citing them. However, the author also consulted many other calendrical, astronomical, and astrological works, besides books on geography and navigation, to update and improve his own composition. In the successive editions of his book, Avelar always added new information. The first edition (do Avelar 1585) had 297 pages, from the title page to the end of the work; the fourth edition (do Avelar 1602) had 575 pages, with a slighter larger mean number of characters per page. Hence, the fourth edition was about twice the size of the first one.

Avelar's *Reportorio dos tempos* was described by some authors as a mere Portuguese translation of a similar Spanish book called *Chronographia, o, Reportorio delos tiempos, el mas copioso y preciso que hasta agora ha salido a luz*, by Jerónimo or Hieronymo de Chaves. This was the most successful book of its kind. It was first published in 1548 and was reprinted twelve times in the sixteenth century, seven times as a posthumous publication. There are, of course, many similarities in content between Avelar's book and Chaves's work, as was the case with analogous publications of the time. The charge of plagiarism was dismissed, however, by a careful comparison between the two works done by Adalgisa Botelho da Costa (da Costa 2007, 81–143).

The full title of Avelar's book contained a misleading advertisement: the most copious that has hitherto been brought to light ("o mais copioso que ate agora sahio a luz"). As a matter of fact, it was smaller than Chaves's *Reportorio*.

The first edition of the book was dedicated to Dom Manoel de Castelbranco, or Castello Branco (1560–1614), Second Earl of Villa Nova de Portimão (Avelar 1585, fol. IIr). Several members of this family, including Manoel, participated in the Battle of Alcácer Quibir (1578) when the King of Portugal Sebastião I (1554–ca. 1578) was killed or disappeared. Manoel was then 17 years old and was captured by the moors. Afterwards he was released and returned to Portugal. His father, Dom João, and his grandfather, Dom Martinho, died in this battle (Bayão 1737, 706).

Why did Avelar dedicate his book to this young earl? The inscription found on the book does not elucidate this. It only mentions that the Castelbranco family had "many titles of honor and greatness." We may presume that Avelar knew Dom Manoel personally, because it was not acceptable to dedicate a work to a person without his or her permission. It is also likely that the subject of the book had some significance to the earl. A single source describes Dom Manoel de Castelbranco as a "distinguished mathematician" (*Encyclopedia e Diccionario Internacional* 1933, vol. 4, 2264) and Diogo Barbosa Machado stated that "he applied himself exceedingly to the study of mathematical disciplines" (Machado 1741–1759, vol. 3, 217–18).5 Was he a private student of André do Avelar? Was Avelar his astrologer? Any further interpretation of their relationship would be mere guesswork.

The context of the composition and publication of Avelar's *Reportorio dos tempos* is not evident. In his preface, he tells a tale about Diogenes the Cynic (ca. 412–323 BCE) to justify why he wrote the book:

There was a time when it was said that King Philip of Macedon would come with his army against the city of Corinth. All the dwellers of that city, in a hurry, became busy with all the things that were necessary for its defense. Some refurbished arms, others carried stones, some mended old walls, others strengthened towers and places to fight. But Diogenes, seeing the hustle and care of that people, and having nothing to do because nobody gave him any occupation, put his cloak over his arms and, in a hurry, began to roll his tub up and down the Craneum mount.6 One of his friends asked him why he was doing this, and he answered: I also move and roll my tub, so that among all those who are busy and hurried, I do not remain the only idle one, having nothing to do. I [André do Avelar] say this because facing this multitude of writers and books that every day come to light, I should not be the only one who does not do his part, as Diogenes intended with his tub. Farewell. (Avelar 1585, fol. IIv)

This story about Diogenes was not invented by André do Avelar; it was reported by Lucian of Samosata (ca. 125–180), in his work "The way to write history," where the anecdote is introduced to provide Lucian's own support for writing that work (Lucian 1905, 110). Of course, this is not an adequate justification for writing and publishing a book; it could only be an excuse for some useless occupation. Why did Avelar present Diogenes as his prototype? Did he see himself as a philosopher? Was he really as idle as Diogenes, having no job and nothing to do? No, we know that he was married and had already one daughter (Tomásia) to take care of (Carvalho 1990, 333). Perhaps the true motive for writing the book was an attempt to get some money. And the book was successful indeed, as it underwent four editions (do Avelar 1585, 1590, 1594, 1602).7

5The Jesuit priest António de Castello Branco, who imparted lessons on the *Sphaera* at Évora in the decade of 1580 (Baldini 1998, 235) was not his relative.

6Avelar wrongly understood the *Craneum* as a mount. It was a gymnasium, that is, a place for physical exercise.

7The website of the University of Coimbra described and made available for download a book published in 1590, with the title: "Reportorio dos tempos muito curioso acrescentado e emendado de nouo…conforme a noua constituição do sanctíssimo Papa Sixto quinto que tirou os abusos," attributing it to André do Avelar. The book was published in Coimbra by António de Barreyra, the

A large part of the book was concerned with astrology. Judicial astrology, that is, the prediction of future events in the life of a single person, had been condemned by the Roman Church because it was understood as conflicting with human free will (Chap. 3). Avelar was well aware of that, and at the beginning of the book he added a proem, which stated: "understanding that everything that be said of the properties of the signs and planets will not remove the freedom of man, nor win over free will, nor bring necessity to human activities; and the whole [content of the book] is subject to correction in obedience to the sacred motherly Roman Church" (do Avelar 1585, fol. IIv).

As stated before, Avelar's *Reportorio dos tempos* is not a mere translation of the similar work published by Jerónymo de Chaves. It seems to have drawn information from a variety of sources, and this leads us to a relevant question: How did Avelar have access to the books he needed, since he and his family were not rich? There were no public libraries in Portugal at that time. The university library had moved to Coimbra. In Lisbon, where Avelar lived, there were only libraries belonging to wealthy families, rich professionals (such as physicians), and those of religious institutions. Therefore, we may assume that he had access to some of these. From the dedications of his books, we may guess that he had access to the libraries of noblemen.

The second edition of the *Reportorio dos tempos*, published in 1590, was dedicated to Dom Álvaro de Lencastre (1540–1626), third Duke of Aveiro. At the begining of Avelar's inscription to the Duke of Aveiro, there is a relevant piece of biographical information:

Last year (when I bade farewell to your excellency to read on the chair of mathematics at the University of Coimbra by order of his Majesty) I promised to your excellency that any of my works that was first brought to light would be put under your protection and support. However, I had a different intent, that of [dedicating to you] the books on the *Sphaera* and its use, that I have [ready] to print at the said University. Nevertheless, in the mean time, as I should not be idle to the curiosity of the mathematical studies [não me soffrendo estar occioso a curiosidade do studo Mathematico], and, on the other hand, desiring to show to your excellency a first gesture [towards fulfilling] this offer and promise, I made in this recast of the treatise on the times [tractado dos tempos] a particular [addition] on the prognostic of the changes of the air, with some principles related both to natural philosophy and to rural astrology, and some brief but compendious rules for sowing, the culture of trees, and the breeding of animals. Besides those reasons, I was impelled [to dedicate this book to you] by seeing that your highness is so fond of the countryside and of its care. (do Avelar 1590, fol. IIv)

printer of the University of Coimbra. This book, however, is not an edition of Avelar's *Reportorio dos tempos*. It is a different work compiled by the printer. Notice that the title page of the 1590 Lisbon edition of Avelar's *Reportorio dos tempos* stated that the printer had received the royal privilege for ten years. Therefore, no one else could publish it during this period. The Coimbra edition contains no declaration of privilege, and the prologue to the reader implies that the printer had produced a compilation taken from different works to compose the book.

The same dedication is reproduced in the third edition of the *Reportorio dos tempos* (do Avelar 1594, fol. IIr). The fourth edition is also offered to the Duke of Aveiro, but it contains a different inscription (do Avelar 1602, fol. A2v).

Hence, André do Avelar was already teaching mathematics at the University of Coimbra in 1589 (and maybe before that year), although he only became a regular professor ("lente") in 1592. The above citation also shows that in 1590 Avelar had already written his *Sphaera*, probably intending to use it at the university, since it was ready to be printed there.

The citation also exhibits a friendly relationship between Avelar and the Duke, once more suggesting that he was on good terms with some noblemen and could probably profit from their favors and access to their libraries. That a dedication to Dom Álvaro de Lencastre appeared in the three editions from 1590 to 1602 (and the last one was not a reproduction of the first) proves that the relationship between them was enduring. It is possible that he also received patronage from the Duke of Aveiro during that period.

Around 1600, Avelar was better known for his *Reportorio dos tempos* than for his *Sphaera.*

#### **5 "Flectimur Sed Non Frangimur"**

The first three editions of the *Reportorio dos tempos* and the only edition of Avelar's *Sphaera* have in the title page a peculiar emblem (Fig. 10.3). The same woodcut was used in the three editions of the "Reportorio." The woodcut used for the *Sphaera* (Fig. 10.1) was a bad copy of the Lisbon original.

Venâncio Deslandes (Deslandes 1888, 127) described the emblem and suggested that it was a representation of the four elements. He wrongly transcribed the phrase appearing on the emblem as "non frangimur sed flectimur." (Fig. 10.4).

The emblem of reeds in the water, being bent but not broken, with the motto "Flectimur non frangimur" (we are bent but not broken) or "Flectimur non frangimur unde" (we are bent but not broken by the waves) had been used since the fourteenth century by two Italian families, Colonna and Acquaviva (Gelli 1916, 286–87). In the fifteenth century, the Pope Alexander VI, born Rodrigo de Borja (1431–1503), banished from Rome the Cardinal Giovanni Colonna (1456–1508) and other members of the family, who took refuge in Naples and Sicily. They then assumed the emblem again (Fig. 10.4), and this was meant as a warning: although the Colonna family was bent by pontifical persecution, the Pope should not consider them dead and buried; they were still alive and powerful, and hoped sooner or later to grow even stronger than before and get pay back (Gelli 1916, 287; Palliser 1870, 73–74). Both the emblem and its history were well known in the sixteenth century and were included in the work "Symbolorum & emblematum" of Joachim Camerarius (1500–1574) under number "95" (Camerarius 1590, fol. 97r).

**Fig. 10.3** Title page of the third edition of André do Avelar's *Reportorio dos tempos*. From (do Avelar 1546). Courtesy of the National Library of Portugal

**Fig. 10.4** The emblem of the Colonna family, with the motto "Flectimur non frangimur undis." According to Mrs. Bury Palliser, the emblem was created by Jacopo Sannazaro (1458–1530). From (Palliser 1870, 74). Public Domain Mark

Why did Avelar incorporate this emblem in his books? Had he suffered some personal persecution? Did he hope to rise from a defeated, humble condition to a higher one? Lack of knowledge about his personal history prevents us from giving any well-founded answer. However, one may conjecture that the emblem was related to his family situation: they were of Jewish origin, and there was a social stigma oppressing this class. As is well known, all Jews had been expelled from Spain in 1492, and from Portugal in 1497. Any Jew willing to remain in Portugal after that time was compelled to become a Christian. The pejorative name "New Christian" was applied to those Jewish converts and to their posterity. Perhaps Avelar yearned for a time when the New Christians would rise once more to their deserved social status or would be allowed to become Jews again.

#### **6 Avelar's** *Sphaera***8**

The only edition of Avelar's *Sphaera* was published in 1593, the year after he became the official reader of mathematics at the University of Coimbra. The title of the book is highly peculiar: *Sphaerae vtrivsq[ue] tabella, ad sphaerae huius mundi faciliorem enucleationem*, meaning "Tablet of both spheres, for easier explanation of the sphere of this world." Here, "tabella" does not mean "table," but a little board or tablet. In the aforesaid title, it meant a summary or abridgment. The word appeared with the same meaning, for example, in the title of one of the books of Louis de Blois (1506–1566): *Tabella spiritualis alias sacellum animae fidelis nuncupata: continens brevem institutionem vitae Christianae* (de Blois 1583). However, Avelar's book cannot be interpreted as a summary of Sacrobosco's work, because it is indeed larger than the medieval treatise. It could be understood as a short version of the *Sphaera* only when compared to the large commentaries that had become usual by the end of the sixteenth century.

The phrase "both spheres" (*sphaerae utriusque*) used in this book was unusual. The only astronomical work I have found with a title that might have inspired Avelar was *De mundi et sphaerae: ac utriusque partium declaratione cum planetis et variis signis historiatis* by Gaius Iulius Hyginus (ca. 64–17 BCE), which was printed several times in the sixteenth century.

Avelar's *Sphaera* was dedicated to Dom Ferdinando (or Fernão) Martins Mascarenhas, the Dean (*Reitor*) of the University of Coimbra and adviser of King Phelippe who became General Inquisitor two decades later. After the dedication, the author addressed the students of mathematics that comprised his intended public. After that, we find several poems dedicated to the readers and to the author of the book by the priest António Velloso of Braga; by Pedro Mendes, professor of Latin and Greek; and by Dom Jorge de Castro (do Avelar 1593, fol. IIr–VIr). Unfortunately, it was impossible to find information about them.

Avelar's *Sphaera* does not cite the name of Sacrobosco at any point, although he closely follows the medieval text. Of course, every reader knew that the book was a new version of Sacrobosco's, therefore Avelar could not have held the expectation of being regarded as the original author of the ideas contained in the book.

Many of the commentaries on the *Sphaera* contained Sacrobosco's full original text, set in a clearly distinct typography and intermixed with elucidations. That was the style followed, for instance, by Pedro de Espinosa,9 a professor of the University of Salamanca, who published a Latin commentary on Sacrobosco that underwent two editions (1535, 1550), a commentary that might have been read by Avelar when he was a student (de Espinosa 1550). The famous and massive commentary produced by Christophorus Clavius (Lattis 1994) also followed the same structure. Avelar, however, did not follow the example of those predecessors. It is simply

8This following section is an expanded and corrected version of (Martins 2003b).

9The name "Pedro de Espinosa" was rather common in Spain in the early sixteenth century. There is no reliable information about the dates of birth and death of the author of this commentary on Sacrobosco (Díaz Díaz 1987, v. 3, 68–69; Delgado 1983).

impossible to identify, by any typographical hint, where he was simply transcribing Sacrobosco's text and where he was presenting his own contribution. Indeed, the style of Avelar's book is that of a paraphrase of Sacrobosco's *Sphaera*.

Sacrobosco started his first chapter with definitions of the geometric sphere by Euclid and Theodosius (347–395). Avelar referred initially to the "material sphere," that is, the armillary sphere, the instrument used to explain the structure of the universe. Immediately afterwards, however, Avelar applied Theodosius's definition to that sphere and introduced the concepts of axis and pole exactly as Sacrobosco had done. In the citations shown below, the corresponding parts are underlined.

The underlined parts show that Avelar, for the most part, just copied Sacrobosco's text without substantial changes. Differences concerning the order of the words, punctuation, and even changes to some terms are not noteworthy, since similar differences appeared in different printed editions of Sacrobosco's own text.

After the definition of the sphere, Avelar presented the main circles of the heavenly sphere, a subject that appeared only at the second part of Sacrobosco's text. The explanation of the greater and smaller circles is slightly different.

André do Avelar did not follow the text of Sacrobosco and did not treat it as a sacred or immutable astronomical revelation. The original *Sphaera* was, of course, his point of departure, but he felt free to produce his own work. In this respect, his approach was uncommon, although there had been several precedents, including Galileo Galilei's (1564–1642) unpublished textbook on the *Sphaera* (Galilei 1656; Martins and Cardoso 2008; Martins and Cardoso 2017).

Avelar's book was divided into four parts like Sacrobosco's work, and it included essentially the same content, but with an inversion of the order of the first and second parts. The first part of Avelar's *Sphaera*, "On the material sphere and the circles of which it is composed," containing twelve chapters and one table and occupying nine numbered leaves, presented the main circles of the celestial sphere and their terrestrial counterparts. The sequence and content are almost identical to the second part of Sacrobosco's *Sphaera*, with some slight differences. For instance, Avelar used 23° 30′ for the obliquity of the ecliptic, a better estimate, at that time, than Sacrobosco's value of 23° 33′.

The second part, called "On the sphere of the world, or natural [sphere], and its parts," was divided into eighteenth chapters and one table, filling forty-five numbered leaves. It is similar to the first part of Sacrobosco's book, but some parts were put into a different order. For instance, Avelar discussed the size of the earth before presenting the celestial structure (ether, motions, and form of the heavens). He mentions the theory of trepidation and the need for ten heavenly orbs, instead of the nine mentioned by Sacrobosco, following, at this point, the proposal that had been introduced by King Alphonso X, el Sabio (1221–1284). Besides this change, Avelar added some quantitative data and some tables. One of them provides the declination of the sun throughout the year, essential information for the determination of latitudes. There are other relevant differences. Avelar introduced several mentions of the *Astronomica* of Marcus Manilius (fl. 1st century), a book that was seldom cited in commentaries on Sacrobosco's *Sphaera*. The outlook of Manilius's work was mainly astrological, and references to his contribution betray Avelar's deep involvement with astrology. Accordingly, in the second part of his *Sphaera* he presented some astrological information about the signs and established relationships between the four elements, the four humors, the seasons, and the four ages of mankind. This part of the book also mentions new information that became available because of the Iberian navigations, such as knowledge of the Southern Cross (Fig. 10.5), dark nebulae, the Magellanic Clouds, and a new evaluation of the size of the earth.

The third part of Avelar's *Sphaera*, containing fourteen chapters and several tables encompassing thirty-nine leaves, closely follows the structure and the content of Sacrobosco's third chapter. It deals with the rising and setting of the stars and constellations, the yearly motion of the sun, the diversity of duration of days and nights, and the climates. Avelar added to this part some quantitative tables, one of them showing the degrees of the equinoctial corresponding to each of the zodiacal signs, both in the case of the right sphere and the oblique sphere and, in particular, for the latitude of Lisbon. In his discussion of the climates, Avelar stated that Claudius Ptolemy (died 160) had described twenty-one parallel circles and seven climates, but the recent authors had introduced twenty-three climates and fourtynine parallel circles. He provides a table with the data for those climates and the

**Fig. 10.5** Representation of the Southern Cross ("Cruzeiro") and the Magellanic Clouds, according to Avelar. From (do Avelar 1593, fol. 12v). Courtesy of the Biblioteca Universidad de Sevilla

variation of daylight length during the year. Following Sacrobosco, Avelar presents copious literary citations from Publius Vergilius Maro (70–19 BCE), Publius Ovidius Naso (43 BCE–18), and Marcus Annaeus Lucanus (39–65).

The fourth and last part of Avelar's *Sphaera* is quite short: six chapters and a few tables, encompassing eleven leaves. Like Sacrobosco's fourth chapter, it deals with the motions of the sun and the moon, of the planets, and of the eclipses. Avelar provided a more detailed theory than Sacrobosco, mentioning the contributions of Alphonso X and presenting data relative to the motion of the moon.

#### **7 The Sources of Avelar's** *Sphaera*

André do Avelar certainly consulted other works besides Sacrobosco's to write his *Sphaera*. It is difficult, however, to find out which sources he used. Part of this difficulty is due to Avelar himself, who did not have an inclination to name his authorities. It is possible to notice this tendency in his *Reportorio dos tempos*: Chaves had provided a number of references in his *Chronographia o reportorio de los tiempos*, but Avelar did not reproduce this information, even in the cases where he was clearly translating Chaves's book (da Costa 2007, 91–93). Note that in the late sixteenth century, several authors of academic books provided specific references to authors, the title of their works, and their relevant parts or chapters. Sometimes those references appeared inside the text, but there was an increasing use of marginal notes, the

antecedent of our footnotes. One may find a profuse employment of this kind of resource in the *Comentarii Conimbricensis*, the commentaries about Aristotle's works produced by the Jesuit teachers of Coimbra (Casalini 2017).

In his *Sphaera*, Avelar usually only reproduces the meager information contained in Sacrobosco's work: vague allusions to Aristotle, Ptolemy, Alfarganus (805–870), and other authors, without any hint as to which books the stated ideas are drawn from. He did, however, mention a few other authorities. One of them was king Alphonso X (1221–1284) (do Avelar 1593, fol. 26v, 96v), who was never cited by Sacrobosco, since the *Sphaera* was written earlier. Because of the importance of Alphonso X as a reformer of medieval astronomy, he was cited in many of the commentaries on the *Sphaera*. It was natural, therefore, that Avelar should include this authority in his book.

Another author cited by Avelar but not by Sacrobosco was Marcus Manilius, who is explicitly referred to in four distinct passages (do Avelar 1593, fol. 10v, 21r, 30r, 34r). The sixteenth century commentaries on the *Sphaera* seldom cited Manilius.

Since Avelar's book was composed for use at the University of Coimbra, it could completely avoid subjects related to navigation such as the tables of declination of the sun, used for ascertaining the latitude. This was an expected subject in the teaching of the *cosmógrafo-mor* or at the *aula da esfera*, but not at the universities. However, he did include such information, as well as data provided by navigators. He did not point out, however, which sources he used to describe the Southern Cross and the Magellanic Clouds (do Avelar 1593, fol. 11v–12v). At another point, he remarks on the visible signs of Earth's roundness and the new measurement of the geographical degree, amounting to 17.5 leagues, as determined by the "navigators of Spain" (do Avelar 1593, fol. 16r–17v).10 He also referred to "more recent" authors who had expanded Ptolemy's division of the earth from seven to twenty-three climes (do Avelar 1593, fol. 88v), but nowhere did he present the source of this information.