The Hidden Praeceptor: - Recherche en IA spécialisée au MIT

The Hidden Praeceptor:
How Georg Rheticus
Taught Geocentric
Cosmology to Europe

Matteo Valleriani
Max Planck Institute for the
History of Science
Technische Universität Berlin
Tel Aviv University

Beate Federau
Max Planck Institute for the
History of Science

Olya Nicolaeva
University of Zürich

A corpus of 360 distinct early modern printed editions (depuis 1472 à 1650)
containing Johannes de Sacrobosco’s Tractatus de sphaera is “dissected” into
a corpus of 540 text-parts, 241 of them re-occurring at least once. Through
the exploration of the data, we recognized a relevant position for four anon-
ymous authors in their social network. We demonstrate that the text-parts
originally assigned to the anonymous authors were authored or edited by Georg
Rheticus. By means of data analysis, we conclusively establish that Rheticus
profoundly impacted the content of such textbooks for the introductory class in
geocentric astronomy all over Europe between 1538 et 1629.

The present research has been conducted in the frame of the project “The Sphere. Knowledge
System Evolution and the Shared Scientiﬁc Identity of Europe” at the Max Planck Institute
for the History of Science (https://sphaera.mpiwg-berlin.mpg.de) and “Images and Conﬁg-
urations in Corpora of University Textbooks” in the frame of BIFOLD (Berlin Institute for
the Foundations of Learning and Data: https://bifold.berlin) (ref. 01IS18037A). We would
like to thank Elio Nenci (Università Statale di Milano) for his invaluable support concerning
the research results presented in the section Anonymous 1538a, parties 1, 2, 3, et 5. We also
would like to thank Insa-Christiane Hennen (Leucorea Stiftung, Wittenberg) for drawing
our attention to the document preserved at the Ratsarchiv Wittenberg. Enfin, nous serions
like to thank Elizabeth Hughes for editing this article.

Perspectives on Science 2022, vol. 30, Non. 3
© 2022 by The Massachusetts Institute of Technology.
Published under a Creative Commons Attribution 4.0 International (CC PAR 4.0) Licence

https://doi.org/10.1162/posc_a_00421

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1. Wittenberg, 1531
A small printer—Joseph Klug (1490–1552)—completed a new printed
edition of the late medieval Tractatus de sphaera by Johannes de Sacrobosco
(1196–1256) and sold it locally for students at the University of Wittenberg
who were attending the Faculty of Liberal Arts (Sacrobosco and
Melanchthon 1531). This event appears, at ﬁrst sight, to be rather irrelevant;
since the ﬁrst printing of the same textbook in 1472, eighty-three editions
were printed, and two other editions, besides Klug’s, were also printed
dans 1531. In truth, cependant, this event started a dynamic that turned
Wittenberg into a place of production of university textbooks, triggering
the production of textbooks of similar content and design all over Europe.
Klug’s 1531 edition is the beginning of the emergence of an “epistemic
community” of textbook editions that became dominant in Europe.

Our research is based on a corpus of historical sources consisting of early
modern printed books that contain, in different forms, a speciﬁc treatise on
cosmology: Johannes de Sacrobosco’s Tractatus de sphaera, a university text-
book used for a qualitative introduction to geocentric cosmology and ﬁrst
compiled at the University of Paris during the thirteenth century. Ce
corpus, moreover, further collects 126 different editions of university text-
books used for teaching the same subject. They do not, cependant, contain
Sacrobosco’s treatise but an introduction to spherical astronomy that
follows the same design as Sacrobosco’s work, discusses the same subjects
in the same order, and at least partially uses the same visual apparatus. Dans
total, 360 different editions were identiﬁed between 1472 et 1650,
and these were printed in forty different places across the continent of
Europe.1

Considering a possible and realistic average print-run of about 1,000
copies for each edition (Gingerich 1988), the corpus is representative of
environ 350,000 university textbooks that circulated and were used
by students over the course of 180 years across Europe. Because Sacrobosco’s
text was the most common for an introductory class in astronomy, we can
consider this corpus as representative of the basic knowledge in astronomy
possessed by the educated citizens of Europe during the early modern

1. The corpus has been collected for the project “The Sphere. Knowledge System Evo-
lution and the Shared Scientiﬁc Identity of Europe” (PI: Matteo Valleriani). The collection
is available online through the project website: https://sphaera.mpiwg-berlin.mpg.de
(accessed March 4, 2021). For the function of this treatise and how it transformed over
the centuries (see Valleriani 2017). For a description of the corpus concerning the printing
locations of the editions, their book formats, their printers, and publishers, as well as their
langue (see Valleriani 2020b).

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temps. The investigation of such a corpus of sources and, in particular, le
reconstruction of the transformation processes the content of such textbooks
underwent allows us to understand the evolving formation of a common
scientiﬁc identity in Europe as produced by the growing network of
universities.

A previous study ( Valleriani et al. 2019) has shown that, starting
entre 1531 et 1538 (Sacrobosco and Melanchthon 1538), Wittenberg
was able to put two new, distinct editions of Sacrobosco’s treatise on the
market that were “observed” and copied at least partially all over Europe.
Autrement dit, the Wittenberg astronomy textbooks were so widely imi-
tated that their content can be regarded as fully hegemonic all over
Europe.

Both Wittenberg editions of 1531 et 1538 were printed by the same
printer, Joseph Klug, who was particularly close to Philipp Melanchthon
(1497–1560) at that time and published many of the Reformer’s major
theological works. The reason that the Wittenberg editions became so sig-
niﬁcant can be understood through the content of the textbooks themselves
as such textbooks typically contained not only the fundamental treatise of
Sacrobosco but also further treatises or fragments thereof, paratexts, et
commentaries.

Le 1531 edition of Sacrobosco was printed and sold together with
Melanchthon’s famous letter to Simon Grynaeus (1493–1541). This open
letter, which served as an introduction to the work, was a defense of astrol-
ogy and encouraged his students to study cosmology and astronomy. Comme
several historical case studies have shown, this letter became well known
internationally and trans-confessionally, and was republished many times
in conjunction with scientiﬁc astronomical works (Pantin 1987; Lalla
2003; Reich and Knobloch 2004). In our corpus alone, this letter can
be found in ﬁfty-eight different editions. In the book, after the letter, stu-
dents could ﬁnd Sacrobosco’s original and uncommented text immediately
followed by another short composition of Melanchthon. In this case it is a
four-verse epigram, De triplici ortu et occasu siderum. The students could
learn it by heart and thus never forget that there are three ways to consider
the rising and setting of the stars: the cosmical, the heliacal, and the achro-
nic.2 Finally, the work concluded with a fragment (Book 3, Prop. XXII) de
the even more famous Epitome of Johannes Regiomontanus (1436–1476)

2. The heliacal and cosmical rising and setting of a star take place before and after it
has been in conjunction with the sun, respectively from visible to invisible and vice versa.
The achronic rising or setting of a star takes place after sunset.

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on Ptolemy’s Almagest.3 This proposition offers deeper insight into the
causes of the different lengths of the days and nights throughout the year.
It was reprinted eighty-seven times alone in our corpus and was obviously as
widespread as the Epitome itself. What was peculiar in this editorial initiative
is that all three accompanying texts were published in this form and
appended to Sacrobosco’s text for the very ﬁrst time. The strikingly innova-
tive character of this edition was further enhanced by the then still unusual
format for textbooks, the octavo, which quickly became a standard format all
over Europe. Klug reprinted the same work in 1534 and reissued the 1534
edition in 1536 (Sacrobosco and Melanchthon 1534, 1536).4

Dans 1538, cependant, he produced a new edition that at ﬁrst glance appears
to be an enlargement of the previous ones. Beside the aforementioned
texts, it also contains a fragment of al-Farghānī’s (d. 861) (Differentia
XXIIII ) Brevis compilatio astronomica in which the subject of the rising
and setting of the planets is discussed; another open letter by Melanchthon
addressed to Achilles Pirmin Gasser (1505–1577), prefatory to the ensu-
ing text; Sacrobosco’s Computus ecclesiasticus; and a Cisiojanus.

Sacrobosco’s Computus is a calendrical work used to teach students how
to calculate the days of the movable feasts of the liturgic calendar in
advance. It was very widespread during the thirteenth and the fourteenth
centuries and always used together with the work De sphaera. In the corpus
of the printed textbooks containing De sphaera, this edition represents its
ﬁrst appearance. The Cisiojanus is a typical medieval work on calendric sys-
tems as well, in this case a mnemonic-mechanical aid for remembering the
non-movable feasts. It consists of a series of verses to be learned by heart
that apparently make no sense unless each syllable is used as an acronym
for days and saints of the liturgical calendar (Kully 1974).

Melanchthon’s letter to Gasser is particularly relevant for our argument
because the theologian informs us that it was actually Georg Joachim
Rheticus (1514–1574) who came up with the idea of inserting Sacrobosco’s
Computus into the 1538 edition.

Al-Farghānī’s fragment was also printed in this edition for the ﬁrst time
in the corpus, which serves as evidence of the initiative to insert a series of
innovations into the corpus in two steps represented by the two editions.
In the second step, with the exception of Melanchthon’s letter to Gasser,
the texts were only considered new because they were printed together
with De sphaera for the ﬁrst time. En fait, they were originally produced

3. Regiomontanus’ Epitome was written in 1463. Its ﬁrst print was (Regiomontanus

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1496).

the ﬁngerprints.

4. We identiﬁed the 1536 edition as a reissue of the 1534 edition through comparing

Perspectives on Science

411

between the ninth and the thirteenth centuries. As we have shown else-
où (Valleriani et al. 2019), it is by means of this second step that
Wittenberg achieved high visibility, causing the 1538 edition to become
un modèle.

Looking closer at the 1538 travail, cependant, there is another relevant dif-
ference. This is shown by the fact that the original text of Sacrobosco has
been changed and especially enriched. The new text is not a standard com-
mentary and no commentator is indicated. This re-edited original text of
Sacrobosco is one of the key elements that became most widely imitated in
the model.

Further studies of ours (Zamani et al. 2020) have shown that the pro-
duction of Wittenberg remained a model for over thirty years, tandis que le
edition was continuously updated especially with reference to its visual
apparatus and was produced by different printers in close contact to each
other.5 In this respect, we were able to identify what we call the great
transmitters. These are editions of the corpus that, after a series of innova-
tion, had a lasting impact until the end of the period under consideration.
More speciﬁcally, we have identiﬁed the period of innovation to be
entre 1531 et 1549. If such editions were reprinted in Wittenberg
within the timeframe from 1549 à 1562, then such editions also main-
tained their impact beyond the ﬁrst thirty years of epistemic dominance of
the Wittenberg model.6

This is the background against which the question concerning the
authorship of such inﬂuential early Wittenberg commentaries emerges.
As those commentaries impacted the content of many other textbooks
and consequently shaped the scientiﬁc identity of Europe, our goal is to
identify the minds behind this transregional phenomenon.

The Authors of the Commentaries

2.
Investigations concerning the authors of the scientiﬁc commentaries and
textbooks of the corpus were hitherto limited to the description of the
intellectual and institutional proﬁles of the more relevant scientists among
eux. Signiﬁcantly, it turned out that all the early modern authors of the
commentaries on Sacrobosco’s treatise, without exception, were involved in

5. A similar result has been recently achieved by a different analysis that focuses on
the production of Wetterbuchlein ( Johnston 2020). An analysis of the distribution of the
paratexts in the Sphaera corpus also reveals that the Wittenberg printers were involved
in a continuous mutual exchange of text-parts ( Valleriani and Sander 2022).

6. Editions could become great transmitters if they were printed in Wittenberg
entre 1549 et 1562, but did not necessarily have to be designed and ﬁrst printed
in Wittenberg like Klug’s editions. Other works ﬁrst printed elsewhere and then adopted
by Wittenberg’s printers also became great transmitters.

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The Hidden Praeceptor

teaching the quadrivium (Valleriani 2020a). Assuming that the inﬂuence
of certain editions over others was due to the prominence of authors of the
commentaries, we looked for a method to identify how authors, printers,
and publishers became aware of other authors and their works. Such aware-
ness is conceived as the condition that allows for authors to exert an inﬂu-
ence or an impact on works of others and therefore for their work to
become a model to imitate. To identify these authors, we used tools of
the social network analysis in the closest possible relation to our analysis
of the historical sources. We ﬁrst considered all authors listed on title pages
of the editions of our corpus. It emerged that no real community could be
identiﬁed because very few of them could have been in contact with each
other. An additional stipulation required that the authors of the commen-
taries had to have been alive at the time of publication. If more than one
living author was listed on each title page, then a potential connection—via
printer and publisher—was possible. With this consideration, only six of
eux (Élie Vinet (1509–1587), Pedro Nuñes (1502–1578), Francesco
Giuntini (1523–1590), Pierio Valeriano (1477–1560), Albertus Hero
(1549–1589), and Philipp Melanchthon) were aware of each other.

We therefore continued by atomizing all the editions into text-parts. UN
text-part is a textual passage that cannot be formally smaller than a para-
graph and covers a well-deﬁned subject with completeness. A text-part in
the corpus of Sacrobosco’s De sphaera, par exemple, is the Theoricae novae
planetarum by Georg von Peuerbach (1423–1461). This text was ﬁrst
included in the Sphaera treatises as early as 1482, and by 1537 it had been
reprinted seventeen times in editions of the Sphaera. If literary
compositions—ordinarily printed in scientiﬁc books beginning in the six-
teenth century—are considered, a text-part can be much more modest in
length. A representative example might be the short carmen written by
Donato Villalta (1510–1560) and dedicated to the scholar Pierio Valeriano
(1470–1560), printed for the ﬁrst time in 1537 and reprinted a further
thirty-two times. Enfin, all the texts constituting the 1531 et 1538 edi-
tions mentioned above are text-parts.

The corpus in its entirety contains 540 text-parts, which we identiﬁed
chronologically by publication date and by investigating their authors
when they were not listed on title pages. By this means we created a
new list of authors of the commentaries that includes not only those cred-
ited on the title pages but all those whose texts were effectively printed in
the editions under scrutiny. In total, they amount to 222.

Then we looked at the recurrences of the text-parts, considering only
text-parts that were published at least twice, with the second publication
released no earlier than the year following the ﬁrst printing. Based on
these criteria, 241 text-parts remained, meaning that 324 text-parts were

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Perspectives on Science

413

published either only once or more than once but in the same year. Le
remaining 239 text-parts recur 1,394 times! Recurrences range from just
1 to a maximum 87.

By considering all the parts and their recurrences and by applying the
same condition mentioned above in order to detect potential communities
of awareness among authors, we created a new social network.7 This net-
work is constituted of thirty-four components, while isolated authors are
ignored. In conﬁrmation of our results from the aforementioned studies,
the main component indeed roughly corresponds to the period of Wittenberg’s
dominance and of the editions that acted as great transmitters. Many of the
authors mentioned in the main component, moreover, were lecturers in
Wittenberg or somehow related to that city (See Fig. 1).

We calculated three different parameters of the network: betweenness
centrality, closeness centrality, and the simple degree values for all the
nodes. Calculating the betweenness centrality identiﬁes those authors
who connect different communities within a component. The closeness cen-
trality tells the distance for each node to all the other nodes of the network;
the higher the value, the more central its position. The degree reveals the
absolute number of edges connected to each node, which in turn tells us
which contemporary authors were most frequently published jointly.

The values related to betweenness centrality show that Vinet and
Melanchthon occupy the highest position followed by two anonymous
authors (Anonymous_1538b and Anonymous_1543b). The closeness cen-
trality values show exactly the same situation, while the degree values
place Anonymous_1543b at the top (132 relations), followed by Vinet
(124 relations), Melanchthon (122 relations), and by Anonymous_1538b
(82 relations).

While the historical roles of Melanchthon and Vinet are well known,
the two remaining anonymous authors have not been identiﬁed to date.
Their texts-parts, which appeared in Wittenberg during the period in
question certainly played important roles. The network moreover shows
the presence of nine additional anonymous authors. Only two of them
are authors of text-parts published in Wittenberg as well. These are Anon-
ymous_1538a and Anonymous_1543a. Their text-parts were published in
the same treatises in which the text-parts of the anonymous authors who
scored high were also published.

7. The datasets used for this network analysis and the one in the section “Rheticus in
the Network of Authors” as well as the data to evaluate its impact in Europe as described in
the last section, are all available at https://doi.org/10.5281/zenodo.4593120 (accessed
Mars 10, 2021) to guarantee the reproducibility of our results.

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414

The Hidden Praeceptor

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Social network visualization of the text-part authors. The network is

Chiffre 1.
not oriented. Betweenness centrality is colored. The tonality of the edge color
changes according to the time: the more recent, the more pronounced.

We hypothesize that the four anonymous authors are all in fact the same
person, namely, Georg Rheticus. A vague but potential clue to support this
theory is given by Rheticus himself in his letter to Paul Eber (1511–1569)
on March 1, 1562 (Burmeister 1968, vol. 3, pp. 162–4). Eber asked Rheticus
on behalf of the publisher Conrad Ruehel (b. 1528) to edit and prepare a
work for printing. In his answer, Rheticus complained that this kind of
task was badly paid, and recounted his experience editing and preparing
the Sphaera and the Computus at the request of Moritz Goltz (1495–1548).
The latter was a bookseller and publisher who had founded a publishers’
association together with Bartholomäus Vogel (1504–1569), and Christoph
Schramm (d. 1549) in Wittenberg in 1533. From a document preserved
at the Ratsarchiv Wittenberg (RatsAWB 113 (Bc101), Gerichtsbuch
1523–1551, fol 133r), we know that Schramm, and therefore Goltz’s

Perspectives on Science

415

publishers’ association, was indeed one of the ﬁnancial sponsors of Joseph
Klug.8 Therefore, we consider it plausible that Rheticus was referring to
his own editorial work on the 1538 edition.

In support of this hypothesis, we will analyze in the following the con-
tent of the text-parts of such anonymous authors in order to infer their
identité. In conclusion, we will analyze in detail their impact on textbook
production in Europe. We begin with the re-edited Tractatus de sphaera
mentioned by Rheticus himself. This was re-edited twice and published
correspondingly in 1538 et 1543. In both cases, the author of the work
on the Tractatus is not declared, and therefore we assigned authorship ﬁrst
to Anonymous_1538a and Anonymous_1543a.

3. Anonymous 1538a
Anonymous 1538a is the scholar who reworked the Sphaera of Sacrobosco
printed by Klug in 1538. Dans la rubrique suivante, we will show why we
believe that this scholar was Georg Rheticus, the scientist who went
down in history for bringing Copernicus’ De revolutionibus to press. Ce
assumption is, in fact, not completely new. Four other scholars have
already advanced this hypothesis (Burmeister 1968; Rosen 1974; Kraai
2003; Pantin 2020). Their assumption is based on the established fact
that Rheticus was appointed as a lecturer at the University of Wittenberg
et, as such, was indeed teaching De sphaera. En particulier, Jesse Kraai
bases his assumption on a manuscript of Rheticus’ pupil Nicolaus Gugler
(1521–1577) that contains notes of two Sphaera classes held by Rheticus
entre 1536 et 1538 (Guglero 1536–1538, 1r–37r). The conclusions
reached by these four scholars, cependant, are based on general assumptions
and not on close readings of the commentary at hand. De plus, they did not
consider the further anonymous works contained in the same treatises, as we
will do later in this paper. Enfin, and possibly more relevantly, the previous
scholars did not notice the impressive impact that such anonymous texts had
all over Europe, as it will be shown in the ﬁnal section of this work.

Dans la rubrique suivante, we would like to enrich the general plausible
arguments of the previous scholars with a series of new pieces of evidence

8. The editor of the Rheticus correspondence, Karl Heinz Burmeister, came to the
conclusion that Rheticus was referring to the 1550 edition of the Sphaera published by
Krafft. He based his argument on the fact that the publisher Conrad Ruehel, who asked
Rheticus through Eber to edit some works in 1562, was apparently also an accountant at
Kraftt’s print shop during those years. But Rheticus referred to Goltz when he mentioned
the work on the Sphaera and the Computus, and Goltz was already deceased by 1548. Pour
Goltz’s commercial and ﬁnancial activities (see Hennen 2022; Limbach 2022).

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resulting from the close reading of the historical sources. We shall start by
analyzing the textual additions of the 1538 edition in comparison to that
de 1531.

The First Addition

3.1.
The ﬁrst addition is at the beginning of the treatise and is made in the text
ﬂow, as if it were part of Sacrobosco’s original text. It concerns Euclid’s
deﬁnition of the sphere from the fourth century BCE. The interesting
aspect here is that the deﬁnition is added in Greek. We believe that this
addition was a consequence of the 1533 ﬁrst Greek (with Latin transla-
tion) printed edition of Euclid’s Elements, which was prepared by the
aforementioned Grynaeus on the basis of two manuscripts provided by
Lazare de Baïf (1496–1547) and Joannes Ruellius (1479–1537), aussi
as of Bartolomeo Zamberti’s (1473–1543) Latin translation published in
1505 (Grynaeus 1533). The proposition added to the Sphaera has exactly
the same wording of Book 11, def. 12 of Grynaeus’ edition. More importantly,
the same Rheticus prepared a Greek edition of Euclid’s Elements (Rheticus
1549) with a Latin translation of Joachim Camerarius (1500–1574),
although he only edited the ﬁrst six books. But we know from Camerarius’
dedicatory letter that the work, according to humanistic precepts, était
intended both for the study of the Elements and of ancient Greek; un
approach that may have animated Rheticus to accomplish this addition
dans 1538.

The Second Addition

3.2.
The second textual addition, printed at the margin, is concerned with
Proclus’ (412–485) commentary on Hesiod’s Works and Days (verse 565)
from the seventh or eighth century BCE. The passage in question is added
where Sacrobosco discusses the achronic setting of the stars by using exam-
ples from the works of Ovid (b. 43 BCE) and Virgil (70–19 BCE). The mar-
ginal comment offers an example from Hesiod (the star Arcturus) and points
to the beginning of Proclus’ commentary, where it is mentioned that the
astronomers developed the achronic method to understand this speciﬁc
passage of Hesiod which “presumably” refers to sixty days after the winter
solstice (Marzillo 2010, pp. 208–9). This comment seems to point to the
authorship of Melanchthon rather than of Rheticus, as the former explic-
itly quotes this work of Hesiod in his letter to Gasser (though not the same
verse) and wrote an entire commentary on that speciﬁc work of Hesiod,
which was published in 1532 (Bretschneider and Bindseil 1843–1860,
vol. 18, cols. 158–274). Cependant, a few clues, which will be discussed
in the section about the work of Anonymous 1543b, seem to justify the

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possibility that Rheticus might be the author of this comment, aussi,
although Melanchthon’s inﬂuence is undeniable.9

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417

The Third Addition

3.3.
The third textual addition, another marginal printed comment, refers to
al-Farghānī’s Compilatio astronomica (Differentia VIII). The comment lies
next to Sacrobosco’s discussion of the length of the Earth’s diameter. Dans
the comment, the measure of space for each degree of longitude (56 milliaria
et 1/3) is added together with the source from which this information is
extracted: “ex Alfragano.” Indeed, exactly the same value is given in the
Latin version of al-Farghānī’s introductory work on astronomy. This work,
divided into thirty chapters (differentiae), was a non-mathematical introduc-
tion to the Almagest by Ptolemy (b. 100), basically the ninth-century Arabic
predecessor of Sacrobosco’s De sphaera. After the twelfth-century Latin
translations of John de Seville (1100–1180) and Gerard of Cremona
(1114–1187), the work was widely disseminated and extremely inﬂuential
in the Latin world. While the ﬁrst printing took place in 1493 (al-Farghānī
1493), the second was produced in 1537 by Johannes Petreius (1497–1550)
(al-Farghānī 1537), a friend of Rheticus and the printer of De revolutionibus
by Nicolaus Copernicus (1473–1543), one year before the Sphaera edition
was printed.

This comment at the margin becomes all the more relevant when we
recall that the Sphaera edition of 1538 also contains a fragment of al-
Farghānī’s work as an additional text-part. This is the Diff. 24, a chapter
that discusses the rising and setting of the planets. A detailed comparison
between the 1493 et 1537 editions on the one hand and this fragment on
the other shows that the 1538 edition was the result of a collation between
le 1537 edition and manuscripts of the same work. The striking similar-
ity between Petreius’ 1537 edition and the 1538 fragment is based on the
fact that the entire punctuation as well as the lexical rendering in a more
classical Latin are basically identical. Cependant, two passages are slightly
changed when the text refers to the visibility of the setting of the planets
depending on the Earth’s climatic zones. A comparison with ﬁve different
manuscripts has shown that exactly the same passages were rendered in

In the preface of his 1532 commentary on Hesiod’s Works and Days, Melanchthon
indeed mentions that Hesiod’s observations of rising and setting stars should be analyzed
against the background of knowledge acquired through the reading of either a commen-
tary on the Sphaera or Aristoteles’ De coelo (Bretschneider and Bindseil 1843–1860,
vol. 18, col. 182).

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The Hidden Praeceptor

different ways and therefore testify to an incorrect transmission.10 This
implies that the 1538 fragment was edited by somebody who understood
the subject matter, as it displays two content-related corrections. From the
manuscripts left by Rheticus’ pupil Nicolaus Gugler, moreover, we know
that Rheticus had been teaching this work of al-Farghānī in the same
period. Malheureusement, Gugler’s notes concern only the Differentiae 1 à
10 and not the 24th printed in the fragment. But the notes about the Diff.
8 show Rheticus’ intense focus on the exact determination of the latitudes
of the climate zones (Guglero 1536–1538, 78r–79r).

The Fourth Addition

3.4.
The next piece of evidence is concerned with the visual apparatus of the
1538 edition. Such an apparatus in mathematical textbooks of the time
could be extremely sophisticated, containing not only rich illustrations
but also diagrams or paper instruments (volvelles). Le 1538 edition is
special because it added a considerable number of illustrations compared
to the 1531 edition, par exemple, which in itself was already richer than
most other Sphaera editions of the period. Before addressing the content-
related illustrations, cependant, we will discuss the visual aids that were
inserted to enable readers to build mathematical instruments.

Le 1538 edition of the Sphaera introduces three new instruments
through this printing technique, which spread thanks to Petrus Apianus
(1495–1552) and his famous Cosmographicus liber, ﬁrst printed in 1524
(Apian 1524). The volvelles of the 1538 Sphere edition are instruments
for determining a) the length of days and nights, b) the sphericity of
the Earth given the latitude as well as the length of the artiﬁcial days,
and c) the time of events in the past (De ortu poetico).

While the second instrument has a clear source in Apian’s work (Apian
1524, p. 24), the ﬁrst and the third are more original. The third testiﬁes to
a focus on the subject De ortu poetico which will be discussed at length in
the section dedicated to Anonymous 1543b. Concerning the second, nous
know that Rheticus was very familiar with Apian’s works in general, comme
he brought some of them as a gift when he ﬁrst met Copernicus in
1539 (Burmeister 1968, vol. 1, p. 39). Rheticus and Apian actually met
in person in 1538 (Danielson 2006, p. 37). Rheticus, moreover, prepared a

10. We compared the fragment printed in the 1538 edition with (al-Farghānī et al.
13th–15th cent., 115v–116v (new enumeration) (BNF); al-Farghānī and al-Bitrūgi 13th
cent., 26r–27v (BNF); al-Farghānī et al. 14th cent. (BNF), 10v–11r; al-Farghānī et al.
14th cent., 71v–72v (BSB); al-Farghānī and Sacrobosco 2004 14th cent., 13r–v (BNF)).
The latter manuscript is the one that turns out to be closer to the wording shown in the
1538 fragment; like the 1493 et 1537 printed editions, it is based on John of Seville’s
translation.

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Chorographie, now missing but fortunately transcribed and printed in 1876,
in which he mentioned an instrument of Apian that he had personally seen
(Hipler 1876, p. 148; Burmeister 1968, p. 51). Concerning the ﬁrst
instrument, we know that Rheticus was working in Wittenberg on math-
ematical instruments for use in astronomy and geography together with
Erasmus Reinhold (1511–1553) et, during his stay in Prussia he built
an instrument to measure the lengths of days and nights, which was then
gifted (with a written description about its use) to Duke Albert of Prussia
(1490–1568) dans 1541. This is shown in a letter by Rheticus himself
(Hipler 1876, p. 129).

The Fifth Addition

3.5.
The next piece of evidence to show that Rheticus is the author of the
“new” Tractatus contained in the 1538 Sphaera edition also concerns the
visual apparatus but more particularly the relation between one speciﬁc
illustration and the added text referring to it. In our opinion, this is the
most relevant and decisive piece of evidence.

Le 1538 edition shows twenty-one more illustrations than the 1531
version, while two of them have been replaced. We know that the revolu-
tion of the visual apparatus in the tradition of the Sphaera corpus actually
began with Apian (Pantin 2020), in particular his Cosmographicus liber and
his Sphaera edition of 1526 (Sacobosco and Apian 1526). One of those new
illustrations was inserted to replace the older illustration typically used
since the thirteenth century to represent the demonstration of the spheric-
ity of the element water.

En particulier, it shows that two observers, one on the mast and one on
the hull of a ship would observe the disappearance of a castle on the shore
at two different moments: The man on the mast can observe it for a longer
period while the ship moves away, and the reason is the spherical shape of
the element water (figue. 2).

According to classical geocentric cosmology, the elements are ordered
according to their weights: Terre, Water, Air, Fire. To explain the possi-
bility of life outside the waters, the concept of tumor terrae was developed
during the Middle Ages. In practice, the center of the earth’s sphere was
conceived to be eccentric in relation to the sphere of water, so that a por-
tion of earth could emerge.11

11. The systematization of knowledge concerning the concept of tumor terrae was ﬁrst
accomplished by Petrus Abelardus in the twelfth century and was based on exegetical argu-
ments concerned with the Book of Genesis (Third day). The physical explanation related to
the eccentricity of the two spheres ﬁrst emerged in relation to William of Moerbeke’s
thirteenth-century translation of Simplicius’ commentary on Aristotle’s De coelo (Nenci

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The Hidden Praeceptor

In the ﬁrst chapter of the Tractatus de sphaera, Sacrobosco demonstrates
Chiffre 2.
the sphericity of the element water around the Earth using the empirical example of
a ship leaving a shore. Medieval illustration (From Sacrobosco et al. 1490, a–III–5).
Courtesy of the Library of the Max Planck Institute for the History of Science.

This is what Sacrobosco’s text also describes in the ﬁrst book, lequel
contains the demonstration of the sphericity of the water element. Apian,
cependant, repurposed the traditional argument and decided to show the
entire terraqueous globe (figue. 3).

Isabelle Pantin shows that the illustration of the terraqueous globe was
a consequence of the reception of the new geographical knowledge, lequel
was being accumulated during the journeys of exploration, and in partic-
ular of the reports concerning Amerigo Vespucci’s travels (Pantin 2020). Dans
terms of classic geocentric cosmology, this was a radical innovation as it
denied validity to the Aristotelian conception of distribution of the ele-
ments. Cependant, probably because of the then relevant authority of the
textual apparatus and of Sacrobosco’s original text, Apian did not change
the wording of the text at all, and the illustration of the new globe
remained completely uncommented.

The illustration was then reprinted in the 1531 Sphaera edition by Klug
(as in all later Wittenberg editions) but Klug also left it uncommented.
The ﬁrst textual change related to the new illustration of the globe can
be found in the 1538 edition, again not as a commentary but as an addi-
tion to the original text. The change is very small but relevant: En effet,
only one heading was added. While the 1531 edition titles this part in
the most classical way, using the incipit (Quod aqua sit rotunda), le 1538
edition reinstated this heading as the incipit of the section text, adding
above it: Terram cum aqua globum constituere.

2018). Later on, at the beginning of the ﬁfteenth century, Paul of Burgos’ formulation
became particularly inﬂuential ( Vogel 1995, pp. 148–9, 265–75).

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Chiffre 3. New illustration of the demonstration of the sphericity of the water
element with the terraqueous globe inserted by Apianus (Sacrobosco and
Melanchthon 1568, b–5–4). Courtesy of the Library of the Max Planck Institute
for the History of Science.

This is the very ﬁrst textual reception of the new thinking about the
distribution of water and earth on the planet’s surface.12 What counts here,
cependant, is the comparison with a manuscript of another pupil of Rheticus,
also a well-known source to his biographers by now. This manuscript con-
tains the notes of two different classes on the Sphaera held by Rheticus during
his second stay in Wittenberg in 1540, and in both of them the subject of the
distribution of earth and water is discussed at length (Rheticus and
Sacrobosco 1540, 12v–13r, 62v–64v).13 To give an example, in the ﬁrst
class the locus is discussed as follows:

Constituit ne aqua integram sphaeram?

Non, alioqui[n] enim necesse esset ipsam universam terram
contegere, quae res commodum animantibus supra terram
habitacionem tolleret, sed aquae superﬁcies iuncta superﬁciei terrae
efﬁcit corpus sphaericum. (Rheticus and Sacrobosco 1540, 13r)

12. Remarquablement, the ﬁrst two volvelles discussed above are inserted in the section of

the text containing the demonstration of the sphericity of the water element.

13. The Ms. Pal. Lat. 1397 contains notes from Rheticus’ classes around 1540
(fols. 1–155) and Sacrobosco’s works copied in 1446, as remarked on by Ludwig Schuba,
who analyzed all the quadrivium manuscripts of the Palatina collection. À ce jour, cependant,
no one has noted that the second part also contains a copy of Sacrobosco’s Computus ecclesiasticus
(Rheticus and Sacrobosco 1540, 156r–170r). For comparison (see Schuba 1992, pp. 164–5).

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The Hidden Praeceptor

These five pieces of evidence attribute authorship to Georg Rheticus of the
new edition of the Tractatus contained in the Sphaera edition of 1538. Nous
consider him as an author in this case, same as if he had commented on the
new Sphaera text.

4. Anonymous 1543a
After Joseph Klug’s aforementioned four editions, the next edition from
Wittenberg was realized by the printer Peter Seitz I (1534–1574) dans
1543. It is evident that Seitz somehow received all Klug’s woodblocks
for this production and the new edition is almost identical, but not quite.
Some changes were made and, as this edition coincides with Rheticus’ sec-
ond stay in Wittenberg, we shall brieﬂy mention the changes that might
be relevant to this argument.

D'abord, al-Farghānī’s fragment was now omitted. But there is an Annotatio
in the original text whose subject refers to Prop. 22 of Regiomontanus’
Epitome, which is still part of the edition. Probably the most relevant addi-
tions are two marginalia in Book 3 of the Tractatus that correct the exact
degrees of the ﬁfth and seventh climate zones, a subject that, as we have
seen, is close to Rheticus’ interests. One last relevant addition concerns a
computational table that reports the maximal length of the natural days
depending on the distance from the Arctic pole, another subject close to
Rheticus and his production of instruments.

We believe, donc, that Rheticus also worked on the 1543 edition
and we can show this more convincingly in the section on Anonymous
1543b below. But ﬁrst, let us consider Anonymous 1538b.

5. Anonymous 1538b
As previously mentioned, the text-part assigned to this anonymous author
is a Cisiojanus, a series of verses to determine the non-movable liturgical
feasts. Disseminated since the thirteenth century, this mnemonic-
mechanical aid developed into regional forms and according to regional
differences in the liturgical calendar. The Cisiojanus printed in the 1538
Sphaera edition corresponds exactly to the one that spread in the fourteenth
century in Silesia, Saxony, Bohemia, and Poland (Grotefend 2007, pp. 20–1).
Because we know from Melanchthon’s letter to Gasser that Rheticus
came up with the idea of inserting the Computus ecclesiasticus, we can infer
that he was also responsible for the insertion of the Cisiojanus. En effet, le
two works complete each other, as one concerns the movable and the other
the non-movable feasts.14 While we do not ﬁnd any direct intervention in

14. As evidence that the Computus and the Cisiojanus complete each other, we found
that these text-parts were each published twenty times in the corpus and always together.

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the text here, we would like to infer that Rheticus acted as an editor of the
entire edition, just as he did in the case of the Tractatus de sphaera. In our
opinion, this was also the case in 1543.

6. Anonymous 1543b
The text-part assigned to this anonymous author is the aforementioned De
ortu poetico. This text deals with the subject of the rising and setting of the
stars with reference to a long series of passages from ancient literature, les deux
Greek and Latin. As we have seen, the subject is a standard topic in the
original text of Sacrobosco’s De sphaera. This additional text-part, donc,
should be seen as an enriching commentary to that section of Sacrobosco’s
text. Contrary to what is often believed, De ortu poetico is not just a collection
of passages from ancient literature that has a relation to astronomy—a col-
lection that would provide the reader with a mnemonic aid for the subject
matter on the basis of the available knowledge of the classic poems of the
past. En effet, De ortu poetico is a sort of tool to enable historians to exactly date
events that took place in the past and for which there are testimonies that
described the position of speciﬁc stars over the ecliptic in order to record the
temps. De ortu is a calendric means of investigating the past that also takes into
consideration the geographical area from which the stars were observed.

We have already seen how the 1538 edition displays a marginal com-
ment that expands the example of Sacrobosco and considers Hesiod’s
travaux. This new text-part is greatly expanded by the addition of a large
variety of ancient authors, with Hesiod playing a crucial role.

Although he did not mention this text-part directly, it was, in fact,
Melanchthon, OMS, in the same letter to Gasser, pointed to the relevance
of the astronomer’s capacity to date past events exactly, a skill without
which history and memory would not exist and chaos would follow.
Now completely forgotten, practicing De ortu poetico had become an
increasingly relevant and sophisticated academic occupation during the
early modern period and continued until the late eighteenth century.15

We believe that the author and editor of this text-part is Rheticus. Cir-
cumstantially we can infer this hypothesis from the fact that De ortu poetico

15. The subject De ortu poetico was discussed in Ps. Proclus De sphaera as well and, comme
tel, had already been greatly expanded by Rheticus’ friend Johannes Stöfﬂer in his com-
mentary printed a few years earlier (Stöfﬂer and Proclus [Diadochus] 1534). Encore, it was
Melanchthon who also published a commentary on the results of his dating of the events
mentioned in Ovid’s Fastorum libri sex in 1539 (Bretschneider and Bindseil 1843–1860,
vol. 19, cols. 473–496). Later on, the subject almost became an academic discipline by
lui-même, as shown by the many works with the title Exercitatio academica De ortu et occasu siderum
poetica published during the seventeenth century. A very mathematically sophisticated
example from the late eighteenth-century is (Pfaff 1786).

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is both a completion of Sacrobosco’s Sphaera and an enrichment of the
calendric topic in the entire edition. Secondly, it has been shown that
le 1538 edition even contains a volvelle for the calculation of times of
past events depending on the position of the stars over the ecliptic and
the position of the observer. This convincingly testiﬁes to Rheticus’ inter-
est in the subject.

The decisive evidence, cependant, comes from a different feature of this
text-part. En particulier, it contains two computational astronomic tables
que, together with the instrument, could greatly facilitate the
mathematical-astronomical workﬂow. These tables are 1) Tabula continens
gradus eclipticae cum quibus stellae insigniores olim oriebantur et occidebant and
2) Tabula continens ingressum solis in XII. signa Zodiaci. Verum item locum solis,
ad singolos dies anni, veterum poetarum temporibus accomodata (Figs. 4 et 5).
The ﬁrst table lists twenty-four stars and the degrees of their rising and
setting over the ecliptic as observable by the ancient authors in Rome and
Alexandria. The second shows on which day of each month the Sun would

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Chiffre 4. Tabula continens gradus eclipticae cum quibus stellae insigniores olim
oriebantur et occidebant (From Sacrobosco and Melanchthon 1568, foldout attached).
Courtesy of the Library of the Max Planck Institute for the History of Science.

Perspectives on Science

425

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Chiffre 5. Tabula continens ingressum solis in XII. signa Zodiaci. Verum item locum
solis, ad singolos dies anni, veterum poetarum temporibus accomodata (From Sacrobosco
and Melanchthon 1568, foldout attached). Courtesy of the Library of the Max
Planck Institute for the History of Science.

enter the constellations of the twelve signs but “adjusted for what concerns
the time of the ancient authors.”

The proof that Rheticus is the author of these tables and, in our opinion
of the whole text-part, comes from an appendix entitled De generibus
ortuum, which Rheticus added in his class on Ps. Proclus’ Sphaera, now
attributed to Geminus of Rhodes (ﬁrst century BCE) (Biank 2019). Once
again, the available source is the manuscript that preserves Gugler’s notes
from Rheticus’ classes between 1536 et 1538. Ici, Rheticus mentions
the complex workﬂow that students should accomplish in order to deter-
mine the time of the rising and setting of the stars observed by the ancient
authors by starting from the Alfonsine tables and the position of Wittenberg
and explicitly says that he has produced these tables for them to obviate this
effort (Guglero 1536–1538, 52v–53r). The appendix, moreover, can be seen

426

The Hidden Praeceptor

as a previous draft of the entire De ortu poetico. Among the examples discussed
in class we now ﬁnd the star Arcturus and the mention of Hesiod as addi-
tional evidence that Rheticus is also the author of the commentary in the
margin of the Tractatus of the 1538 Sphaera edition.

Generally speaking, the subject of De ortu poetico had already been dis-
cussed by a great number of scientists, including those in the Wittenberg
circle, and therefore we surmise that the text published in 1543 was edited
rather than authored by Rheticus. But the tables and the volvelle are, dans
our opinion, to be assigned to him as an author.

7. Rheticus in the Network of Authors
For the reasons listed in the previous sections, we conclude that Rheticus
was the overall editor and designer of the 1538 et 1543 editions of De
sphaera printed in Wittenberg by Klug and Seitz I respectively, et était
therefore responsible for the presence or absence of the speciﬁc text-parts
which constitute such editions. En particulier, we assign Rheticus the role
of editor in relation to al-Farghānī’s fragment, the Computus and the
Cisiojanus, while he is considered as the author of the 1538 et 1543

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Chiffre 6.
Social network visualization of the text-part authors. Authorship of
text-parts previously assigned to Anonymous 1538a, 1543un, and 1543b is now
assigned to Georg Rheticus. The network is not oriented. Betweenness centrality
est coloré.

Perspectives on Science

427

revisions on Sacrobosco’s original text as well as of De ortu poetico, et
especially its tables.

If we now consider only the text-parts he authored and assign the name
and the life dates of Rheticus to them (Anonymous 1538a, 1543a and
1543b) and only then go back to our network, the situation appears quite
different. Dans ce cas, the component consists of twenty nodes, namely
authors. Rheticus ranks in second position after Vinet for both between-
ness and closeness centrality while he scores highest for degree (132 con-
nections) (figue. 6).

The Impact of Rheticus in Europe

8.
As mentioned, this network is based on the text-parts and their recur-
rences, while such text-parts have been identiﬁed if and only if the ana-
lyzed printed edition clearly shows a beginning and an end of the text-part
at hand. Cependant, this does not exclude the possibility that the same con-
tent is present in other editions, eventually printed in a continuum as a part
of a commentary. Only by considering all cases, even beyond those used for
the network analysis, are we ﬁnally able to measure the impact of Rheticus
in the frame of geocentric cosmology education in Europe.

To measure the impact, we count the recurrences of the text-parts Rheticus
both authored and edited, while keeping them distinct: the Tractatus, les deux
versions of 1538 et 1543 (23 occurrences), De ortu poetico (67 occurrences),
the Cisiojanus (20 occurrences), the Computus (20 occurrences), and al-
Farghānī’s fragment (50 occurrences).

The spread of De ortu poetico across the Sphaera corpus is more signiﬁcant
than it might seem at ﬁrst glance. Here we deal with three kinds of recur-
rences: un) reissues of the 1543 text-part, by preserving a nearly identical
layout, including the tables as folded leaves (46 instances in our corpus);
b) occurrences of De ortu poetico within a different and/or longer text-part,
identiﬁed by the presence of the table “adjusted for what concerns the time
of the ancient authors” (figue. 5) (100 instances);16 and c) different versions

16. As we were able to attribute the authorship of the tables (Figs. 5, 6) to Rheticus,
we supported our research by searching for those tables only. In total we found 92 occur-
rences of the table “adjusted for what concerns the time of the ancient authors” (figue. 5). 46
of them were overlapping with the re-occurrences of Rheticus’ text-part De prtu poetico, comme
described in point a). Plus loin 46 pointed us to the passages of the corresponding editions
where the same subject was discussed. We consider the presence of Rheticus’ table to assert
an inﬂuence of his works on those 46 treatises, where the table was found. To identify the
table, a new theoretical machine-learning approach to identify digits in numerical tables by
means of bigrams (Eberle et al., 2020) was developed in the frame of the overarching pro-
ject BIFOLD, to which the Sphaera project also belongs. Then the same group developed a
deep convolutional network able to identify equal or similar tables. The new algorithm will
soon be published.

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The Hidden Praeceptor

of the text-part De ortu poetico, but clearly inﬂuenced by Rheticus’ original
text (8 instances).

The third case is represented by eight editions of Sebastian Dietrich’s
(1521–1574) Novae quaestiones sphaerae (Dietrich 1564, 1567, 1570, 1573,
1578, 1583, 1591, 1605).17 Dietrich based his work on another Wittenberg
textbook: Kaspar Peucer’s (1525–1602) Elementa doctrinae de circulis coe-
lestibus, et primo motu, ﬁrst published in 1551 (Peucer 1551) and then
re-published another eight times up until 1601. Dietrich studied in
Wittenberg between 1538 et 1544, and one year later he began teaching
in the same university. Peucer arrived a few years later than Dietrich, dans
1543, but quickly became one of the three most important pupils of
Melanchthon itself ( Westman 1975). He took over the teaching activity
dans 1550 and became professor in 1553, replacing Erasmus Reinhold.

Peucer’s text is not a direct commentary on Sacrobosco’s text but
includes and expands Rheticus De ortu poetico, as it is easily recognizable
by looking at the passages of ancient literature that are analyzed as exam-
ples in both texts. Among them, the most signiﬁcant common denomina-
tor is represented by the detailed study of Hesiod’s second book of Works
and Days, a work ignored in the original tract of Sacrobosco.18 Peucer’s
text, moreover, also contains Rheticus’ tables. Dietrich ﬁnally transformed
Peucer’s text into a book structured as a series of questions and answers,
leaving the actual content fully unchanged. Concerning the Sphaera, ce
genre, was speciﬁcally conceived as a student aid, possibly to prepare for an
examination.

But Dietrich’s work was not the ﬁrst transformation of the text of
Sacrobosco (and Rheticus’ additions) into a book structured in such a
chemin. A work belonging to this genre had already appeared in 1549. Ce
work—Quaestiones novae, in libellum de Sphaera Iohannis de Sacro Busto—
was authored by Hartmann Beyer (1516–1577). He began as a student
together with Rheticus and then became his pupil. He started his teaching
career as a private tutor in Wittenberg and later also received a chair at the
university there (Burmeister 2015, 103–04). This work, which has been
classiﬁed as a great transmitter (Zamani et al. 2020), was originally printed
in Frankfurt (three times in 1549!) and then a further sixteen times

17. For each edition we have controlled only one exemplar. In three cases, we could
identify the other tables (figue. 6). Dans d'autres cas, the electronic copies we had at our disposal
clearly show the presence of tables that, cependant, have not been unfolded and scanned. Ce
example testiﬁes to the necessity for a still missing standard and professional procedure for
the electronic reproduction of historical sources.

18. For an example of the discussion concerned with Hesiod’s verses 382–386, com-
pare (Sacrobosco and Melanchthon 1543, H–2; Peucer 1551, M–1; Dietrich 1564, p. 208).

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Perspectives on Science

429

altogether in Wittenberg, Frankfurt am Main, and Paris by the great inter-
national publisher and bookseller Guillaume Cavellat.19 Beyer’s work not
only contains Rheticus’ tables but also explicitly and repeatedly mentions
that the subject is developed by considering the position of Wittenberg to
begin the calculations.20

From a geographical point of view those text-parts now assigned to
Rheticus traveled from Wittenberg to Paris, Antwerp, Venice, and Lyon,
via Cologne and Frankfurt—namely, to all major European centers of book
printing in the early modern era. Looking at the temporal distribution,
Rheticus’ work impacted the textbook tradition represented by our corpus
in the extended timeframe from 1538 à 1629. The temporal distribution
of the spread of Rheticus’ text part is in line with the results calculated in
previous studies for the Wittenberg editions in general. It reached a high
distribution after 1543 and the peak between 1550 et 1560, tandis que le
decline in circulation was very slow in time, allowing such texts to execute
a long-term inﬂuence well after the turn of the century (figue. 7).

The plot shows the diffusion of Rheticus’ text-parts—as author (blue)
and as editor (red)—in comparison with other text-parts that fundamen-
tally shaped the astronomical and cosmological knowledge of the late
medieval and early modern periods: the Theoricae planetarum and Regio-
montanus’ Epitome.

Concerning Regiomontanus’ Epitome, the editions of the corpus contain
only the aforementioned fragment that corresponds to Prop. XXII, Book 3.
The comparison is especially important because this text-part is not only
the most frequently republished one but also the part that has been iden-
tiﬁed as the text-part with the highest value as a builder of semantic com-
munities (Zamani et al. 2020).

Under the heading Theoricae planetarum, several works circulated in the
early modern period with the goal of describing the orbits of the planets as
well as the method for calculating their positions. The theoricae were read in
class after the Sphaera class by all those students who were interested in
mathematical education, and represented the ﬁrst step toward mathemat-
ical astronomy. Their inﬂuence on the early modern knowledge on astron-
omy cannot be underestimated (Pedersen 1962, 1981; Aiton 1987; Pantin
2012; Malpangotto 2016). Leaving aside the circulation of these works in
general and considering only those instances in which these works were
printed and published together with Sacrobosco’s Sphaera, we ﬁnd three

19.

For the activity of Guillaume Cavellat in the frame of the Sphaera corpus, voir
https://hdl.handle.net/21.11103/sphaera.100726 (accessed March 7, 2020). For his activity
as a publisher (see Pantin 1998, 2022).

20. As an example, see Sacrobosco and Beyer (1550, 57r, 59v).

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Chiffre 7. Temporal distribution of the diffusion of the text-parts assigned to
Rheticus as author (blue) and as editor (red) in comparison to the Prop. XXII,
Book 3 of the Epitome of Regiomontanus (vert) and to the Theoricae planetarum of
Nur ad-Din al-Bitruji, Gerard of Cremona, and Georg Peuerbach, y compris
various commentaries on the latter (purple).

texts: the theoricae of Nur ad-Din al-Bitruji (d. 1204), those of Gerard of
Cremona, and ﬁnally the theoricae novae of Georg von Peuerbach. The ﬁrst
appears only once, the second ﬁve times, and the third ten times in its orig-
inal form, six times commented by Francesco Capuano (1450–1490), twice
by Francesco Giuntini, and then once respectively by Pedro Nuñes, Silvestro
Mazzolini (1456–1527) and Peter Apianus. In total there are eight authors,
two of whom are from previous centuries.

In our opinion, these comparative ﬁgures enable precise estimation of
the kind of impact that Rheticus, through his work as author and editor,
exerted in Europe during the early modern period, an aspect that was fully
neglected by Rheticus biographers and even by those who already sus-
pected his intervention in some of the text-parts discussed above. These
ﬁgures, in conclusion, allow us to consider him as the “hidden praeceptor”
not just of Germany but of Europe, and this within the conceptual frame
of geocentric cosmology.

Cotisations

–

Analysis of historical sources: B. Federau, Ô. Nicolaeva,
M.. Valleriani

– Data preparation: B. Federau, Ô. Nicolaeva

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– Data Revision: B. Federau, M.. Valleriani
– Analyse de réseau: B. Federau
–
–
– En écrivant: M.. Valleriani

Scripts and Visualization: B. Federau, Ô. Nicolaeva
Results discussion: B. Federau, Ô. Nicolaeva, M.. Valleriani

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al-Farghānī, Ahmad Ibn-Muhammad. 1537. Brevis ac perutilis compilatio

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al-Farghānī, Ahmad Ibn-Muhammad, and Nūr al-Dīn Ishāq al-Bitrūgi.

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Dietrich, Sebastian. 1567. Novae quaestiones sphaerae …. Wittenberg: Johann
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