Graphic Conventions, Visual Idioms, (Dis)Similarity in Astronomical Diagrams
Second International EIDA Conference
22–24 April 2024, Observatoire de Paris
Organisation: Scott Trigg, Divna Manolova, Samuel Gessner, Matthieu Husson
It will be possible to attend the conference in remotly using this link
We encourage in person participation, for this, registration is mandatory by writing an email with your name and the object ‘Participation EIDA conf. 2024’ at the latest on April 21, 2024 12.00 a.m. Paris time to matthieu.husson@obspm.fr.
Rationale
Recent scholarship in the history of the sciences has increasingly explored methodological possibilities of studying images, the study of diagrams being just one possible area of research. A great variety of methods and approaches have been used for analysing the epistemic and documentary aspects of different visual practices, their circulation and transmission within and across cultures, and their relationship to other means of communicating knowledge.
Leveraging cutting edge development in computer vision EIDA (Editing and analysing hIstorical astronomical Diagrams with Artificial intelligence, https://eida.hypotheses.org/) aims to study astronomical diagrams on a cross-cultural Afro-Asiatic-European scale. It focuses specifically on astronomical diagrams as historical sources and examines both their documentary aspect (diagrams as written artefacts in specific manuscripts) and their epistemic aspect (diagrams as scientific tools for historical actors).
Eida’s yearly conference series aims in the long run to shape a collective volume to be published at the end of the project. While the scope and variety of EIDA’s diagram corpus were at the centre of our first conference in 2023 (https://eida.hypotheses.org/conferences/conference), this second conference questions the practice of diagramming: how to differentiate between diagrammatic idioms and how did historical actors employ them in a variety of representations, including but not limited to scientific diagrams? We will interrogate the graphic conventions diagrams rely on and discuss the implications this has with regard to the notion of (dis)similarity that diagrams record and exhibit. On the other hand we will look at the agency of diagrams: how do diagrams operate and do things, and then also in what terms do both actors and observers reflect on/prescribe what diagrams do and how they do it? The development of various digital tools within EIDA also sheds new light on the notions of visual idioms and (dis)similarity, which will be discussed as well in perspective during the conference.
This reflection about the multilayered interaction of the documentary and epistemic aspects of astronomical diagrams will help us refine our understanding of ‘diagramming’ as a practice for astronomers in different contexts. A better grasp of the historical actors’ diagramming practices is an essential prerequisite in developing a natively digital critique of diagrams as central elements in sources from a wide range of astronomical traditions.
The second EIDA conference brings together scholars who are invited to present and reflect on specific diagram case studies. These discussions will be paired with presentations from DH and AI experts on the current state of advancement of computer vision tools of relevance to EIDA’s research objectives. Scholars and experts together will explore the approaches we seek to develop for the study of astronomical diagrams.
Participants
Ségolène Albouy (Imagine, École des Ponts ParisTech), Hamid Bolhoul (Iranian Institute of Philosophy), Christian Carlos Carman (National University of Quilmes), Gaye Danışan, (Istanbul University, Faculty of Letters, Department of the History of Science), Daria Elagina (Universität Hamburg), Samuel Gessner (CIUHCT, Lisbon), Ji Chen (PSL-Paris Observatory & University of Science and Technology of China), Stephen Johnston (University of Oxford), Syrine Kalleli (Imagine, École des Ponts ParisTech), Richard Kremer (Dartmouth College), Divna Manolova (PSL-Paris Observatory, Dyas), Anuj Misra (MPIWG and FU, Berlin), Sajjad Nikfahm-Khubravan (Independent Scholar), Jade Norindr (PSL-Paris Observatory), Diego Pelegrin (National University of Luján), Ioanna Skoura (Independent Scholar), Florence Somer (IFEA, Istanbul), Scott Trigg (PSL-Paris Observatory, PRAIRIE), Stefan Zieme (Humboldt-Universität zu Berlin)
Program
Monday, 22 April
(Salle Danjon)
9:00 – 9:30 Welcome, Introductions
9:30 – 10:30 Syrine Kalleli, Astronomical Diagram Vectorisation with Deep Learning
10:30 – 11:30 Samuel Gessner, Diagrammatic Modes: Reasoning About the Eighth Sphere in the 15th Century
Break (15 minutes)
11:45 – 12:45 Stephen Johnston, Representing the Sphere: Between Diagram and Illustration in the Latin West
Lunch
14:30 – 15:30 Scott Trigg, Imaginary Circles and Physical Orbs: New (?) Ways of Visualizing Planetary Models in Islamicate Astronomy
15:30 – 16:30 Florence Somer, An explanation of the use of the astrological diagrams from the Sassanid to the Abbassid period: the reconstruction of a practice
Break (15 minutes)
16:45 – 17:45 Stefan Zieme, The geometrical diagrams of the Almagest: George of Trebizond and the revision of lines and angles
Tuesday, 23 April
(Salle du Conseil)
9:30 – 10:30 Ségolène Albouy, Similarity Search for Astronomical Diagram Corpora
10:30 – 11:30 Rich Kremer, From manuscript to type: Graphic conventions in the Epitome of the Almagest by Peurbach/Regiomontanus
Break (15 minutes)
11:45 – 12:45 Ioanna Skoura, The diagram used by Ptolemy for the determination of solar eccentricity and apogee: some remarks on its tradition
Lunch
14:30 – 15:30 Hamid Bohluhl (via Zoom), Shadow and Light in Islamicate Astronomical Diagrams: Eclipses and Lunar Phases
15:30 – 16:30 Anuj Misra, Drawing Meaning on Paper: Astronomical drawings in the Sanskrit tradition
Break (15 minutes)
16:45 – 17:45 Ji Chen, The process of valuing astronomical diagrams during the late Ming and Early Qing China
Wednesday, 24 April
(Salle Denisse)
9:30 – 10:30 Jade Norindr, Building the EIDA platform: digital tools for diagram editions
10:30 – 11:30 Divna Manolova, Canonicity and Diagrammatisation in the Medieval Greek Manuscript Tradition of Cleomedes’ The Heavens and its Commentary by John Pediasimos
Break (15 minutes)
11:45 – 12:45 Gaye Danışan, An Essay on Information Visualization Patterns in Ottoman Calendars (1550-1750) (via Zoom)
Lunch
14:30 – 15:30 Daria Elagina, Texts and Diagrams: The Application of Astronomical Diagrams in Ethiopic Colophons
15:30 – 16:30 Sajjad Nikfahm-Khubravan, Diagrams as Method of Proof: al-Battānī and Analemma (via Zoom)
Break (15 minutes)
16:45 – 17:45 Christián C. Carman & Diego Pelegrin, Editing Copernican diagrams: A comparison between the diagrams of the autograph manuscript of De Revolutionibus and the 1543 edition (hybrid)
Abstracts
Ségolène Albouy, Similarity Search for Astronomical Diagram Corpora
After automatically extracting the diagrams, the subsequent stage in an automated workflow for easing the process of critically editing diagrams involves similarity-based alignment. The primary objective of the similarity search is to facilitate the exploration and comparison of diverse geometric representations of celestial phenomena. The overarching goal is to distinguish duplicates and reinterpretations of identical diagrams across various manuscripts and traditions. This functionality relies on an innovative artificial vision technique known as SegSwap (“Learning Co-segmentation by Segment Swapping for Retrieval and Discovery,” Xi Shen et al., 2022). Specifically designed for detecting replicated patterns in iconographic corpora, such as paintings, this method will constitute a step forward in the comprehensive study of astronomical diagrams, allowing for in-depth exploration beyond conventional temporal and spatial limits.
Hamid Bohluhl, Shadow and Light in Islamicate Astronomical Diagrams: Eclipses and Lunar Phases
The aim of this paper is to investigate the depiction of eclipses and lunar phases in Islamicate astronomical treatises. While these diagrams may initially appear as two-dimensional illustrations in manuscripts, this study argues for a significant distinction between those employing simplified, abstract elements of the phenomena and those seeking to portray physical reality through tangible components. In particular, the paper explores the interpretation of these diagrams as strictly two-dimensional geometric illustrations versus representations meant to convey three-dimensional perspectives. Two-dimensional eclipse diagrams serve as fundamental tools for geometric reasoning, while more realistic depictions often appear in non-mathematical contexts to convey the physical circumstances of celestial events. Through an analysis of the context and the depiction of shadow and light as tangible elements within these diagrams, the paper supports this assertion and examines the (dis)similarities across various texts in their representation of these celestial phenomena. Furthermore, the paper delves into how lunar phase diagrams aim to delineate physical reality, with a focus on the role of colors. By examining the techniques employed by diagram makers to enhance realism in these depictions, the study suggests a deeper understanding of the visual and epistemic culture of diagram making in Islamicate astronomical treatises.
Christián C. Carman & Diego Pelegrin, Editing Copernican diagrams: A comparison between the diagrams of the autograph manuscript of De Revolutionibus and the 1543 edition
Toward the end of his life, Nicholas Copernicus entrusted Georg Joachim Rheticus with the edition of his De revolutionibus orbium coelestium. We know that Rheticus took a copy of Copernicus’ autograph manuscript to Nuremberg to prepare the edition; and we also know that Rheticus had to quit the supervision of the edition before it was completed, leaving it in charge of Andreas Osiander. The first edition of Copernicus’ book was published in 1543. Unfortunately, the copy of the manuscript taken by Rheticus to Nuremberg is lost, but Copernicus’ autograph manuscript has been preserved. Several investigations have shown the differences between the text of the manuscript and the text of the 1543 edition, but there has been no analysis focusing on the differences between the diagrams of the manuscript and the edited book. In this talk, we will propose a series of preliminary analytical tools that allow us to organize the remarkable differences between the diagrams of the autograph manuscript and those of the 1543 edition.
Gaye Danışan, An Essay on Information Visualization Patterns in Ottoman Calendars (1550-1750)
The Ottoman scholars combined the multi-layered information between different data elements into a calendar format containing only necessary information through symbols, tables, and diagrams. The structure of these calendars, which was organized according to macrocosm and microcosm analogy, indicates the complex fabric of information visualization in Ottoman society. By examining the visualization techniques and their cultural significance, we can understand how information was conveyed and interpreted in Ottoman tradition. Therefore, this presentation aims to introduce visualization patterns related to astronomical or cosmological concepts in Ottoman ideas and initiate a discussion on the intricate fabric of information visualization by examining some examples of structural features, visual representations, and cultural significance in these calendars.
Daria Elagina, Texts and Diagrams: The Application of Astronomical Diagrams in Ethiopic Colophons
The land of written civilization from the 1st millennium BCE, the highlands of Eritrea and Northern Ethiopia represent a peculiar case of a cultural area with a long and uninterrupted manuscript tradition. Parchment manuscripts, introduced to Ethiopia and Eritrea in the first centuries CE, continue to serve as a crucial tool for knowledge transmission in the region to this day. Through many centuries the manuscript culture of Ethiopia and Eritrea has transmitted the lore of multi-faceted knowledge traditionally designated in the Ethiopic culture as ḥassāb, ‘Computus’. Besides numerous texts, tables, and other material the corpus of ḥassāb (traditionally designated as bāḥra ḥassāb, ‘Sea of Computus’) transmits a number of astronomical diagrams. The corpus of bāḥra ḥassāb remains a largely understudied aspect of the manuscript culture of Ethiopia and Eritrea. However, as appears from observations on extended colophons in Ethiopic manuscripts, the astronomical diagrams transmitted as part of bāḥra ḥassāb appear to have been used by traditional scholars to provide astronomical information for the days of the beginning and completion of their writing activities. One such scholar, Mǝhǝrkā Dǝngǝl, active around the early 17th century left two extended colophons with data derived from astronomical diagrams. One colophon is attached to the Ethiopic version of the Chronicle of John of Nikiu, a historiographical text which Mǝhǝrkā Dǝngǝl translated from Arabic into Ethiopic with the assistance of an Egyptian deacon. The other colophon concludes the Commentary on the Pentateuch composed by Mǝhǝrkā Dǝngǝl based on various sources. The astronomical data in textual form transmitted in these two colophons can be traced back to the astronomical diagrams attested in the manuscripts of bāḥra ḥassāb. The process of the comparison of textual and graphical information uncovers the practices of application of astronomical diagrams as an element of bāḥra ḥassāb and the role of the astronomical diagrams in the literary activities in Ethiopia and Eritrea in the 17th century.
Samuel Gessner, Diagrammatic Modes: Reasoning About the Eighth Sphere in the 15th Century
This exploration into dynamics of early astronomical knowledge delves into manuscript diagrams representing the arcane motion of the Eighth Sphere, particularly those circulating in the 15th century. The focus centers on Niccolò Conti’s ‘De triplici motu’ treatise (1450) and the pertinent chapter from Peurbach’s ‘Theoricae novae’ (1453). Underlining the belief that ‘diagrams do not always work the same way,’ I introduce the concept of ‘diagrammatic modes,’ emphasizing the pivotal role of this concept in revealing 15th-century thoughts about the problem of the eighth sphere. Conti and Peurbach emerge as central figures, presenting similar diagrams but in distinct modes. Conti aligns with traditional ‘theorica planetarum’ literature, while Peurbach pioneers a groundbreaking use of diagrams to represent the 3D geometry of the Eighth Sphere’s motions. The rarity and uniqueness of the latter’s diagrams, along with their fortune when copied and printed, underscore the significance of this distinction. While existing literature extensively explored Peurbach’s figures in the ‘Theoricae novae,’ this study pursues a perspective that sets it apart from current scholarship. It focuses on recognizing and distinguishing various ‘diagrammatic modes.’ By differentiating modes of using diagrams, the study puts forward a nuanced understanding of them as tools of reasoning in early modern astronomy. The case study serves as a critical lens for the reevaluation of established notions on diagrams, offering insight into their diverse roles.
Ji Chen, The process of valuing astronomical diagrams during the late Ming and Early Qing China
In contrast to the widespread use of diagrams in European astronomy, traditional Chinese astronomy almost had no utilization of such visual representations except for star charts and some diagrams of astronomical instruments. This situation did not change until the large-scale introduction of Western astronomy by the Jesuits in the late Ming dynasty, and the advantages of astronomical diagrams were gradually recognized in the early Qing dynasty. In the presentation, I will introduce the utilization and condition of astronomical diagrams in the Chong zhen li shu (Chongzhen reign treatises on calendrical astronomy, 崇禎曆書), which was compiled in the late Ming dynasty and officially adopted in the early Qing dynasty, and compare them with those in subsequent official calendars. Besides, as European astronomy gained official acceptance, an increasing number of unofficial scholars began studying European astronomy. Therefore, I will also explore different attitudes of these unofficial scholars towards astronomical diagrams. Finally, based on the above discussion, I will outline the process of valuing astronomical diagrams during late Ming and early Qing China.
Stephen Johnston, Representing the Sphere: Between Diagram and Illustration in the Latin West
My starting point is a Sacrobosco manuscript in the New York Public Library. Dated to c. 1260, it is one of the earliest sources for his De Sphaera and, in addition to this text, also includes the Calendar, Computus, Quadrans and Algorismus attributed to him. The volume was evidently intended for a wealthy client and the works all have historiated initials and illuminated diagrams. At the end is an additional short work of arithmetical problems (Cautele) followed by a single leaf with a diagram of an armillary sphere. It is not part of De Sphaera but is clearly related to it, and is striking in its layout, labelling and contents. One of the features of this diagram is the presence of both the right horizon and an oblique horizon. In the remainder of the paper I will trace the presence of the oblique horizon in representations of the sphere, from further medieval manuscript diagrams through to Renaissance paintings. Examining a diversity of visual media not only casts light on the conventions and agency of diagrams but even opens up novel questions about their relationships with the elusive realm of material spheres.
Syrine Kalleli, Astronomical Diagram Vectorisation with Deep Learning
I will present a deep learning model which builds on recent advances in the field, and performs vectorisation by reconstructing diagrams using basic geometric shapes such as lines, circles, and arcs. By extracting the geometric content from astronomical diagrams, this approach not only enables the automatic creation of critical editions but also paves the way for content-based search in the large database of diagrams. In this presentation, I will first briefly review related works, and then present my approach for tackling this vectorisation task. To address labeled data scarcity, we rely on synthetic data generation. I will finish by presenting our results on a large and diverse corpus of real diagrams, highlighting both the achievements and the encountered challenges, along with potential limitations for this task.
Richard Kremer, From manuscript to type: Graphic conventions in the Epitome of the Almagest by Peurbach/Regiomontanus
Composed around 1460, this important and well-known study of the Almagest contains perhaps twice as many diagrams as does Ptolemy’s Greek work. The original copy has disappeared but three early manuscripts are known: Venice, Marciana lat. 328 (for Cardinal Bessarion); Vienna, ÖNB 44 (for King Matthias Corvinus of Hungary); and Cracow, BJ 595 (humanist hand, Rome 1496). Three printed editions were issued in Venice 1496, Basel 1543, Nuremberg 1550. Using analytical tools being developed by Christían Carman to compare the diagrams in the autograph manuscript and printed edition of Copernicus’s De revolutionibus, I will present some examples from the Epitome corpus to explore the consistency of astronomical graphic conventions in the late 15th-century shift from manuscript to print.
Divna Manolova, Canonicity and Diagrammatisation in the Medieval Greek Manuscript Tradition of Cleomedes’ The Heavens and its Commentary by John Pediasimos
Continuing the enquiry I started during the EIDA kick-off conference in 2023, this contribution is dedicated to the exploration of ideas of canonicity and diagrammatisation. My research is based on a source corpus of 84 manuscripts preserving Cleomedes’ treatise The Heavens and then on 57 manuscripts among them that I have been able to consult until now. While every member of the corpus contains The Heavens, some also contain its respective commentary composed by the Constantinopolitan scholar and teacher John Pothos Pediasimos during the last decade of the thirteenth century. Previously, I surveyed the diagrams of The Heavens and proposed to define some of them as canonical; next I studied all variations of the instances of one of the canonical diagrams as preserved in medieval Greek manuscripts. I suggested that the codification of a diagrammatic canon, the increased complexity of the canonical diagrams’ design and the inclusion of non-canonical diagrams were markers of a process of diagrammatisation of the treatise. Now, to continue this line of enquiry, I will study the impact the composition of Pediasimos’ commentary and its own diagrams had on the diagrammatic tradition of The Heavens. In other words, I will examine whether diagrams operate differently across ancient texts and their commentaries and will test the hypothesis that studying diagrams in an exegetical context may be another venue of understanding processes of diagrammatisation in medieval manuscript cultures.
Anuj Misra, Drawing Meaning on Paper: Astronomical drawings in the Sanskrit tradition
In the transcriptive practices of Sanskrit scribes, the drawings of diagrams in astronomical manuscripts may appear largely accessorial insofar as their presence (or absence) is both remarkable and ordinary. For the most part, as one navigates the blank white spaces interspersed among the Sanskrit text on a folio, it is alluring to imagine these blank “canvases” as spaces left to lie in wait for drawings to appear (in the future). And when such drawings are indeed found, it is immensely rewarding to see them as elaborate diagrams, sometimes adorned with bells and whistles like labelling, symmetry, colouration, decoration etc. What is notable in these imitations of an “oral geometry committed to paper”, is their lack of homogeneity: various scribes may copy the same diagram in various capacities, for various purposes, and under various remunerative terms. These variations, although seemingly ad hoc, do carry with it a signature of the diagrammatic currency with which Sanskrit scribes traded in the market of astronomical discourse. In this talk, I explore facets of astronomical drawings in the Sanskrit tradition that could help build a representational ontology of categories, conventions, perspectives, and pictograms to aid in our digital study of astronomical diagrams.
Sajjad Nikfahm-Khubravan, Diagrams as Method of Proof: al-Battānī and Analemma
Nowadays, the sine theorem is the main tool for solving problems in spherical astronomy. Discovery of this theorem dates back to the 10th century when several astronomers and mathematicians of the Islamic world claimed credit for it independently. But this does not mean that astronomers before the 10th century were not able to solve the spherical astronomical problems. In his Almagest, Ptolemy benefited from the so-called Menelaus theorem for solving some of these problems. Nevertheless, applying this theorem had some practical limitations. This encouraged astronomers to seek other solutions. The adoption of the trigonometric function of sine from Indian astronomy by astronomers of the Islamic world in the 8th astronomy led to the development of another technic: the method of analemma. This method was based on orthogonal projection of a sphere on a plane. In his renowned astronomical handbook, al-Battānī (d. 929) solved a series of spherical problems by offering accurate formulas. Only in two of these problems did he discuss the methods by which he arrived at his formulas, which turn out to be based on the construction of analemmas. In this paper, by analyzing these two examples, we show the foundation of al-Battānī’s methods in solving spherical problems.
Jade Norindr, Building the EIDA platform: digital tools for diagram editions
In parallel with EIDA’s research objectives, the digital team is laying the groundwork for an information system dedicated to AI-assisted editing of historical astronomical diagrams. The EIDA platform aims to be a tool to carry out the questions asked by researchers, and shed new light on sources through computational methods and automation of the processing of historical documents. By defining a data model suited to the description of manuscripts and printed sources and implementing an algorithm for the automatic extraction of diagrams, we have taken the first steps toward a workflow integrating artificial intelligence to accelerate the research process. Following a presentation of the architecture we are currently working with, we will explore the tools to be developed, and open discussions about perspectives for digital exploration, analysis, and editing of astronomical diagrams.
Ioanna Skoura, The diagram used by Ptolemy for the determination of solar eccentricity and apogee: some remarks on its tradition
The subject of my presentation is the diagram used by Ptolemy in Almagest III.4 for obtaining the numerical parameters for the eccentric model of the Sun. As far as it concerns the Ptolemaic text which dictates the drawing of this diagram, it displays no significant variants in its manuscript tradition. But this is not the case for the diagram, whose tradition does not coincide with the corresponding textual tradition. Examining the extant witnesses of this diagram we realise that there were two distinct traditions of it. In one of them, the diagram is in conformity with the accompanying text, while in the other it has certain additional elements not dictated by the text. After first presenting some examples of the diagram from both traditions and discussing the (dis)similarities it displays, I will focus on a certain additional element. Specifically, I will discuss the additional letter label which appears in the diagram in some manuscripts and I will argue that its presence contradicts the Ptolemaic conventions related to the lettering of his diagrams.
Florence Somer, An explanation of the use of the astrological diagrams from the Sassanid to the Abbassid period: the reconstruction of a practice
To account for their astrological observations, calculations, and interpretations in the service of a patron, astronomers in late antiquity drew up astral charts that allowed them to visualize a chart of the sky at a specific time. Namely, the exact degree of positioning of these planets in the three different decans of the constellations and the angular relations of the planets to each other. Such square diagrams allowed them to give an answer to questions of destiny by translating the answer of the stars. By placing astrology in the place it occupied, as a science, in the East at the beginning of the 8th century, this presentation aims to show how the diagrams of the astrologers of the Abbasid period, copying those of the Sassanid period, give us an understanding of what the incomplete or lost texts cannot say: the practice of the astronomers of the Sassanid imperial court as it was taken up by the caliphal court of the Abbasids since the 8th century.
Scott Trigg, Imaginary Circles and Physical Orbs: New (?) Ways of Visualizing Planetary Models in Islamicate Astronomy
The tradition of Islamicate astronomy known as ʿilm al-hayʿa, or “the science of the configuration [of the orbs],” aimed to set forth a cosmology based on uniformly-rotating physical orbs, while at the same time preserving the predictive accuracy of models inherited from Ptolemy’s Almagest. Indeed, many works in this tradition identified “doubts,” and unresolved “problems” that arose when interpreting the Almagest models in terms of physical bodies, and offered innovative solutions, yet the manuscript diagrams presenting these models remain little studied by modern historians. Alongside their discussion of models for planetary motion, authors frequently included two different diagrams for visualizing the same model: one diagram depicting physical orbs and another depicting “imaginary circles.” Using examples from authors such as al-Kharaqī (d. 1158), al-Ṭūsī (d. 1274), and al-Shīrāzī (d. 1311), I explore what types of knowledge could be gleaned from these two different types of diagrams, and analyze how the diagrams functioned on a material and mental level to help the reader visualize planetary motion. I highlight the historiographic challenges of situating these diagrams not only in the tradition of the Almagest itself but also Ptolemy’s Planetary Hypotheses, wherein he attempted to translate the abstract circles of his Almagest into a unified physical system. Ultimately, I suggest that Islamicate authors adapted and transformed the “visual idioms” and diagramming practices from both works in order to support different ways of reasoning geometrically.
Stefan Zieme, The geometrical diagrams of the Almagest: George of Trebizond and the revision of lines and angles
In December 1451, after less than a year of work, George of Trebizond completed his translation of the Almagest from Greek into Latin. The translation was commissioned by Pope Nicholas V through Cardinal Bessarion, the latter also supplied George with a Greek manuscript from his personal library. Today George’s translation is still extant in ten manuscript witnesses all dating from the second half of the 15th century. It was also printed in three early modern editions in 1528, 41, and 51. Among the manuscript witnesses there is one that contains George’s autograph marginal corrections, another that was owned by Regiomontanus who annotated his copy, a deluxe copy formerly owned by King Matthias Corvinus of Hungary, and a deluxe presentation copy for the later Pope Sixtus IV. A unique feature of George’s translation is that the numerous diagrams accompanying Ptolemy’s text are numbered. Nevertheless, the total number of diagrams in the different manuscript witnesses still varies up to about 30 % and may contain as few as 186 to as many as 245 diagrams. In this talk I will analyze the differences in the diagrams of George’s translation, which originate from revision of the diagrams in correspondence to the text. I will also comment on how to utilize the diagrams in order to determine George’s Greek base manuscript of his translation from Bessarion’s library, still extant at the Biblioteca Nazionale Marciana in Venice. Based on the diagrams, I will eventually discuss the exemplar and the editorial principles of the early modern printed editions.
