1/34<h2>A peculiar book design that looks like a bat</h2>7418 This manuscript belongs to a peculiar format tradition that has been called “bat books” because instead of flipping through the pages one has to unfold the pages, like a bat spreading its wings. Even when closed, this specificity is perceivable, since the book is designed to be hung upside down – again, like a bat resting on a ceiling.

2/34<h2>A bat book in disguise to fit in a normal book collection</h2>7418 But the binding of this manuscript was rebound when it entered the Royal French Library Collection in 1711, mimicking the binding of a classical codex – a book as we know it. ﻿Today, we know of 63 bat books manuscripts preserved in public libraries. Thus type seems to have been invented in the middle of the 14th c., and it gradually specified as a prefered format for astronomical content (calendars and tables, that needed to be looked at and read through in one glance). This manuscript, however, is quite late in regard of this tradition. That, its content, and its type of folding, make it a singular piece.

3/34<h2>An attempt to match the lunar and solar cycles</h2>7418 This circular diagram is a visual representation of an attempt to align the solar and lunar cycles, based on the Metonic Cycle (from Meton of Athens, a 5th c. B.C. Greek astronomer).

4/34<h2>Clever ways to avoid shifts between the lunar and solar cycles</h2>7418 The center is divided into four quarters indicating the completion of four metonic cycles ("Primus ciclus", "Secundus Ciclus","Tertius ciclus" and "Quartus ciclus"). Each quarter is graduated in 19 divisions, but instead of beginning with each time with a "1", it goes "15-16-17-18-19-1-2-3-4-5-6-7-8-9-10-11-12-13-14", distributing five divisions more to each quarter. A lunar year, is achieved in as much time as it takes to get back to the exact same syzygy (Sun-Earth-Moon configuration that, from Earth, makes the Moon appear a certain way). But this lunar cycle doesn’t coincide with the solar cycle. A tropical year (the time it takes for the Sun and Earth to get back to the exact same position one towards the other) is longer than twelve lunar months. One then has to find the most common denominator between those two kind of cycles the periodically realign the two calendars. Continue learning about <a href="https://alfa.obspm.fr/manuscripts/bnf7478?screen=DrtUODZQdD80JatJqlw1" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">this manuscript.</a>

5/34<h2>Metonic cycles and Golden Numbers</h2>7418 To avoid any offset between these two calendars that give temporal references to humans depending on what kind of activities they focus on, the Metonic Cycle was used: indeed, it points out at as much regularity as possible, stating that every 19 solar years, the Moon is approximately at the same phase on a given date, allowing us to align the lunar and solar calendars. The position of any given solar year in the Meton Cycle is called “Golden Number”&nbsp;and is displayed in the inner red numbered circle (from 1 to 19, four times. Year 1456 in rank 13 on the Metonic cycle, year 14[5]7 is 14, and year 1458, 15, and so forth.

6/34<h2>Keeping precious content together</h2>7276A This parchment binding is equipped with leather straps. These served to keep the volume closed and protect the paper pages contained in it. A reader needed to untie the straps before he could read the texts inside, play with the amazing paper instruments contained in this volume. This kind of binding was not uncommon in the 16th century.Also back then, it was a habit to write down notes on a book cover as seen here: the ink inscription looks like a student note, indicating a value for the lunar node's period of revolution.

7/34<h2>Paper tools</h2>7276A This is the nightmare for every librarian as such loose pieces are very hard to preserve and not to loose. Five delicate colored paper discs are kept in an envelope sticked to the inside of the front cover of this volume. These are parts of paper instruments that were well known to the medieval astronomers: instruments that visualize and help explain the intricate motions of the planets. Visible on the two larger discs there is the graduation of the zodiac in twelve signs of thirty degrees each, used as the reference frame to indicate the positions of the planets.The smaller green and yellow rings materialize the idea of a planetary orb, the space through which a planet is revolving around the Earth. Within each orb a little paper disc (yellow or brown) is attached by a thread that represent the epicycle of the planet. The epicycles are equipped with paper handles to facilitate the turning.

8/34<h2>Increasing complexity</h2>7276A Not all of these paper instruments are the same as they can include more or less mobile parts. On the top left (1) the structure of motion for Mars, Jupiter or Saturn is shown - these planets are all 'superior planets'. They have the green orb shifted off center. The direction and quantity of this shift, called 'eccentricity', is characteristic for each of the three. In addition the body of the planet moves on an epicycle. The size of the epicycle is different for each.The top right (2) appears to represent Mercury (although its epicycle is missing). Its characteristic is the dark green eccentric orb. While the planet moves through it the center of this orb itself moves on a small circle (see 3).The remaining two instruments represent the Moon and Venus (with the Sun) respectively.

9/34<h2>Multimedia teaching in the 16th century</h2>7276A This representation of the complex motion of the Moon is built as a layered moveable diagram. Four parts can be moved around various centers. The position of the Moon is depending on several motions, among them is the mean motion of the Sun - here represented by the red disc below all the others.The black ring (determining the Moon's apogee, i.e. the point farthest from the center) and the blue ring (the orb of the Moon's epicycle) both depend on the mean Sun. According to Ptolemaic astronomical theory the apogee and the epicycle must be equally distant from the mean Sun. The instrument, as shown on this photo, is not in an astronomically meaningful position.For good teaching it is not enough having a fancy device at your disposal, but it also needs someone who is able to move every part of it to the correct position. Continue learning about <a href="https://alfa.obspm.fr/manuscripts/bnf7276a?screen=rBry9AbSFj6T5Q2YvoVq" rel="noopener noreferrer" target="_blank">this manuscript.</a>

10/34<h2>A moveable zodiac</h2>7276A Here is a different representation of the motion of trepidation (access and recess) of the zodiac of the eighth sphere with respect to the ninth sphere. In this case, and differently from the previous device, both small circles (1 and 2) centred on the equinoctial points are represented. Instead of a thread only representing the ecliptic, a paper tab is introduced, showing half of the zodiac (3). The invisible part of the zodiac is not represented. Note the elegant lemniscate shaped curve at the center (4). This indicates the motion over one full trepidation cycle performed by the beginning of Cancer, the point halfway between the equinoctial points. The paper strip contains a small window at its center allowing the user to correctly position this midpoint. In an unusual way, here the the zodiac is represented vertically while the North and South poles are to the side. This is possibly a strategy to get to fit a larger diagram on the page. The diagram also represents the central, and two extremes positions of the axis of the poles as the moveable zodiac goes through a revolution.

11/34<h2>Several works arranged in a chronological order</h2>7281 This manuscript exhibits, in a way, the history of medieval astronomy and its different phases. Indeed, it includes various works from Al-Fargani's Liber de scientiae stellarum (some kind of compendium of Ptolemaic astronomy dating from the 9th century) to 15th&nbsp;century treatises in the movement of the skies, all arranged in a chronological order.

12/34 <h2>A History of Astronomy Manuscript in the form of a Library</h2>7281 The variety and texts, and the aforementioned organization of the works tend to indicate that this manuscript has been designed as a toolbox for a reader who was in need of easily accessible references and texts, thus arranged in an orderly fashion. It may have primarily been a student manuscript, more than tools used by a seasoned practitioner of astronomy. Reading marks, notes, diagrams and calculations were added afterwards in the margins, on blank pages or on leaflets. Adding content might have been more important to the owner(s) of the manuscript than the aesthetics or the readability, since many comments were added while the letterheads remained at the project state. Apart from the main scribe, texts have been copied with two other hands, and the marginal annotations give examples of at least four scribal hands: one of Jo.B., two gothic from the second half of the 15th century and a humanistic one from the beginning of the 16th century.

13/34<h2>In search of the scribes, owners and readers identities</h2>7281 The manuscript as a whole was assembled during the 15th century, and the name of the main scribe was a certain « Jo. B » (probably John...) whose monogram is visible for instance on folios 85v, 160r, 232r and 273r.

14/34<h2>In search of the scribes, owners and readers identities</h2>7281 At the very end of the manuscript, folio 284v we can read, by different hands, the names « Loys Lepuiset » and « Johannes Avis », who may have been owners of the manuscript.

15/34<h2>In search of the scribes, owners and readers identities</h2>7281 After the Renaissance, we can trace it back to the Bibliotheca Colbertina in the 17th century, a collection of more than 8000 volumes that has been transferred to the Royal Library of France in 1732. The red leather cover of the manuscript (or “Royal Morocco binding”) is yet again&nbsp;embossed with the gold royal seal. Continue learning about <a href="https://alfa.obspm.fr/manuscripts/bnf7281?screen=9F03b5K09xvxfdTvGzdb" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">this manuscript.</a>

16/34<h2>Editing ancient texts implies taking care of all the different versions of a said work</h2>7281 A note from the 17th century indicates that « this version differs from the Nuremberg edition of 1537 and the Parisian one of 1546 available at the librarian dominus Arnaudi Pratoris Forcalcaris » (« ista versio diversa est a versione que edita est Noribergae anno 1537 et Parisius anno 1546 apud bibliotheco Arnaudi Pratoris Forcalcaris »), telling us that this version is the translation by Gerard of Cremona.

17/34 <h2>Nine eclipses record almost faded</h2>Escorial Probably because of time, the brown ink used to write this small table at the bottom margin of the page is, in places, almost fading away.&nbsp;Deciphering it, it is possible to recognize the handwriting and to attribute it to John of Murs, one of the most important Parisian astronomers of the first half of the 14th century who is, with others, responsible for the first Latin version of the Alfonsine tables. In this table,&nbsp;John of Murs recorded the result of computations of nine lunar or solar eclipses occurring in between 1341 and 1352. He lists the time of the eclipse, its magnitude, its duration and if it is a solar (in three cases) or a lunar eclipse (in six cases).&nbsp;This is one of the multiple passages of the manuscript where John of Murs shows his deep interest in the computation of eclipses.

18/34<h2>Two detailled eclipse computations and observations</h2>Escorial This folio was written by John of Murs, a very important Parisian Astronomer of the early fourteenth century, responsible, with others, of the introduction in Latin of Alfonsine astronomy. The text accounts for John of Murs' various attempts at computing a solar eclipse visible from Paris in 1333. This is a unique document where we see a first rank astronomer of the period at work: he is comparing different tables and methods of computations and evaluating them.

19/34<h2>Two detailed eclipse computations and observations</h2>Escorial What is even more striking is that in this very same folio John of Murs records also how he observed the eclipse in the presence of different important witnesses including a princess and three Franciscans. The result of this observation are one of the elements he takes into account when thinking about the best computation methods.

20/34<h2>Two detailed eclipse computations and observations</h2>Escorial Four years later, in 1337, a new solar eclipse could be observed. John of Murs then comes back to this same part of the manuscript and includes a shorter report of his computations and observation. Continue learning about <a href="https://alfa.obspm.fr/manuscripts/escorial10?screen=fHRzCCnRzRIE7YEnaDIz" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">this manuscript.</a>

21/34<h2>Velocities as possible parameters in eclipse computation?</h2>Escorial This folio was entirely used by the famous 14th century astronomer John of Murs. He included different information all related to a particular step of eclipse computation.

22/34<h2>Velocities as possible parameters in eclipse computation?</h2>Escorial Among other things he mentions the names and works on the same topics by two other important Parisian astronomers of the same period with whom he might have been in contact: John Vimond and John of Saxony.

23/34<h2>Velocities as possible parameters in eclipse computation?</h2>Escorial The main table of the page lists different quantities related to eclipse computation (shadows of the Moon, the Earth, velocities of the Sun and the Moon). It focuses in particular on the lunar velocities and, along with the accompanying text, it seeks to explore if lunar velocities are well understood enough to become a quantity around which eclipse computations can be organised.

24/34<h2>Velocities as possible parameters in eclipse computation?</h2>Escorial On this page we find two tables copied by the famous 14th century astronomer John of Murs. The one to the right is a classical table for eclipse computation which is included here from the Toledan tables. The one to the left is more original. It also concerns eclipse computation and more specifically velocities of the Sun and Moon as well as shadows. The original point here is that shadows are presented as a “function” of velocities.&nbsp;It is an important innovation as velocities then become a central quantity of eclipse computation. As far as we know, this is the only known table in the whole Alfonsine corpus (more than a 1000 manuscripts) proposing this relation! Probably John of Murs' proposition was not considered pertinent by his contemporaries and by later astronomers.

25/34<h2>One very precious piece of text!</h2>Erfurt In this small piece of text, we see the association of two Parisian astronomers: John of Lignères and John of Saxony.

26/34<h2>One very precious piece of text!</h2>Erfurt They are the authors for the two most copied texts in alfonsine astronomy in the 14th and 15th century.&nbsp;This text is what we call an explicit (closing words) of a text by the astronomer 1️⃣ “Magistri Johannes pychardii de lineriis” (i.e. John of Lignères, second line). The text was copied by the hand of 2️⃣ “Johannes de danecowe” (i.e. John of Saxony, end of fourth and beginning of fifth lines). Moreover we learn that John of Lignères text was composed in 1322 (fourth line) and copied by his pupil John of Saxony in 1323 (fifth line in roman numerals). Continue learning about <a href="https://alfa.obspm.fr/manuscripts/erfurt377?screen=qCejtBGFJTqVwPF9S9X6" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">this manuscript.</a>

27/34<h2>Learnig from shadows</h2>Erfurt These three little diagrams represent the same instrument: a gnomon. This is probably the most simple astronomical instrument one can conceive: a vertical stick casting shadows on the ground. It is interesting to see how the same object is pictured in different ways. It is even more interesting if we understand that these different representations show the instrument as it should be used in a procedure described in the text nearby that allows finding the cardinal points and the meridian line of the place where the gnomon is set.&nbsp;The diagrams, as well as the texts, are copied by John of Saxony as he was learning astronomy from the text of his master, John of Lignères.

28/34<h2>The gnomon in a mathematical demonstration</h2>Erfurt This diagram, and the small text that is just nearby to its right, concern the gnomon and work with shadows. It is a marginal annotation by John of Saxony to the text of his master, John of Lignères in Paris around 1323. The text and diagram provide a geometrical proof, mentioning several propositions of Euclid Elements, for two procedures described in John of Lignères text and allowing to connect the time of day and the length of the shadow. It is very rare to witness such grounding practices which might have been an integral component of advanced astronomy teaching in medieval universities.

29/34<h2>(What's the story) ÖNB, 5203?</h2>Vienna In 1476 Bernhard Walther (1430-1504), a Nuremberg merchant and enthusiastic pursuer of astronomical observations,&nbsp;purchased the complete library of Regiomontanus together with some instruments from Regiomontanus’s heirs.This manuscript was later acquired by a Nuremberg polymath and editor, Johannes Schöner (1477-1547), who is also responsible for assembling the volume, foliating it, and adding a table of contents and many titles throughout. This manuscript includes the work of three hands: besides Regiomontanus’s, that of Georg Peuerbach, and an unidentified third hand. Georg Peuerbach (1423-1461), a well-known Austrian astronomer and mathematician especially renowned for his account of Ptolemaic astronomy, was Regiomontanus’s teacher in Vienna. This manuscript comprehends works on various topics, ranging from astronomy and astrology, to music, mathematics and physics.

30/34<h2>Ptolemy for beginners</h2>Vienna The first 24 folios of this manuscript are covered by Peuerbach’s Theoricae Novae. This is the most famous work by Puerbach and consists of an exposition of Ptolemaic astronomy in a more elementary way. The work is copied by Regiomontanus and includes his own notes. Inserted right at the beginning of the Theoricae Novae, this flyleaf includes Regiomontanus’s annotations on&nbsp;the equation of the sun with two diagrams of the solar model, which represents the first model any student of astronomy would have to deal with. The equation of the sun is a crucial quantity used to determine the ‘true sun’, namely the true position of the sun, from a fictitious solar position called ‘mean sun’.

31/34<h2>Mercury is so special</h2>Vienna At the bottom of this folio, in the right margin it is found a little diagram in black and red ink. This diagram is meant to show the effect of the ‘small circle’ of Mercury. Mercury complex motion have always been a concern for astronomers. In the Ptolemaic traditions, Mercury model is specific because, in addition to the usual epicycle and deferent circle, it has a supplementary ‘small circle’ in order to adjust the planet distance to the earth. This peculiar device is usually not reflected in the structure of Mercury tables but can be perceived in some of their values. Peurbach and then Regiomontanus were particularly interested in this small circle and its effect. In this diagram and marginalia we can see one attempt of Johannes Schöner to reflect on the ‘small circle’ of Mercury. Continue learning about <a href="https://alfa.obspm.fr/manuscripts/vienna5203?screen=Al0Uh0bvqiLWC3xB9zMg" rel="noopener noreferrer" target="_blank" style="color: rgb(29, 28, 29);">this manuscript.</a>

32/34<h2>C'mon, hit the right chord!</h2>Vienna Five folios (ff.28r-32v) includes Regiomontanus’s text on the calculation of tables of sines and chords, later published, in 1541, by Johannes Schöner. The handwriting of the treatise dates in about 1462. This is a witness of an important shift in astronomical computation with the introduction of a large radius (r = 6,000,000, at intervals of one minute) and extra accurate sine table. This particular folio is also interesting for its mix of diagrams, tables and text.

33/34<h2>Think big!</h2>Vienna About a dozen folios include tables of squares (ff. 33r-41v) and of cubes (ff. 48r-50r). This folio exhibits an incomplete table for the extraction of square and cube roots. The peculiarity of this table is the inclusion of extremely big values; this stands as a clear hint of a crucial mark of change in the computational practice of expert astronomers.

34/34<h2>An astronomical recipe</h2>Vienna About five folios (ff. 54r-58v) include a small text about the computation of an oblique ascension table as well as the actual tables (tables used to find rising and setting time of stars). The title of this work is provided at the top of the page by the hand of Johannes Schöner. This manuscript also includes a text on the equation of time (ff. 70r-71v)&nbsp;by Regiomontanus. Trigonometrical tables of right and oblique ascension are often found with tables of the equation of time, which is an essential tabular quantity in all sets of historical astronomical tables.

In this path we show manuscripts that are “hors cadre”. In a certain way there are only exceptions but we propose some of different kinds. Some are exceptional for their initial codicological organization (batbook) ; others for their visual organization (instruments manuscripts; others for their intellectual content (a ‘history’ of astronomy by the texts put together at the end of the 15th century ; others for their author (Regiomontanus, John of Saxony, John of Murs autographs).