1/43<h2>Weaving parchment and astronomical traditions</h2> Here we can see a parchment tear repaired with stitches: a vibrant reminder of the animal origin of the writing material used in this manuscrit.&nbsp;The text copied here is a part of John of Lignères canons ``Priores astrologi…” redacted around 1321 and to become one of the most successful texts of the whole Alfonsine tradition. The presence of these canons in a manuscript which for the most part was copied about 20- or 30 years before with older material shows that the introduction of Alfonsine elements in the Latin astronomical tradition was a gradual process. Continue learning about <a href="https://alfa.obspm.fr/heritage/touching?screen=NsBCOEJcj575PmsCtl9m" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">the materiality of a manuscript.</a>

2/43<h2>Organising the page</h2> The organisation of the page content is typical of university manuscripts. A main text copied with a bookhand and nice rubrication is surrounded by a wide margin in which marginal comments, diagrams and tables are added.&nbsp;The text copied here, Sacrobosco Algorismus, concerns basic arithmetic with integers. It is one of the manuals of the medieval art faculty in which mathematical astronomy was also taught.The little diagram on the top left of the page shows the power of two and three and their mutual product. The table below is&nbsp;around different powers of tens and the digits. Continue learning about <a href="https://alfa.obspm.fr/heritage/seeing?screen=6QBdATZcl0SjGI4t4aHZ" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">the visual aspects of a manuscript. </a>

3/43<h2>Astronomy and the Calendar</h2> The text concerns the calendar and the determination of different Catholic religious dates. From the middle of the 13th century onward astronomers had a great interest in these matters as they tried to improve the calendar based on their astronomical knowledge. This manuscript is one the numerous examples of this strong connection.

4/43<h2>Time cycles' in your hand</h2> Also striking here is the use of the hand as a support for a table demonstrating some of the cycles ruling the calendar. We can see that these cycles are not managed with numbers but with letters and syllables.&nbsp;By contrast astronomical cycles are managed with (sexagesimal) numbers in tables arranged in grids of rows and columns. This fundamental contrast in the intellectual tools used in the two domains is one of the elements explaining how long it took for astronomical knowledge to produce a calendar reform. Alfonsine astronomers were conscious of this issue and looked for ways to soften the gap. Continue learning about <a href="https://alfa.obspm.fr/scientific/disciplines?screen=RnK7iBKQEeK3xNwATLlV" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">the disciplines associated with the corpus.</a>

5/43<h2>Geometry of a lunar eclipse</h2> The text here is Sacrobosco's de Sphaera, a basic university textbook written in the 13th century exposing the core elements of medieval cosmology: The Earth at the center of the cosmos surrounded by different spheres: first for the four elements (earth, water, air and fire) and then for the different celestial objects: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn and the fixed stars. The layout of the page with a bookhand rubricated (i.e. with red and blue) text and a series of marginal comments in a more cursive hand including different diagrams is also typical of late university manuscripts.In this part of the text Sacrobosco explains the geometry of an eclipse. Here we see typical diagrams showing the Moon in the Earth's shadow and the situation of various observers, marked by a tower.

6/43<h2>Head and tail of the dragon</h2> This is a beautiful diagram for lunar eclipses. We see the Moon below in the shadow of the Earth, with its nice castle. On the top of the diagram we see the Sun with its intriguing spiral lines from the center. Note the use of blue for the Moon and of oblique lines in the cone to mark shadowed parts.Another intriguing point concerns the Moon which seems to be revolving around two distinct circles with slightly different centres. The Moon's revolution occurs on a circle inclined about 5° on the ecliptic. While this fact is in most cases of little influence on the way we see the Moon, it is of utmost importance in case of an eclipse. Lunar and solar eclipses can occur only when the Moon is close enough to the ecliptic that is when it is at the intersection point between the ecliptic and its circle of revolution. These two points, called the head and tail of the dragon, were almost considered a sort of planet and were taken into account in astrological predictions.

7/43<h2>Geometry of a solar eclipse</h2> This is a beautiful diagram for solar eclipses. We see the Moon below the Sun producing a shadow which falls on only part of the Earth. Only one out of the four castles represented on the Earth is in the Moon's shadow. On the top of the diagram we see the Sun with its intriguing spiral lines from the center. Note the use of blue for the Moon and of oblique lines in the cone to mark shadowed parts.&nbsp;﻿Another intriguing point concerns the Moon which seems to be revolving around two distinct circles with slightly different centres. The Moon's revolution occurs on a circle inclined about 5° on the ecliptic. While this fact is in most cases of little influence on the way we see the Moon, it is of utmost importance in case of an eclipse. Lunar and solar eclipses can occur only when the Moon is close enough to the ecliptic that is when it is at the intersection point between the ecliptic and its circle of revolution. These two points, called the head and tail of the dragon, were almost considered a sort of planet and were taken into account in astrological predictions.

8/43<h2>Geometry of lunar phases</h2> Although the phenomenon of the Moon's phases is much less spectacular than that of eclipses, it is one of the most striking and common. Here we see a nice diagram explaining this phenomenon with the Sun on the top and eight different positions for the Moon around the Earth. This is a kind of dynamical diagram where one is invited to mentaly follow the Moon over the course of a lunar month. It is interesting also to note the different graphical treatments used on the surface of the Sun, Moon and Earth. The Moon is partly in shadow and partly in light and this is represented by the shaded and light part on its surface. The Sun is radiating light and this is marked by the dotted and full spiral line growing out of its center. The Earth is inhabited and this is marked by the castle.

9/43<h2>Nine eclipses record almost faded</h2> 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. Continue learning about <a href="https://alfa.obspm.fr/historical/paris?screen=knVNWyPuplPkrinmlg9N" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">the Parisian corpus.</a>

10/43<h2>The quadrant: a fundamental instrument</h2> Here is a diagram of an instrument called the quadrant. It was, like the astrolabe, an instrument used for daily motion astronomy: to measure altitude of celestial objects above the horizon, to measure shadows, find local time and do different kinds of related computations. Two main types of such instrument were circulating. The one represented here is a “quadrans vetus” (old quadrans). A striking thing about this diagram, and over similar one representing instruments, is the great accuracy of the drawing. all the different parts, scales and lines are in proportion to each other. One could actually use the diagram to perform some computation which does not involve taking measures of external objects. The instrument feels like ready to be embodied out of the page or simply cut and pasted on a solid support.

11/43<h2>Gnomon and basic geometry</h2> Here is a nice diagram on the topic of shadows and gnomon. This is the most simple astronomical instrument allowing us to compute time, solar altitude and directions. This diagram was also the basis of different geometrical reasoning grounding these computations which are based on the numerous similar right angle triangles in the figure. Note how many of the sides of these triangles are labeled with a specific name allowing to refer to them either in a proof or in a procedure. Learn more about <a href="https://alfa.obspm.fr/scientific/spherical?screen=qfwkjma6OFyElpSdCb0P" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">spherical astronomy.</a>

12/43<h2>Astrolabe</h2> We have here a couple of diagrams representing different parts of an astrolabe. This instrument is probably the most famous astronomical instrument of the medieval period. It was described by Ptolemy but is mainly a construction of Islamicate astronomers. The astrolabe is also one of the first scientific objects to circulate, in al-Andalus, from Islamicate to Christian scholars. The instrument is used for many purposes in relation to daily motion astronomy: to find time, to measure altitude of celestial objects, to compute the length of day and night, to compute the ascendant, etc. A striking thing about these diagrams, and over similar ones representing instruments, is the great accuracy of the drawing. All the different parts, scales and lines are in proportion to each other. One could actually use the diagram to perform some computation which does not involve taking measures of external objects. The instrument or its parts feels like ready to be embodied out of the page or simply cut and pasted on a solid support. Even in the representation of a technical object, this kind of realism of the image is interesting also for a global and long term history of visualisation.

13/43<h2>Solar theory</h2> This diagram, from a text known as the Theorica planetarum, is a recurrent element of&nbsp;university manuscripts dealing with mathematical astronomy. In this particular instance, the outer scale of this diagram, representing the zodiac, looks like it has been extracted from an astrolabe ream (?). The inner diagram is more abstract and mathematical. It represents the theory of the Sun. The Sun itself is represented six times as a small circle enhanced with red ink: once on the limit of the four quadrants; two more times in symmetric intermediary position. The circle on which the Sun revolves is centered on h. It is thus eccentric with respect to the Earth which is also the center of the zodiacal outer ring (point e). This eccentricity is the geometrical device used to account for the varying speed of the Sun over the course of the year (faster when it is near the Earth at the bottom of the diagram, slower when it is far from the Earth at the top of the image).&nbsp;Apart from the top and bottom position, we see that for the four others, three lines are drawn from e and h toward the Sun. Each time two of them are parallel, and one oblique. These lines allow us to define a mean and a true position of the Sun.&nbsp;These two quantities are the basis on which a complementary tabular expression of the solar theory allows computations of the Sun position in the zodiac as seen from the Earth.

14/43<h2>Theory of the superior planets</h2> This diagram, from a text known as the Theorica planetarum is a recurrent element of&nbsp;university manuscripts dealing with mathematical astronomy. In this particular instance, the outer scale of this diagram, representing the zodiac, looks like it has been extracted from an astrolabe ream (?). The inner diagram is more abstract and mathematical. It represents the theory of what ancient and medieval astronomers working in a Ptolemaic frame called the superior planets: Mars, Jupiter and Saturn.

15/43<h2>Theory of the superior planets</h2> The planet itself is represented as a very small circle (here toward the bottom of the image) on the periphery of a slightly larger one called an epicycle.

16/43<h2>Theory of the superior planets</h2> Over all the planet is represented six times: once at each of the four quadrants and two more times in symmetrical intermediary positions.The circle on which the epicycle revolves is eccentric with respect to the Earth. It is called, in medieval astronomical theory, the deferent circle. This eccentricity, coupled with the epicycle, is the geometrical device used to account for the varying speed and even retrogradation of the superior planets as seen from the Earth.

17/43<h2>Theory of the superior planets</h2> In fact each planet has three centers. The middle one is the center of the deferent on which the epicycle circulates. The top one is the equant point around which the epicycle centre moves at a constant pace. The bottom one is the Earth.

18/43<h2>Theory of the superior planets</h2> Apart from the top and bottom position, we see that for the four others, four lines are drawn from the planet centers toward either the planet itself or the center of its epicycle. Each time two of them are parallel, and two are obliques. These lines, with a few others that are not drawn here, allow the definition of different quantities (mean motions and equations).&nbsp;These quantities are the basis on which a complementary tabular expression of the theory allows computations of the planetary position in the zodiac as seen from the Earth.

19/43<h2>Theory of the superior planets</h2> The last set of lines in this diagram is striking because they are uniquely associated with numbers. One of the effects of the model is to push the epicycle closer or farther away from the Earth. While the geometrical mechanism to do so is rather simple (eccentricity) it is difficult to account for this in a tabular expression of the model. These lines represent an approximation, initially conceived by Ptolemy, used in the planetary model to account for this. Both in the tables and in the diagram they are called “minuta proportionalia.” As often diagrams and tables are shaped in a close relationship. Continue learning about <a href="https://alfa.obspm.fr/scientific/planetary?screen=YGuSNrH9l5dwXmJo9Vfh" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">planetary astronomy.</a>

20/43<h2>Theory of trepidation</h2> This diagram, from a text known as the Theorica planetarum, is a recurrent element of&nbsp;university manuscripts dealing with mathematical astronomy. It represents the theory of what ancient and medieval astronomers working in a Ptolemaic frame called the eight sphere, carrying the zodiac and the fixed stars. The proper motion of this sphere, also known as the precession of the equinoxes, is very slow and only perceptible over a time span of about a century. It is nonetheless very important because the sphere of the fixed stars carries most of the reference points against which the motion of all the other celestial objects are measured. Different hypotheses concerning the motion of this sphere were circulating. Ptolemy, and after him many astronomers, thought of a continuous motion at a constant pace. Others, following a text attributed to the Arabic astronomer Thabit ibn Quara, thought that this motion had a varying speed throughout the centuries and a maximum value. This motion was called trepidation. Parisian Alfonsine astronomers, and after them all Latin astronomers in Alfonsine astronomy followed&nbsp;a combination of the two hypotheses.&nbsp; The diagram presented here follows the hypothesis of trepidation. A striking element of these diagrams is that contrary to planetary diagrams it contains no straight line. This is because the different circles represented here are to be imagined on a sphere.&nbsp;The motion of trepidation is based on two epicycles, which instead of being on a plane like planetary epicycles, are on the surface of a sphere.

21/43<h2>John of Murs computing eclipses! </h2> The little table at the bottom margin of the page records the fundamental element of a Solar eclipse. According to the information here this solar eclipse took place on July 7, 1339, had a maximum intensity at 2h 11min and 20 sec after noon for a total duration of 2h13min and 22 sec.&nbsp;The precision of these values, far beyond the range of naked eye observations, clearly indicate that they are coming from a computation.&nbsp;These kinds of computation records, of eclipses or any other astronomical phenomena, are rare and precious. However, Alfonsine astronomers progressively developed a trend of noting down computations in their manuscripts, or even systematically as a type of commentary to astronomical treatises. This proved to be a long lasting initiative as well into the modern period this habit was maintained by European astronomers.In this manuscript we find many such computation records. It can be considered as one of the first witnesses of such a practice. Moreover we know who is the author of these computations. It is John of Murs, one of the most important Parisian astronomers of the early 14th century responsible for the recasting in Latin of the Alfonsine tables. Continue learning about <a href="https://alfa.obspm.fr/scientific/eclipse?screen=DvVatEU7ZRZ90BsappvC" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">eclipses.</a>

22/43<h2>Two detailled eclipse computations and observations</h2> 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.

23/43<h2>Tow detailed eclipse computations and observations</h2> 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.

24/43<h2>Two detailed eclipse computations and observations</h2> 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/heritage/exceptional?screen=rZxoe3a3oePlii5nOnKX" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 0);">exceptional manuscripts.</a>

25/43<h2>'Arabic' and 'Christian' years</h2> These small tables, inserted here in the manuscript by the famous Parisian astronomer John of Murs, betray his interest in calendrical questions: they compare the length of the “Arabic” and “Christian” years.

26/43<h2>Understanding parallax</h2> This is a diagram about parallax which is a correction, linked to the distance of a celestial object with respect to its observer, that was fundamental in eclipse computation. Parallax allows to take into acount the position of the observer on the earth.&nbsp;The diagram shows two symmetrical positions. Let us consider only one.

27/43<h2>Understanding parallax</h2> On the outer great circle, under the label “sol” we see a small circle representing the Sun.&nbsp;A straight line starts from this point. Following it to the left we meet another small circle representing the Moon under the label “luna”. Continuing to follow the same line, we meet a third small circle, which also represents the Moon in another position. Finally the line ends in a point which is the center of a circle representing the Earth under the label “terra”. It is important to note that the Sun and Moon are aligned as seen from the center of the Earth. Now on the outer circumference of the Earth we see a second series of straight lines pointing to the Moon. Following these straight we realise that the two luminaries are no longer in conjunction! This is the effect of parallax and it must be corrected in order to compute eclipses.

28/43<h2>Understanding parallax</h2> Why now is the Moon represented twice? To understand this, it is first important to notice that these two representations of the Moon are both on the circumference of the same small circle which is named the epicycle of the Moon.&nbsp;In one case the Moon is close to the Earth, thus the parallax effect is important, in the other case the Moon is far from the Earth, thus the parallax effect is smaller. Indeed, usually&nbsp;different parallax tables are computed for these two opposite situations. As often diagrams and tables are shaped in a close relationship.

29/43<h2>Size of the earth shadow</h2> These diagrams demonstrate one important element of the theory of lunar eclipses: the diameter of the Earth shadow varies with the distance of the Sun to the Earth. When the Sun is at its greatest distance from the Earth (on the left of the diagram) the Earth shadow is going to have a small diameter (on the right of diagram). On the contrary, when the Sun is closer to the Earth (second Sun on the right of the diagram) the Earth shadow is going to be larger (on the left of the diagram). The different captions indicate either celestial objects “sol” for the Sun, “t’ra” for the Earth, or directly expressions corresponding to quantities that are found in numerical tables expressing these same mathematical relations. Like other diagrams in the manuscript, this one makes an interesting use of texture and colors (red) to mark light and shadow.

30/43<h2>Solar eclipse diagrams</h2> This is a canonical diagram representing a solar eclipse. On the left, the moment of first contact, in the middle totality, on the right the moment of last contact. The procedure to construct these diagrams is explained in different texts which are generally the end point of eclipse computation.

31/43<h2>Lunar eclipse diagrams</h2> This is a canonical diagram representing a lunar eclipse. On the left, the moment of first contact, in the middle totality, on the right the moment of last contact. The moving body in this diagram is the Moon, while the fixed circle in the middle is the Earth's shadow.&nbsp;The specific dotted and plain spiral line covering the Moon just before and after the eclipse shows, following the representation convention of this manuscript, that it reflects light. The procedure to construct these diagrams is explained in different texts which are generally the end point of eclipse computation.

32/43<h2>John of Murs computation of a lunar eclipse</h2> This small text at the bottom of the page is from the hand of the famous early 14th century Parisian astronomer John of Murs. It is the report of a computation concerning a lunar eclipse occurring on April 18, 1334. There are several such reports by John of Murs in this manuscript concerning either lunar or solar eclipses. Two points can be pointed here.

33/43<h2>John of Murs computation of a lunar eclipse</h2> First, John of Murs clearly used the Alfonsine tables for this computation: the end of the small text here reads: per tabulas Alfonsii regis castelle ('by the table of the King Alfonse of Castille').

34/43<h2>John of Murs computation of a lunar eclipse</h2> The care with which the report has been copied, is shown for instance by the nice capital letter used to open the text.

35/43<h2>John of Murs computation of a lunar eclipse</h2> This care is shown as well by a closer study of the text revealing that John of Murs chose to report the values of very specific quantities marking important steps in the computation and not the full computation (which would have taken several pages). This note is thus a conscious will to add a new type of text (computation report) to the existing corpus of mathematical astronomy text. In particular it is not a “spontaneous” draft computation reported here only by chance.

36/43<h2>Comparing lunar equation in the Toledan and Alfonsine traditions</h2> This small table at the bottom of the page and its companion text are from the hand of the famous 14th century Parisian Astronomer John of Murs. They are comparing the values of a quantity from the lunar theory, the equation of the argument of the Moon, as tabulated by two different astronomical tables sets: the Toledan tables and the Parisian Alfonsine tables. For this particular quantity the Toledan tables generally propose larger values than the Alfonsine tables. The latter were promoted and included in Latin mathematical astronomy by John of Murs and a handful of his colleagues at the Paris Arts faculty around the 1320’s. The former were established about a century before. This will have different consequences on computing the moon and eclipses.

37/43<h2>Velocities as possible parameters in eclipse computation?</h2> 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.

38/43<h2>Velocities as possible parameters in eclipse computation?</h2> 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.

39/43<h2>Velocities as possible parameters in eclipse computation?</h2> 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.

40/43<h2>Velocities as possible parameters in eclipse computation?</h2> 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.

41/43<h2>The length of the year</h2> While the table copied on this page is by an unknown hand, the text surrounding it was copied by the famous 14th century astronomer John of Murs. The topic addressed here concerns a fascinating phenomenon: the precession of the equinoxes or the motion of the eight sphere. This is a very slow motion of the stars, discovered by Hipparchus two centuries before the common era.&nbsp;It has important consequences, although disclosed only after several centuries, on the calendar as well as on astrology. It was thus a central concern for astronomers, to some extent even until today. Alfonsine astronomy, as expressed in Latin sources shaped by John of Murs and his colleagues at the Arts faculty propose a peculiar theory of this motion of the stars with a double motion. The consequences of this theory, in particular on the length of the year, are explored here with the tables and text.

42/43<h2>Another eclipse computation</h2> This folio was used by the famous 14th century astronomer John of Murs to report a solar eclipse computation for 1339. There are a few others like this in the manuscripts. This one shares with them the fact of being a “clean” report with only very specific selected steps of the computation record on the page.

43/43<h2>Another eclipse computation</h2> it is original also because it contains a diagram of the figure of the eclipse at the time of totality.

End of the 13th century, this university textbook manuscript contains the Toledian tables and many autograph notes from John of Murs with a strong astronomical content.