Shaping Mathematical Practices Of The Science of the Stars

Extant manuscripts, early library catalogues, lists of loans and wills are key witnesses for better understanding the mathematical practices and innovations in different milieux at the end of the Middle Ages. A systematic exploration of those sources unravels intellectual exchanges, scientific practices and methods. They also allow to delineate ‘communities of learning’, composed of scholars versed in similar readings and practices. Those networks of medieval scholars, fostered by the university system and collegial institutions, catalysed the rapid development of new approaches or adaptations in the scientia stellarum, astronomy and astrology, an active branch of mathematics at that time. This lecture looks at how astronomical practices have been shaped by those communities at the end of the Middle Ages. More particularly, I will focus on a group of fourteenth-century Oxonian scholars sharing a same background and interest in astronomy and astrology. Modern historiography has mainly focused on the so-called calculatores, eclipsing the scientific activities of this circle of astronomers and astrologers. The practices of this group also allows us to better understand the earliest phase of reception of continental astronomical adaptations in England. This community also raises the question of the complementary practices between astronomy and astrology, and the growing specialisation of scholars in one or the other of these disciplines.

This lecture was recorded by Dr Laure Miolo on 18 October 2023 at Barnard's Inn Hall, London

The transcript and downloadable versions of the lecture are available from the Gresham College website:
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Transcript

0:05

So in the late Middle Ages, producing a witch and wok often involved synthesizing values authorities and sources. However, it was not a solitary task, as many works resulted from longstanding exchanges of ideas within networks or groups of acquaintances and friends. Although the publication process was distinct from present day practices, sharing an initial version of one's works with a companion or a discipline represented one of the primary stages of publication before creating a presentation copy intended for a patron or another recipient. Formal or informal exchanges existed in different disciplines and astronomy and astrology were not exceptions to this rule. As the following discussion will show the lack of strict regulation, uh, of the study of the science of the store. So science of the stores include during the Middle Ages, astronomy and its practical aspect. Astrology. So the study of the science of the story in the early medieval university, especially in Paris and Oxford, uh, probably encouraged the rapid exchange of ideas between different groups of scholars. Examining the practices of the science of the source through the lens of humanities of learning, has recently explored and enhanced by constant muse allows for a better understanding of the genesis of a wide range of forks and provide insight into the circulation of ideas. As Muse and John Crossley have rightly underlines. The transmission of ideas always depends on the existence of networks of communication, and often also of the physical transport of books and manuscripts. Informal networks of friends could often constitute just as powerful a community of learning as some formal institutions, whether in the 12th century or the 15th century, and we'll see that we'll focus on the 14th century. So the different aspects of this definition may be applied to different groups of scholars found in the universities of Paris and Oxford in the 14th century. The study of both groups is made possible by the abundance of surviving manuscripts, often autographs that circulated in this context. So here you have in front of you two autograph copy, one produced in Oxford by Simon Brien and another one by Jean de Muir, produced in Paris. You will soon become more familiar with them. So the sources often show that those colors gathered around comparable astronomical texts and tables. This was facilitated by the shared access to sources through colleges, but also through friends. The spread of new texts and practices was thus facilitated by the formation of networks of scholars with similar interests. Although the existence of those groups are tested for no year period. For this paper, I will focus on the 14th century and the university con con context. First, I will examine the official statutes of the science of the stars in the universities of Paris and Oxford. Then I will outline the formation of this group of scholars. They came together around various text and sources of authority. Finally, I will discuss the dissemination of scientific ideas and text produce in these networks as well as the specializations of certain scholars. So the practice of the science of the stores in the universities of Paris and Oxford is characterized on various levels. Astronomy was formally taught in the faculty of arts along with other mathematical sciences. So those mathematical sciences were called quadrivium and natural philosophies, or in quadrivium we have arithmetic, geometry, astronomy and music, astronomy, and of course astrology. So this served as a pro education. However, compared to compared to other disciplines, the teaching and practice of mathematics suffer, suffer from a relative marginalization as reflect reflected in the university stages. Sorry. So here you can see, for example, we have the mention of quad rium. So mathematical science, but we don't have the details of the text, which is very different for other disciplines such as theology or philosophy in the same statutes. However, uh, so in contrast to natural philosophy, which benefited from a series of regulations, uh, governing its teaching following values, debates between the faculty of arts and the faculty of theology, mathematics have ultimately been regulated to a lesser degree by statutes. This is probably because the disciplines of the court review have remained outside the disputes based on Aris solution doctrines. The combinations of 1270 and 1277 only relate to astral determinism and do not aim at individual texts. Instead, they addressed activities like astrological elections and interrogations. The relative silence of the statutes clearly does not reflect the reality of how astronomical and astrological knowledge was transmitted within the universities of Paris and Oxford. It only attest to a greater autonomy in teaching and practices. The near lack of formal exercises, such as disputation or question dedicated to the science of the stores, demonstrates the independence of this discipline in the academic landscape. This autonomy did not prevent the creation of educational materials and the standardization of teaching. For example, Oxford was more detailed than Paris when it prescribes the study of John of Sacro Dessa nonetheless. So the Copus astronomic was the author in Paris in the 1250s and witnessed in hundreds of manuscript and utilized as a guidebook until the close of the 14th century. So it's a collection basically of text of arithmetic, as you can see, and also astronomy. The content of this teaching is better understood when considering the various references to deform. So defora designated prescribed text. So those kind of nces may be found, for example, in manuscripts, but also in catalogs such as, for example, the catalog of the college de mentioning this book, Defora, which contained in fact John of Sabo trilogy. So Dera algorithms and Comus less regulated in Paris. The teaching of the TNT Tel Room or science of the stores in Latin was also less frequent and certainly optional. The Colgate Institution facilitated this type of small group teaching during with D Booth. So fifth days, several example illustrates this practice. So in 1340 sooner a student, a student of Master Conrad de Meghan burg and translator of the desper delivered a lecture on the sphere, potentially based on Journal of Sacro Bosco sphere. In 1358, a bit later, Robert Lenor sought permission to teach two astrological text, namely the pseudo locum and pet quad reported to this testimonies pertain to the teaching delivered by the faculty of arts, which seems to have been restricted to basic text except probably the locum, but I won't enter into too much detail in that. Nonetheless, alongside the preparatory instructions, that was a more advanced dissemination and practice of astronomy and astrology by experience matter of arts who were frequently associated with the higher faculties of theology and medicine. Although there is of course, uh, evidence of this form of lessons in light of their conscience, it can be assumed that they patent to an advanced teaching. In 1320, master Joe Freedom mo of the University of Paris discussed astronomical tables in histories, inized flows, calendario room pointing out the inadequacies of the elephantine tables. And in fact, those issues were explained during a lecture he gave the same year. Another master, John Vimo published a set of tables of which the Cohon reads that they were composed for the use of the students of the university, university, sorry, of Paris and all losers. There is no evidence of official university teaching in these mentions. However, it appears that that, that this represented a higher level of instruction were bonds between masters and disciplines developed as well as communities of practitioners of the science of the stars within the university. The college or Collegium in Latin constituted a raiser autonomous place were statutes regulated the daily life of the community of scholars in addition to board and lodging. And in the absence of a university library, at that time until at least the 15th century, colleges provided access to a library comprised of books donated by patrons or former fellows. Soki. So Cate structural cultivated the sense of community and esp core and many, uh, enduring intellectual connections persisted, persisted well after leaving the university, there are values clues in text and conce that point towards the college. The so as a center of scientific production in the 14th century, the scientific contents of its slavery were exceptional and reflected the scientific practices of some of its fellows. Those scholars were inspired, uh, to visit the college and to access this amazing library such as Jean Deir, for example, who are notated many scientific manuscripts house in the Saban. You have here one example of a manuscript from the College of Saban and notated by Jean Deir, who also in fact drew this horoscope chart of the date of Usman death as indicated by the Cohon in some of Jean Demi's work. He produced them during his tenure as a host of the college. So during c the beginning of the 1320s, and in 13, 13 19 for his cans to the the alpine table. So astronomical tables, he was a simple host, so a member of the college not, um, um, a fellow, a similar context is found at Merton College in Oxford West College. From the same generation shared a similar interest in astronomical and astrological writings and practices. This sense of the community prompt them to offer reciprocal aid to one another in his astrological predictions of the conjunctions of certain and Jupiter of 1357 and 13 60, 65, sorry, John Chenin cite Simon Breeden's calculation of the motion of the Ace fair that he completed in 1340. You can see here the mention of Simon Brien in the manuscript. This calculation was likely commissioned by John himself in that same year. Simon also resigned his position as merchant procurator in favor of a elect Aire, a nest teamed master who was known other than John Sheen. Nan noted for his astrological works collaborations endure beyond the stay in college as evident in wills related to former fellows. The communal memory of this group was preserved in written works and manuscript and also in certain bequests along with books be decreased to his former college, Simon Brien. So still the same in his will dated to 1368 left a large Astro labbe to his colleague and Fred and friend William Reed sighted here. Uh, so part of he was part of the Merchant circle too. So beyond the shared environment of activity and living, the defining characteristic of these communities of learning is a shared engagement with the science of the stores and with particular text and tables. In the 14th centuries, there was a partial focus on assimilating a fresh array, uh, of tables in parameters. Those tables were originally compiled as the court of Alphonso 10 of Casti between 1263 and 1272 by two Jewish astronomers, Isaiah, Sid and Juda and Moses Cohen. It is not known in what form they crossed, uh, the Pyrene, but they were used for the first time in Paris in 1319. Although a marginal notation from 1304 recently discovered by David jut provides preliminary evidence of its use either in France or in Italy, it is probable that the tables were brought to Paris without any canons. So canons are the text which which usually describe how to use the tables to compute a variety of values such as planetary positions or astronomical phenomena. Therefore, one of the initiatives of the Parisian circle was to familiarize themselves with this materials to create canons to accompany the tables and to base some of their works on the alpine parameters. The recognition of Alfon Soin as an equal authority to Pmy appears to have been established in the earliest works, employing those parameters. John Deir praised the alpine tables in two of his early works and as and as achieved that he had experimented with them through observations in his expo in Tan Regal Fancy just here completed in 1321, Jean Deur provides values empirical proofs to verify particular values such as, for example, the accurate length of the tropical year of the main motion of the sun. One of his precise observations relates to the measurement using a large quadrants cariaga of the meridian altitude of the sun at the moment of the vernal equinox, which occurred in IL in 1319, while John Deir was still affiliated with the faculty of history. And John Deir, as you can see, is also the author of Treatise on this instrument Instruments the Coga as early as 1321. The assembly of canonical copies of tables and canons seems to have been undertaken over a short period of time by several Parisian masters with close links. The development of this corpus involves the production of model writings on the basis of Al Albertan siege. The alpine tables establish a shared foundation for comparable techniques. The manuscript and text of this expert reveal several indications of the cooperation and even the intellectual lineage in some cases. So ideas and works seems to have circulated rapidly within this group, although the text of first course insight into these connections and collaborations, the personal manuscripts of certain astronomers elucidates, uh, these interactions in his notebook where he records observations, mainly computations, but also drafts copy of his treatises. Jean Deir refers to the work of values of his contemporaries. So here I will give you three examples, but there are many in this manuscript. So first on the blank leaf, John Deir compiles tables detailing the precise holy velocities of the sun and moon. In the heading. As you can see here, uh, the note, he notes that the lunar veloc align with John Vimo table of lunar velocities in minutes per day, as well as that John of Saxony, so both contemporaries On another leaf. John discusses a technique for calculating the time of pap in conjunction through lunar parallax in longitude. He makes a comparison between the methods used by John of Saxon, a northern contemporary and John of Sicily, um, who was also a Parisian of astronomer of the late 13th century. Now, at the end of his calculation of the solo eclipse of May 13th 33, a detailed computation, John inserted a note referring to fin who was calculated, uh, who had calculated, sorry, the equation of time for the todo latitude. So these values references are all linked to preparatory calculations that Jean Demir did not preserve in his own works. They testified to a period of learning and the beginnings of certain practices certainly justified again by the absence of original cans accompanying, um, the tables intellectual lineage great, um, contributed greatly, uh, to the dissemination of works and ideas when some of these scholar worked together at the same level. Informal teaching certainly led to the creation of master discipline relationships. This lineage is evident in the case of John of Linear and two of his own disciplines. John of Saxony and John of Genu. John of Saxony was probably one of the first to hold John of linear's canons in his hands. This can be deduced from his autograph copy of the Canons on the premium er, so on the spherical astronomy if you want, and the planetary cans, it is dated. So the copy is dated 1323 as you can see on the telephone. So one year after the completion of the cans by fin who completed his cans in 1322. This manuscript also contains work by other members of the circle, such as John Deir again, but also John Vimo. This text were all written between 1320 and 1324 when John of Saxony was still a student. This manuscript testified to the intense activity of this group from the early 1320s and to the early determination of their writings among their students, John of Genoa followed in the footstep of his master's Astronomical Works, which is cited in several of his writings. His dependence on the work of Journal of Linear is evident in his canes eclipse, so basically canons on eclipses, which he completed in 1332 when he had just obtained his medical degree in one of the paragraphs preceding the Colophon. John of Genoa justified his choices and sources with regard to the method of of calculating the duration of the eclipse. John of Geno advised the reader to rely, as you can see on Alani, but also John of linear whose scans are longer than they are difficult. So this is for the rectification of the parallax that he advised to rely on those otters, both disciplines, John of Saxony and John of Genoa made John of linear an authority on Parisian ine astronomy who can serve as a foundation and model, and were soon to be transmitted to England shortly. Um, so in the 1330s, the dissemination of recently written treatise is an integral aspect of the publication procedure. The ultimate version of a text is circulated within a group of scholars in order to benefit from suggestions or advice, so something very modern. This group served as an optimal forum for the circulation of ideas and first drafts. Nonetheless, obtaining tangible evidence of his preliminary exchanges is extremely infrequent for the medieval period, as most often it is a definite, a definitive version of the medieval work which survived in manuscripts to this day. A rare counter example is a personal list of learned contained in John Deon's book. As you can see here, the document provides an inventory of work of works that were lent by Jean Deir to various persons including a number of Parisian masters. The majority of these loans pertain to compositions by Jean Deir, including his very own can to the Alpine tables completed in INE 1339. Uh, at the saw this list provides evidence of Jean in influential network at the University of Paris, as well as you know, the locations such as the Court of Neva and the Papal Korea. So basically when people were returning the text, John of Muir Jean Deir was basically crossing out the entry. So that's why you have, uh, all these entries clo crossed out. So it's an entry per, uh, individual. The rape division of contemporary works among a group of scholars, or the influence played by key figures is particularly striking when considering the Merchant College Circle. Simon Breeden physician and theology and William Reed Bishop of Chichester and Bibi o file seem to have been the key figures in the construction of a community motivated by the study of the science of the stars. A manuscript compiled by William Reed from 1368 to 1385 may be perceived as a portable library of the compositions of his contemporaries. This volumes present a distinctive dossier concerning planetary conjunctions and their associated astrological prognostications. It also highlights the fact that astronomy was often a vehicle for the calculation of astronomic astrological shots and elaboration of predictions. The manuscript, uh, jig B 1 76 present at the Boian Library and compiled by William Reed contains one of only two works, uh, composed by William Reed. So the Almanac Soce composed in 1337. It is not strictly speaking an almanac or an ephe this, but raise a list of the daily true positions of the sun given for a four year cycle here, 13 41, 13 44. The Almanac is derived from the alpine parameters recently transmitted to England, which were later used by William Reed for his tables based on the Oxford Meridian in 1340. The same work may be found in another copy by the same scribe, so the copy is UHB 1 78, still a manuscript of the Boian Library. This manuscript belonged and was partly copied by Simon Breeden friend of William Reed. So both copies were in fact copied by Simon Breeden himself, himself, sorry, the Alman ole was therefore circulated soon after William read composite. It is possible that Simon collaborated with William during this time, as Simon was concurrently working on his commentary of book three of the Al Majet, which focused on the movement of the sun. The link between Simon Brien and William Re, William Re sorry, is also evidenced by the administrative role they played in the college, so merchant college and by the church benefits they individually obtain in Wiam in Kent and in Chichester. The same manuscript also present further evidence of the collaboration between William Reed and John Chenin. It includes William Reed's initial computations using his own set of table for the meridian of Fox, Oxford based i I, uh, on the Alpine parameters to support John Sheen's prediction of the 1345 triple conjunction. This collaboration emphasizes the expertise of both individual with one specializing in astronomical calculations and the other astrological predictions as it is also specified. Uh, by, in the table of contents of the manuscript written by William REIT's clerk, it is written William Calculated and John Sheen prognosticate the English astrologers. So John Sheen, uh, prediction did not depend solely on William REIT's calculations at the end of his judgment on the conjunctions of 1357 and 1365, he explicitly mentioned his reliance on Walter Elden calculations for the duration and intensity of the partial lunar eclipse that occurred on the 31st July, 1357. And its subsequent catastrophic consequences, it seems evident from both mentions that certain scholars processed expertise in the realm of astronomical computations while others were more oriented to towards the field of astrology. We have here the very beginning of a sort of specialization, if you want, so to conclude. Although evidence of joint reflection and collective work on a copy of scientific text and table is mostly scattered examination of personal manuscripts of medieval scholar provides insight into their working methods, scientific practices and relationships with their contemporaries in certain circle. There were in fact a real advanced teaching of the science of the stars or razor a transmission of series and practices by assimilating the tables that had recently arrived from Spain. Astronomers can be observed at work testing parameters and drawing up canons for using these tables. However, the importance of universities and especially colleges in cultivating regulated communities and intellectual exchanges cannot be denied in the practice of science of medieval science. A few years later in Oxford, astronomy and astrology flourished in the merchant circle, partly shaped by the use of the elephantine values. Overall, the study of extent manuscripts, documents and medieval libraries provides a unique opportunity to better understand the development of medieval science. It offers unique insights into scientific practices and the circulation of failure and on how, uh, that these were shaped by individual interests, network of practitioners and institutions. Thank you very much for, for your attention. Thank you very much. It's a very trivial question. What's the feral letter B? Oh, So it's a system that you, you can find basically, uh, in calendars, uh, in order to know exactly. So basically a file letter is design designating a day. So you have, uh, more or less perpetual calendar, uh, so you can see in computal manuscripts. And so of course, in order to know exactly, uh, when was the, the day you had to find the golden numbers corresponding to a letter, and then you had, uh, the specific day of Easter. And so this specific day, if it's AC for example, it'll be, uh, for example, every Wednesdays will be AC for a specific year. So it's a kind of final letters. Thank you. Um, so, uh, question we've had online, uh, which is, when does astrology stop being kind of respectable, being taught and studied in universities? Yeah, so it's an interesting question because I would like to to stress because, uh, it's probably, uh, unusual when you don't know medical science that astrology at that time is just the practical part, uh, of astronomy. So it's an application if you want, of astronomy. Uh, when does it stop to be, uh, taught? I would say, uh, probably in the late 17th century, because we have still in fact chairs in astrology, uh, until the late 17th century, if I'm not wrong. But maybe I have colleagues, early modernist colleagues that, uh, uh, uh, will be, uh, probably will have a better answer, but I think it's late 17th century. Yeah, exactly. It's later than we think. Yeah, absolutely. Uh, you'll have to pardon my ignorance with this question as well, but am I right that in the time that these measurements were being taken, the prevailing view was that the earth was flat? Oh, that wasn't correct. No, It's, I'm sorry, but it's incorrect. Uh, it's, uh, a common view to say that during the Middle Ages, uh, people thought that the earth was flat, but it was not at all the case. In fact, uh, people knew that the earth was, uh, a sphere, uh, since even, uh, I mean, even during the antiquity before Tmy, it was known that the earth was a sphere, and you probably saw, um, so I'm coming back to the work this era by John of Rosco, and that's why, in fact, okay, so here, for example, uh, you have this, this, this diagram of the different spheres surrounding, uh, the earth, but the earth is also a sphere, uh, on this diagram. So no, during the, its, they knew that, uh, it was a sphere. Yeah. Thank you. Uh, so final question, um, I jotted down. Yeah. So is anyone at this time, obviously the things you've shown us that are in Latin, but is anyone writing in English or French for people who might need astronomical calculations for navigation or something like this For navigation? Uh, it was probably less the case. It's a case later, probably in the late 15th century and in the 16th century that you found, for example, John of Sacro is embedded, uh, within, uh, um, manual of navigation, et cetera. Uh, astronomical, um, uh, computation was especially, uh, were especially done for, uh, calculating astronomical phenomena such as eclipses or comets, for example. Uh, you can find some astronomical navigation, but, uh, they were using some instruments and, uh, so it's a bit less a case, I would say, but I'm not a professional of a historian of navigation. But So, um, yeah, we, we need to move on to our next lecture, but let's thank Laura again for a fantastic tour. Thank you Very much.