Mathematical Book Histories
Printing, Provenance, and Practices of Reading
- 2024
- Book
- Editors
- Philip Beeley
- Ciarán Mac an Bhaird
- Book Series
- Trends in the History of Science
- Publisher
- Springer International Publishing
About this book
This book both articulates and responds to increasing scholarly interest in the materiality of the book. Taking as its base the unique collection of mathematical books in the Russell Library at Maynooth, it addresses questions related to printing techniques and print culture, book production, provenance, and reading practices. It considers the histories of individual items of the Russell Collection, their previous locations and owners, and explores ways in which annotations, underlinings, hand-drawn diagrams, and the like reveal patterns of reading and usage. Finally, it seeks to elicit more information on a previously under-researched topic: the historical role of mathematics in the extensive network of Irish colleges that once covered Catholic Europe, located in places such as Salamanca, Rome, Douai, and Prague. Alongside delivering important new insights into print culture as a medium for transmitting scientific ideas, Mathematical Book Histories is thus also intended to contribute to a broader understanding of the role and significance of mathematics in the context of clerical instruction and more broadly in the academic tradition of Ireland up to the beginning of the twentieth century. Many of the volumes in the Russell Library reflect the remarkably rich book-trade that flourished in seventeenth and early eighteenth century Dublin and which was quite distinct from that in London. Booksellers often bought in their wares directly from abroad, with the result that publications could enter collections that did not enter the purview of contemporary English or Scottish scholars in Britain.
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Table of Contents
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Frontmatter
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Introduction
Philip Beeley, Ciarán Mac an BhairdThe chapter delves into the rich history of mathematical books, focusing on the unique collection at the Russell Library in Maynooth. It explores the intricate details of printing techniques, book production, and the significant role of mathematics in Irish education. The collection includes works from renowned authors and provides insights into the historical context of mathematical education, annotations, and the provenance of the books. The chapter also highlights the importance of understanding the materiality of books and the collaborative nature of their production. Additionally, it discusses the role of mathematics in teaching practices and the broader academic tradition in Ireland. The detailed analysis of specific case studies, such as the works of Christian Wolff and Jean Prestet, adds depth to the understanding of mathematical education and book history. The chapter concludes by emphasizing the significance of investigating the histories of mathematical books to gain insights into teaching methods and the evolution of mathematical thought.AI Generated
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AbstractThis Introduction situates Mathematical Book Histories and its various chapters in the broader context of current work on the history of the book. It considers how a library collection such as that of the Russell Library came to be formed, what the collection can tell us about mathematical teaching practices, and the kind of information on reader engagement that can be gleaned from annotations, marginal working, hand-drawn diagrams, and the like. It also provides useful insights into various aspects of early modern mathematical book production, ranging from initial proposals and subscriptions to the collaborations of booksellers, printers, engravers, correctors, and others. Above all, it shows that as material objects mathematical books can often reveal on close reading more than initially meets the eye. -
Teaching Practices and Mathematical Reform
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Frontmatter
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Mathematics at Maynooth Until 1850: Teachers, Teaching, and Texts
Ciarán Mac an Bhaird, Barbara McCormackThe chapter delves into the origins of Maynooth College, tracing its establishment back to the late 18th century and the influences of Irish colleges in Europe. It focuses on the early professors who taught mathematics at the college, their teaching methods, and the textbooks they used. The development of the college's mathematical library is also a key topic, with the chapter exploring the provenance and significance of the mathematical texts housed in the Russell Library. The chapter highlights the evolution of mathematical education at Maynooth, from its early beginnings to the more structured curriculum that emerged in the late 19th century. It also sheds light on the personal and professional lives of the early professors, providing a rich historical context for understanding the development of mathematics education in Ireland.AI Generated
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AbstractIn this chapter, we consider three aspects of mathematics at Maynooth College from its foundation until the mid-nineteenth century: the teachers of mathematics, the material that they taught, and the college’s mathematical collection. To place these in context, we start with a brief overview of events that led to the college’s establishment. Then, interrogating a range of sources, including archival materials and various histories, which feature perspectives on different facets of the college, we consider the lives and contributions of the first four professors charged with teaching mathematics at Maynooth. Their stories, often included in evidence and testimonies for various parliamentary reports, provide insight into the role of mathematics at this institution, and the lasting influence of French textbooks on the mathematics taught. They also allow us to explore student and staff opinions towards the subject. Furthermore, the significance and breadth of the mathematical texts now contained in the Russell Library, reveal that the scientific interests of the staff in question often continued beyond the material that they taught, including topics not endorsed by the Catholic Church. -
Christian Wolff’s Elementa Matheseos Universae, Methodology, and Mathematical Education
Davide CrippaChristian Wolff’s Elementa Matheseos Universae, a four-volume work first published in 1710, was a groundbreaking text in 18th-century mathematics. It was notable for its comprehensive coverage of mathematical disciplines, including arithmetic, geometry, and applied mathematics, and its emphasis on rigorous, methodical presentation. Wolff's work was influential in shaping the teaching of mathematics and the scientific method during the Enlightenment. The text also highlights Wolff’s innovative use of definitions, axioms, and proofs, along with his emphasis on practical and empirical learning methods. This chapter delves into the historical context, methodological contributions, and educational impact of Wolff’s work, making it a valuable resource for understanding the evolution of mathematical education and methodology.AI Generated
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AbstractChristian Wolff (1679–1754), well known as a leading philosophical figure in the Enlightenment, has received relatively little attention from historians of mathematics despite his having had a vast mathematical production. The main reason for this neglect is that Wolff was not an original mathematician, his mathematical activity being predominantly devoted to the writing of textbooks and compendia. In this contribution, I shall survey his most successful textbook: Elementa matheseos universae. Originally published in two volumes in 1713–1715, it went through several editions and extensions throughout the eighteenth century, becoming a reference text for the teaching and learning of mathematics in continental Europe until about halfway through the eighteenth century. In my survey, I shall pay particular attention to Wolff’s methodological considerations, advancing the thesis that they should be understood in connection with his pedagogical concerns about teaching mathematics in the most proficient way. -
Two Books on the Elements of Algebra
Christopher D. HollingsThe chapter begins by introducing the historical context of two algebra textbooks published in the mid-1790s, which were reviewed by historian William Smyth. Despite the perceived lack of financial reward for authors of such textbooks, the chapter argues that these works could generate significant intellectual and financial capital. The focus then shifts to the authors, Bewick Bridge and James Wood, exploring their backgrounds, academic achievements, and the context in which their textbooks were written. Bridge's Algebra was designed for students at the East India Company College, while Wood's was aimed at Cambridge undergraduates. The chapter compares the contents of the two textbooks, noting that Wood's was more advanced and covered a broader range of topics. It also discusses the reception and impact of these textbooks, highlighting their enduring influence on mathematical education. The chapter concludes by comparing the two textbooks and their authors, emphasizing their distinct readerships and the ongoing relevance of their work.AI Generated
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AbstractWe examine two early nineteenth century algebra textbooks held in the Russell Library: Bewick Bridge’s Treatise on the Elements of Algebra and James Wood’s Elements of Algebra. We consider their contents, their readership, and their place within nineteenth century mathematical publishing. -
Ramus Amongst the Jesuits? A Historiographical Inquiry into the Appearance of an Early Ramist Mathematical Text at the Irish College of Salamanca
Kevin Gerard TraceyThe chapter focuses on a 1558 edition of Petrus Ramus’s adaptation of Euclid’s Elements, housed at the Russell Library, St Patrick’s College, Maynooth. This edition, initially unassuming, holds significant historical value, reflecting the philosophical and pedagogical debates of the time. The text’s sparse annotations hint at early modern teaching methods and the tensions between Ramus’s innovative pedagogy and the established academic norms. The chapter explores Ramus’s turn to mathematics after his philosophical controversies and his use of mathematical teaching as a tool for educational reform. It also delves into the broader context of mathematical education in early modern Europe, highlighting the influence of figures like Oronce Finé and the Jesuit Order on the development of mathematical pedagogy. The chapter offers a unique perspective on the intersection of mathematics, philosophy, and education in the sixteenth century, making it a fascinating read for those interested in the history of mathematics and education.AI Generated
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AbstractThis chapter approaches the Russell Library’s copy of Petrus Ramus’s Euclides (1545) diachronically, combining evidence from the 1558 edition’s intellectual and material construction with an exploration of its biography and subsequent use. Firstly, Euclides is located as a work whose text and paratexts were part of a vibrant mathematical culture as well as a longer lineage of Euclidean adaptations. The edition’s later appearance in an institution overseen by the Society of Jesus then affords both a review of the role attributed to introductory mathematics in competing early modern pedagogical and methodological endeavours, and a means to engage with the novice, early modern readers who encountered such strategies and their attendant texts.
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Anomalies and Mysteries
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Frontmatter
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Thomas Salusbury’s Lesser Half: The First Volume of Mathematical Collections and Translations
Constance HardestyThomas Salusbury’s Lesser Half: The First Volume of Mathematical Collections and Translations was a significant publication that brought Galileo’s works to an English-speaking audience. The chapter delves into the historical context of Galileo’s condemnation by the Inquisition and the subsequent banning of his works. Salusbury’s translation faced numerous challenges, including delays, errors, and the absence of key promised content, such as the biography of Galileo. Despite these issues, the publication had a notable impact on the scientific community, with endorsements from prominent mathematicians and support from the Royal Society. The chapter also highlights Salusbury’s struggles as a translator and the broader implications of his work on the dissemination of scientific knowledge.AI Generated
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AbstractUntil now, little has been known about Thomas Salusbury’s Mathematical Collections and Translations (1661, 1665), and much of what has been assumed does not stand up to scrutiny. The work is best known for the mystique that surrounds the sole surviving copy of the second part of the second volume, which includes fragments of the first full-length biography of Galileo. Overshadowed by that prized rarity, the book as a whole has been neglected. Now, the discovery of two subscription campaigns spaced several years apart establishes the Mathematical Collections as a work of intellectual heft and consequence. Intended for gentle readers, the two-volume work presents foundational works of mathematical physics in an uncomplicated progression from Archimedes through Galileo to contemporary English natural philosophers. The first subscription campaign, in about 1660, attracted John Wallis, Seth Ward, Christopher Wren, and other eminent mathematicians who founded or shaped the Royal Society. The second campaign, launched soon after the Great Fire, was endorsed by the Society itself. This essay presents the Mathematical Collections as contemporaries experienced it, exposing the translator’s purpose and practice, the identities of those who supported the project, and the frustrations of a collaborative publishing project that persisted for nearly a decade. It argues that the Mathematical Collections is essential to our understanding of the Royal Society and vice-versa. The long-overlooked book offers a unique vantage point to explore organized efforts to advance the new physics during the Society’s formative years. -
Two Books and a Plot: When Mathematics Meets History
M. Pilar GilThe chapter 'Two Books and a Plot: When Mathematics Meets History' delves into the rich historical tapestry of the Irish College in Salamanca, founded in 1592. It chronicles the political and religious motivations behind its establishment, highlighting the support from the Spanish crown and the role of the college in educating Irish exiles. The narrative is interwoven with the story of Juan de Aguilera, a prominent figure in the college's early years, and his significant contributions to mathematics and astrology. The chapter also explores the broader context of scientific and mathematical advancements in Spain during this period, shedding light on the challenges and innovations that shaped the intellectual landscape. Additionally, it delves into the life and work of Antonio Núñez de Zamora, another notable figure associated with the college, and his contributions to the understanding of comets and celestial phenomena. The chapter concludes with a fascinating look at the Salamanca Archives, housed in Maynooth, which preserve the college's historical documents and offer a window into the lives and experiences of the Irish exiles who studied and taught there.AI Generated
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AbstractThis chapter explores two mathematical books of Spanish origin deposited in the Russell Library within the Salamanca collection, a compendium of administrative documents and books pertaining to the wide network of Irish colleges in the territories of modern-day Spain and Portugal. Through the examination of the two volumes: Juan de Aguilera’s Canones Astrolabii Universalis and Antonio Núñez de Zamora’s Liber de Cometis, written in the sixteenth and seventeenth centuries, respectively, topics such as the influence of astrological concepts in the treatment of astronomical questions, as well as the increasingly sought-after mathematical precision in the literature of the period, are considered. The chapter focuses mostly on the materiality of these books, in particular in the marks of ownership, the significance of annotations in the margins and of interspersed notes on their pages while discussing the collection's provenance and placing it in context with the relevance of mathematical sciences in the Iberian Peninsula in general and the collection's importance in the background of the Jesuit programme of instruction in particular. The analysis of these books, combined with the description of the Salamanca collection's provenance, provides us with a broad perspective that extends beyond mathematics to the social and political aspects of those centuries, which include not only the territories of the Spanish crown, but also the British Isles. -
A Seaworthy Book? Samuel Sturmy’s Mariner’s Magazine (1669) from Conception to Reception
Boris JardineSamuel Sturmy’s Mariner's Magazine (1669) is a comprehensive volume on mathematical navigation, featuring a wide range of nautical, terrestrial, and celestial topics. The book's complex structure includes seven separate books, numerous tables, and contributions from various mathematical practitioners. Sturmy, a former sailor and customs officer, aimed to impress the Royal Society with the book, which contains valuable data on magnetic variation and tides. The Russell Library copy of the first edition is notable for its extensive annotations and possible use on transatlantic voyages. The chapter also explores the book's reception, subsequent editions, and its enduring influence on navigation and mathematical practice.AI Generated
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AbstractThe lure of marginalia attracts the scholar, the collector and the librarian alike. In the age of mass digital reproduction, the unique copy acquires a certain aura—and as historical interest turns to reception and social history, marks of use become clues for historian-detectives. In the Russell Library, Maynooth, one volume stands out for the variety of these marks: Samuel Sturmy’s 1669 Mariner’s Magazine has a scored and worn cover, a missing portrait and folding plate, paper instruments cut to shape and held together with string, two much older paper volvelles loosely laid in and, as the catalogue states tantalizingly, ‘extensive ms notes including list of thirteen names’. Owing to a set of fortunate historical and archival circumstances it is possible to give context to this copy by telling the complete story this compendious book of practical mathematics, from its origins in Sturmy’s experiences at sea and his relations with Bristol merchants and London virtuosi, to its printing, reprinting and reception. That is part of my task here. But those extensive manuscript notes lead in another direction, to the fate of this one particular copy, which may have itself gone to sea, across the Atlantic to the early colonies of British America. This, then, is an attempt at a comprehensive account of a single work, and also a single volume.
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Renewal and Reception
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Frontmatter
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Jean Prestet’s Éléments des Mathématiques: A Cartesian textbook by a Cartesian Author?
Catherine GoldsteinJean Prestet's 'Éléments des Mathématiques' is a pivotal text in the history of mathematics, authored by a Cartesian scholar during the 17th century. The chapter examines the dual nature of the book, which combines spiritual and corporeal elements, reflecting the classical dichotomy of ideas and form. It delves into the historical context, including the role of the publisher André Pralard and the intellectual circle of Nicolas Malebranche. The text highlights Prestet's commitment to Cartesian methodology, emphasizing the universality and economy of algebra over geometry. Notable innovations include Prestet's approach to Diophantine analysis and his systematic treatment of numbers and letters in algebra. The chapter also explores the challenges and achievements of Prestet's textbook, positioning it within the broader landscape of mathematical pedagogy and philosophical thought of the era.AI Generated
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AbstractAlthough the idea of ‘Elements of mathematics’ is usually closely linked to that of geometry, some early-modern authors also proposed alternatives. Jean Prestet, a protégé of the philosopher Nicolas Malebranche, developed an analytic basis for mathematics, which he presented as largely Cartesian. Prestet’s emphasis on arithmetic and algebra pushed him to subject to proof what had been hitherto seen as obvious facts, to treat symbolic expressions as integers, and to renew and extend Diophantine analysis as well as combinatorial questions. These features, in return, challenged both Prestet’s publisher and Descartes’ viewpoint. These interconnected aspects of Prestet’s treatise, several editions of which are kept in the Russell Library, are discussed here. -
Advancing the ‘Analytick Doctrine’: The Making of John Kersey’s Elements of Algebra
Philip BeeleyJohn Kersey's 'Elements of Algebra' was a significant work in the development of algebraic studies in England. The chapter delves into the publication history of the book, highlighting the challenges faced by Kersey and his publisher, Moses Pitt, in the aftermath of the Great Fire of London. It also discusses the content of the book, which included a comprehensive introduction to algebra and a commentary on William Oughtred's 'Clavis mathematicae'. The chapter further explores the reception of Kersey's work, noting the praise it received from contemporaries such as John Collins and the impact it had on subsequent mathematical publications. Additionally, the chapter provides context on the broader mathematical landscape of the time, including the work of other mathematicians such as John Pell and the challenges faced by the mathematical publishing industry in England.AI Generated
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AbstractOf the three major works on algebra written in the English language in the second half of the seventeenth century, that of the London mathematician John Kersey was by far the most successful. Not only was his Elements of Algebra reprinted more than four times, appearing well into the next century, but it also came to achieve the status of recommended reading at the two English universities. However, up to now little has been known about the author or how his book came to achieve the significance it ultimately acquired. Drawing on previously untapped sources, this chapter traces Kersey’s spectacular rise from lowly steward employed by a noble family in Buckinghamshire to esteemed mathematics teacher and author in the metropolis, and how through his friendship with John Collins he came to write a mathematical work which it was hoped would be able to compete with the best then being published on the continent. -
Collaboration and Rivalry in the Publishing of Newton’s Mathematics: A Study of Russell Library, St Patrick’s College, Maynooth. Shelfmark: Sc. 22. 3
Niccolò Guicciardini, Scott MandelbroteThis chapter examines the intricate dynamics of collaboration and rivalry among mathematicians in the publication of Isaac Newton's mathematical works, centered around a specific collection of essays held in the Russell Library. The focus is on the historical context and key figures such as George Cheyne, John Keill, and William Jones, who played pivotal roles in the dissemination of Newton's mathematical ideas. The chapter delves into the political and personal motivations that drove these mathematicians, highlighting the complex web of alliances and disputes that arose from the priority dispute between Newton and Leibniz. It provides a detailed analysis of the publication of Newton's mathematical essays, including the role of William Jones as an editor and his interactions with Newton. The chapter also sheds light on the broader European context of the calculus controversy, emphasizing the collective nature of scientific production and the importance of manuscript circulation in the dissemination of mathematical knowledge.AI Generated
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AbstractThe purpose of this chapter is to study a miscellany of mathematical essays gathered in a volume held at the Russell Library, St Patrick’s College, Maynooth. The study of this volume will allow us to learn about the strategies of publication and manuscript circulation adopted by mathematicians belonging to Pitcairne’s and Newton’s circles and about the prestige they sought to acquire by showing prowess in the new techniques of the infinitesimal calculus, in particular the so-called ‘method of quadratures’ or ‘inverse method of fluxions’, i.e. the method of integration, as Leibniz and Johann Bernoulli would say. The study of this collection has something to teach us about the collaboration and disputes that characterized mathematics in the early eighteenth century, and that were catalyzed by attempts to publish particular mathematical works of Isaac Newton -
Anticipating The Analyst—Understanding Berkeley’s Early Mathematical Antagonism Through Contemporary Texts
Clare MoriartyGeorge Berkeley, known for his philosophical works in metaphysics and epistemology, also had a significant early engagement with mathematics, marked by antagonism. This chapter delves into Berkeley's early mathematical writings and notebooks, revealing his skepticism towards mathematical dogmatism and his belief in the over-application of mathematics in natural phenomena. It explores his criticism of the over-estimation of mathematical agreement and his concerns about the illegitimate extrapolation of mathematical results to metaphysics and science. The chapter also highlights Berkeley's interactions with prominent mathematicians of his time, such as John Keill, and his evolving views on the role of mathematics in philosophy. Through a detailed analysis of Berkeley's texts and his correspondence, the chapter offers a nuanced understanding of his anti-mathematical sentiments and their impact on his philosophical thought.AI Generated
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AbstractBerkeley is best known to mathematicians and historians of mathematics for his interventions in the history of the Newton-Leibniz calculus. The Analyst was published in 1734 and was the subject of much discussion in the learned world—some of it highly contentious. In this article, the motivations for that critical work are explored through Berkeley’s earlier engagements with mathematicians and the status of their work in contemporary philosophy. It is argued that important anticipations of Berkeley’s animosity towards mathematics can be found in their nascent form in Berkeley’s early responses to contemporary mathematicians and mathematical philosophers, such as John Keill, Bernard Nieuwentijt, Nicolas Malebranche and René Descartes. The Russell Library boasts key holdings and early editions of texts that illustrate this trajectory, and by exploring their interconnections we can better understand the outright mathematical hostility eventually found in The Analyst and its epistolary aftermath.
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Backmatter
- Title
- Mathematical Book Histories
- Editors
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Philip Beeley
Ciarán Mac an Bhaird
- Copyright Year
- 2024
- Publisher
- Springer International Publishing
- Electronic ISBN
- 978-3-031-32610-3
- Print ISBN
- 978-3-031-32609-7
- DOI
- https://doi.org/10.1007/978-3-031-32610-3
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