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. 

Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers’ marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.

Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers' marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.

Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

Der zweite Band der philosophischen Korrespondenz zeigt Leibniz wahrend seiner Tatigkeit in Hannover und Wolfenbuttel, unterbrochen durch die mehrjahrige Reise nach Suddeutschland und Italien (1687 1690). Eine besondere Stellung nimmt der gewichtige Briefwechsel mit Antoine Arnauld ein, in dem es nach dem Anfang 1686 verfassten ersten metaphysischen Systementwurf, dem sogenannten "Discours de metaphysique," vor allem um Fragen des Substanzbegriffs und eine vertiefte Explikation seiner metaphysischen Grundpositionen geht. Wichtige metaphysische Diskussionen werden ebenfalls im Briefwechsel mit Foucher erortert, die schon nahe heran an den Entwurf des "Systeme nouveau de la communication des substances" von 1695 fuhren. Nach der Italienreise ist es dann vor allem die ausfuhrliche Korrespondenz mit Fardella, seit 1694 Professor fur Mathematik in Padua, in der es Leibniz um die Erorterung metaphysischer Grundgedanken geht. Leibniz ist bereits auf dem Weg zu seinem "Specimen dynamicum" von 1695. Infolgedessen spielt in dieser Zeit auch seine erneute (erstmals 1684 offentlich gemachte) und vertiefte Auseinandersetzung mit Descartes und dessen Materiebegriff und die Entwicklung eines eigenen Kraftbegriffs eine grosse Rolle, so z. B. in den Korrespondenzen mit Bossuet, Pellisson-Fontanier, Huygens und Bayle. Leibniz beginnt einen Briefwechsel mit Basnage de Bauval in Den Haag, dem Herausgeber der "Histoire des ouvrages des savants," in dem es um allgemeine Neuigkeiten aus der respublica literaria, aber auch um die Kritik an Descartes geht. In den mit Bossuet, Pellisson-Fontanier und von Seckendorff gewechselten Briefen geht es daruber hinaus auch um theologische Probleme und Fragen der Reunion. Hauptthemen dieser Jahre sind demnach vor allem die Fundamentierung seines metaphysischen Systems und die damit verbundene Descartes-Kritik, wobei die Begriffe der Kraft und der Substanz im Zentrum stehen, insbesondere auch die logische Begrundung des vollstandigen Begriffs der singularen Substanz. Der erste Band der philosophischen Korrespondenz, der bereits 1926 allerdings ohne wissenschaftlichen Apparat erschienen war, ist im Marz 2006 in einer zweiten, vollstandig neu bearbeiteten und erweiterten Auflage mit Uberlieferungen, Varianten, Kommentaren, Register und Konkordanzen vorgelegt worden."

The tremendous growth of the mathematical sciences in the early modern world was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants' accounts, instrument making, teaching, navigation, and gauging. In many ways, mathematics shaped the knowledge culture of the age, infiltrating workshops, dockyards, and warehouses, before extending through the factories of the Industrial Revolution to the trading companies and banks of the nineteenth century. While theoretical developments in the history of mathematics have been made the topic of numerous scholarly investigations, in many cases based around the work of key figures such as Descartes, Huygens, Leibniz, or Newton, practical mathematics, especially from the seventeenth century onwards, has been largely neglected. The present volume, comprising fifteen essays by leading authorities in the history of mathematics, seeks to fill this gap by exemplifying the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.

The Correspondence of John Wallis (1616 -1703) is a critically acclaimed resource in the history of early modern science. Volume IV covers the period from 1672 to April 1675 and contains over eighty previously unpublished letters. It documents Wallis's role in the crucial debate over the method of tangents involving figures such as Sluse, James Gregory, Hudde, Barrow, Newton, and Christiaan Huygens. In this way it illuminates further an important part of the history of the calculus. Wallis's letters also provide valuable new insights into mathematical book production and the importance of the international exchange of books in the growth and dissemination of mathematical knowledge. We learn more about the part played by the intelligencer John Collins and the astronomer royal John Flamsteed in the edition of Jeremiah Horrox's Opera posthuma, published by Wallis in 1673. There are also new insights on the background to Wallis's early work on equations, and the reasons why he criticized Gaston Pardies's proposed tract on motion. The causes of the breakdown in Wallis's epistolary relation to Christiaan Huygens following the publication of the Horologium oscillatorium in 1673 are also revealed. Many letters reflect Wallis's active involvement in the Royal Society. Through the medium of correspondence the Savilian professor participated in numerous debates such as those over the anomalous suspension of mercury in the Torricellian tube or Hevelius's use of plain sights in positional astronomy. The volume allows us to gain a deeper understanding of the background to these debates. Furthermore, the volume throws important new light on the history of the University of Oxford and of the University Press in the early modern period. As keeper of the University Archives, Wallis was one of the institution's highest officers. Scarcely any event of note concerning the University did not require his involvement in some way, and this is reflected in numerous letters and documents which the volume publishes for the first time.