This book examines how calculus developed in Britain during the century following Newton.

An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

The mathematical methods employed by Newton in the Principia stimulated much debate among contemporaries. This book explains how Newton addressed these issues, taking into consideration the values that directed his research. It will be of interest to researchers and students in history and philosophy of science, physics, mathematics and astronomy.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians. This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.

This book tells one of the greatest stories in the history of school mathematics. Two of the names in the title—Samuel Pepys and Isaac Newton—need no introduction, and this book draws attention to their special contributions to the history of school mathematics. According to Ellerton and Clements, during the last quarter of the seventeenth century Pepys and Newton were key players in defining what school mathematics beyond arithmetic and elementary geometry might look like. The scene at which most of the action occurred was Christ’s Hospital, which was a school, ostensibly for the poor, in central London. The Royal Mathematical School (RMS) was established at Christ’s Hospital in 1673. It was the less well-known James Hodgson, a fine mathematician and RMS master between 1709 and 1755, who demonstrated that topics such as logarithms, plane and spherical trigonometry, and the application of these to navigation, might systematically and successfully be taught to 12- to 16-year-old school children. From a wider history-of-school-education perspective, this book tells how the world’s first secondary-school mathematics program was created and how, slowly but surely, what was being achieved at RMS began to influence school mathematics in other parts of Great Britain, Europe, and America. The book has been written from the perspective of the history of school mathematics. Ellerton and Clements’s analyses of pertinent literature and of archival data, and their interpretations of those analyses, have led them to conclude that RMS was the first major school in the world to teach mathematics-beyond-arithmetic, on a systematic basis, to students aged between 12 and 16. Throughout the book, Ellerton and Clements examine issues through the lens of a lag-time theoretical perspective. From a historiographical perspective, this book emphasizes how the history of RMS can be portrayed in very different ways, depending on the vantage point from which the history is written. The authors write from the vantage point of international developments in school mathematics education and, therefore, their history of RMS differs from all other histories of RMS, most of which were written from the perspective of the history of Christ’s Hospital.

James Jurin (1684-1750) occupied a central place in the medical and scientific circles of Augustan and Georgian England. His dispassionate yet forceful advocacy of smallpox inoculation using an innovative statistical approach brought him widespread recognition both in Britain and abroad. He was Secretary to the Royal Society for seven years and participated vigorously in the most important scientific debates of the period. Jurin's correspondence, recently made available to the public, provides rich material for the study of eighteenth-century natural philosophy and medicine, especially of the smallpox inoculation debates. This volume reproduces a broad and valuable selection of letters, as well as a list of Jurin's publications and a calendar of the complete correspondence. The introductory biographical essay describes how Jurin combined a career as a successful London physician with that of a natural philosopher.

This two-volume set presents a comprehensive and up-to-date history of eighteenth-century philosophy. The subject is treated systematically by topic, not by individual thinker, school, or movement, thus enabling a much more historically nuanced picture of the period to be painted.

This Encyclopedia offers a fresh, integrated and creative perspective on the formation and foundations of philosophy and science in European modernity. Combining careful contextual reconstruction with arguments from traditional philosophy, the book examines methodological dimensions, breaks down traditional oppositions such as rationalism vs. empiricism, calls attention to gender issues, to ‘insiders and outsiders’, minor figures in philosophy, and underground movements, among many other topics. In addition, and in line with important recent transformations in the fields of history of science and early modern philosophy, the volume recognizes the specificity and significance of early modern science and discusses important developments including issues of historiography (such as historical epistemology), the interplay between the material culture and modes of knowledge, expert knowledge and craft knowledge. This book stands at the crossroads of different disciplines and combines their approaches – particularly the history of science, the history of philosophy, contemporary philosophy of science, and intellectual and cultural history. It brings together over 100 philosophers, historians of science, historians of mathematics, and medicine offering a comprehensive view of early modern philosophy and the sciences. It combines and discusses recent results from two very active fields: early modern philosophy and the history of (early modern) science. Editorial Board EDITORS-IN-CHIEF Dana Jalobeanu University of Bucharest, Romania Charles T. Wolfe Ghent University, Belgium ASSOCIATE EDITORS Delphine Bellis University Nijmegen, The Netherlands Zvi Biener University of Cincinnati, OH, USA Angus Gowland University College London, UK Ruth Hagengruber University of Paderborn, Germany Hiro Hirai Radboud University Nijmegen, The Netherlands Martin Lenz University of Groningen, The Netherlands Gideon Manning CalTech, Pasadena, CA, USA Silvia Manzo University of La Plata, Argentina Enrico Pasini University of Turin, Italy Cesare Pastorino TU Berlin, Germany Lucian Petrescu Université Libre de Bruxelles, Belgium Justin E. H. Smith University de Paris Diderot, France Marius Stan Boston College, Chestnut Hill, MA, USA Koen Vermeir CNRS-SPHERE + Université de Paris, France Kirsten Walsh University of Calgary, Alberta, Canada

Thomas Reid was an intellectual polymath interested in all aspects of Enlightenment thought. Paul Wood reconstructs Reid's career as a mathematician and natural philosopher and shows how he grappled with Sir Isaac Newton's scientific legacy.

Volume XXIV of History of Universities contains the customary mix of learned articles, book reviews, and bibliographical information, which makes this publication such an indispensable tool for the historian of higher education. Its contributions range widely geographically, chronologically, and in subject-matter.