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The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles ́ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle. The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.
Distinctions of Reason and Reasonable Distinctions is an intellectual biography of John Wallis (1616-1703), professor of mathematics at Oxford for over half a century. His career spans the political tumult of the English Civil Wars, the religious upheaval of the Church of England, and the fascinating developments in mathematics and natural philosophy. His ability to navigate this terrain and advance human learning in the academic world was facilitated by his use of the Jesuit Francisco Suarez’s theory of distinctions. This Roman Catholic’s philosophy in the hands of a Protestant divine fostered an instrumentalism necessary to bridge the old and new. With this tool, Wallis brought modern science into the university and helped form the Royal Society.
The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.
This book offers an analysis of the ground breaking mathematical work of Gregorio a San Vicente and his student and shows that the Flemish Jesuit Mathematics School had profound influence on mathematics in the seventeenth century.
Offers comprehensive treatment of Thomas Hobbes’s thought, providing readers with different ways of understanding Hobbes as a systematic philosopher As one of the founders of modern political philosophy, Thomas Hobbes is best known for his ideas regarding the nature of legitimate government and the necessity of society submitting to the absolute authority of sovereign power. Yet Hobbes produced a wide range of writings, from translations of texts by Homer and Thucydides, to interpretations of Biblical books, to works devoted to geometry, optics, morality, and religion. Hobbes viewed himself as presenting a unified method for theoretical and practical science—an interconnected system of philosophy that provides many entry points into his thought. A Companion to Hobbes is an expertly curated collection of essays offering close textual engagement with the thought of Thomas Hobbes in his major works while probing his ideas regarding natural philosophy, mathematics, human nature, civil philosophy, religion, and more. The Companion discusses the ways in which scholars have tried to understand the unity and diversity of Hobbes’s philosophical system and examines the reception of the different parts of Hobbes’s philosophy by thinkers such as René Descartes, Margaret Cavendish, David Hume, and Immanuel Kant. Presenting a diversity of fresh perspectives by both emerging and established scholars, this volume: Provides a comprehensive treatment of Hobbes’s thought in his works, including Elements of Law, Elements of Philosophy, and Leviathan Explores the connecting points between Hobbes’ metaphysics, epistemology, mathematics, natural philosophy, morality, and civil philosophy Offers readers strategies for understanding how the parts of Hobbes’s philosophical system fit together Examines Hobbes’s philosophy of mathematics and his attempts to understand geometrical objects and definitions Considers Hobbes’s philosophy in contexts such as the natural state of humans, gender relations, and materialist worldviews Challenges conceptions of Hobbes’s moral theory and his views about the rights of sovereigns Part of the acclaimed Blackwell Companions to Philosophy series, A Companion to Hobbes is an invaluable resource for scholars and advanced students of Early modern thought, particularly those from disciplines such as History of Philosophy, Political Philosophy, Intellectual History, History of Politics, Political Theory, and English.
This book, translated from Italian, discusses the influence of Galileo on Hobbes’ natural philosophy. In his De motu, loco et tempore or Anti-White (~ 1643), Thomas Hobbes describes Galileo as “the greatest philosopher of all times”, and in De Corpore (1655), the Italian scientist is presented as the one who “opened the door of all physics, that is, the nature of motion.” The book gives a detailed analysis of Galileo’s legacy in Hobbes’s philosophy, exploring four main issues: a comparison between Hobbes’ and Mersenne’s natural philosophies, the Galilean Principles of Hobbes’ philosophical system, a comparison between Galileo’s momentum and Hobbes’s conatus , and Hobbes’ and Galileo’s theories of matter. The book also analyses the role played by Marin Mersenne, in spreading Galileo’s ideas in France, and as a discussant of Hobbes. It highlights the many aspects of Hobbes’ relationship with Galileo: the methodological and epistemological elements, but also the conceptual and the lexical analogies in the field of physics, to arrive, finally, at a close comparison on the subject of the matter. From this analysis emerges a shared mechanical conception of the universe open and infinite, that replaces the Aristotelian cosmos, and which is populated by two elements only: matter and motion.
This volume offers a series of insights into the fascinating topic of errors and false opinions in early modern Europe. It explores the semantic richness of the category of ‘error’ in a time when such category becomes crucial to European thought and culture. During decades of increasing normativity in the social and religious sphere as well as in the epistemological status of disciplines, recognizing and correcting error becomes an imperative task whose importance can hardly be overestimated. The efforts at establishing religious, political, and scientific orthodoxy led philosophers, doctors, philologist, scientist, and theologians, to reconsider the very foundations of knowledge in the attempt to dispel errors. Spanning geographically from Italy to France, England, and Germany, the articles here gathered provide stimulating glimpses into one of the most fascinating, multifaceted, and controversial aspects of early modern culture.