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Author: Vincent Jullien Publisher: Birkhäuser ISBN: 3319001310 Category : Mathematics Languages : en Pages : 499
Book Description
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.
Author: Vincent Jullien Publisher: Birkhäuser ISBN: 3319001310 Category : Mathematics Languages : en Pages : 499
Book Description
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.
Author: Stewart Shapiro Publisher: Oxford University Press, USA ISBN: 0198809646 Category : Mathematics Languages : en Pages : 593
Book Description
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.
Author: Davide Crippa Publisher: Springer ISBN: 3030016382 Category : Mathematics Languages : en Pages : 184
Book Description
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.
Author: Jason M. Rampelt Publisher: BRILL ISBN: 9004409149 Category : Philosophy Languages : en Pages : 329
Book Description
An intellectual biography of John Wallis (1616-1703), professor of mathematics at Oxford. Despite war, church upheaval, and a revolution in science, Wallis advanced mathematics and natural philosophy within the university, bridging old and new.
Author: Toke Knudsen Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110769964 Category : History Languages : en Pages : 272
Book Description
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.
Author: Ad J. Meskens Publisher: BRILL ISBN: 9004447903 Category : Education Languages : en Pages : 307
Book Description
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.
Author: Marcus P. Adams Publisher: John Wiley & Sons ISBN: 1119635039 Category : Philosophy Languages : en Pages : 544
Book Description
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.
Author: Gregorio Baldin Publisher: Springer Nature ISBN: 3030414140 Category : Science Languages : en Pages : 234
Book Description
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.
Author: Marco Faini Publisher: Firenze University Press ISBN: Category : Philosophy Languages : en Pages : 147
Book Description
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.
Author: Vincent Jullien
Author: Vincent Jullien
Author: Stewart Shapiro
Author: Davide Crippa
Author: Jason M. Rampelt
Author: Toke Knudsen
Author: Ad J. Meskens
Author: Marcus P. Adams
Author: Gregorio Baldin
Author: Raffaele Pisano
Author: Marco Faini