Euclid Vindicated From Every Blemish
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Euclid Vindicated From Every Blemish
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Author : Gerolamo Saccheri
language : en
Publisher: Springer
Release Date : 2014-08-07
Euclid Vindicated From Every Blemish written by Gerolamo Saccheri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-07 with Mathematics categories.
This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work. Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the time. In particular, the Parallel Postulate had escaped demonstration since the first attempts at it in the Classical Age, and several books on the topic were published in the Early Modern Age. At the same time, the theory of proportion was the most important mathematical tool of the Galilean School in its pursuit of the mathematization of nature. Saccheri's attempt to prove the Parallel Postulate is today considered the most important breakthrough in geometry in the 18th century, as he was able to develop for hundreds of pages and dozens of theorems a system in geometry that denied the truth of the postulate (in the attempt to find a contradiction). This can be regarded as the first system of non-Euclidean geometry. Its later developments by Lambert, Bolyai, Lobachevsky and Gauss eventually opened the way to contemporary geometry. Occupying a unique position in the literature of mathematical history, Euclid Vindicated from Every Blemish will be of high interest to historians of mathematics as well as historians of philosophy interested in the development of non-Euclidean geometries.
Euclid Vindicated From Every Blemish
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Author : Gerolamo Saccheri (1667-1733)
language : en
Publisher:
Release Date : 2014-08-15
Euclid Vindicated From Every Blemish written by Gerolamo Saccheri (1667-1733) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with categories.
Diagrammatic Representation And Inference
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Author : Ahti-Veikko Pietarinen
language : en
Publisher: Springer Nature
Release Date : 2020-08-17
Diagrammatic Representation And Inference written by Ahti-Veikko Pietarinen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-17 with Computers categories.
This book constitutes the refereed proceedings of the 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, held in Tallinn, Estonia, in August 2020.* The 20 full papers and 16 short papers presented together with 18 posters were carefully reviewed and selected from 82 submissions. The papers are organized in the following topical sections: diagrams in mathematics; diagram design, principles, and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; logic and diagrams; and posters. *The conference was held virtually due to the COVID-19 pandemic. The chapters ‘Modality and Uncertainty in Data Visualization: A Corpus Approach to the Use of Connecting Lines,’ ‘On Effects of Changing Multi-Attribute Table Design on Decision Making: An Eye Tracking Study,’ ‘Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs,’ ‘The DNA Framework of Visualization’ and ‘Visualizing Curricula’ are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
A Concise History Of Mathematics For Philosophers
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Author : John Stillwell
language : en
Publisher: Cambridge University Press
Release Date : 2019-06-06
A Concise History Of Mathematics For Philosophers written by John Stillwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-06 with Science categories.
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
Menelaus Spherics
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Author : Roshdi Rashed
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-10-23
Menelaus Spherics written by Roshdi Rashed and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Philosophy categories.
Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.
Coleridge And The Geometric Idiom
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Author : Ann C. Colley
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-16
Coleridge And The Geometric Idiom written by Ann C. Colley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-16 with Literary Criticism categories.
When Coleridge described the landscapes he passed through while scrambling among the fells, mountains, and valleys of Britain, he did something unprecedented in Romantic writing: to capture what emerged before his eyes, he enlisted a geometric idiom. Immersed in a culture still beholden to Euclid's Elements and schooled by those who subscribed to its principles, he valued geometry both for its pragmatic function and for its role as a conduit to abstract thought. Indeed, his geometric training would often structure his observations on religion, aesthetics, politics, and philosophy. For Coleridge, however, this perspective never competed with his sensitivity to the organic nature of his surroundings but, rather, intermingled with it. Situating Coleridge's remarkable ways of seeing within the history and teaching of mathematics and alongside the eighteenth century's budding interest in non-Euclidean geometry, Ann Colley illuminates the richness of the culture of walking and the surprising potential of landscape writing.
Thomas Reid On Mathematics And Natural Philosophy
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Author : Paul Wood
language : en
Publisher: Edinburgh University Press
Release Date : 2017-08-31
Thomas Reid On Mathematics And Natural Philosophy written by Paul Wood and has been published by Edinburgh University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Science categories.
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.
Definition And Essence From Aristotle To Kant
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Author : Peter R. Anstey
language : en
Publisher: Taylor & Francis
Release Date : 2025-01-31
Definition And Essence From Aristotle To Kant written by Peter R. Anstey and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 with Philosophy categories.
This volume brings together 12 essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant. Definition and essence have been central to philosophical theorising since antiquity and remain so to this day. This volume presents a series of explorations of key authors and themes connected by a common set of questions: What are definitions and essences? What are the connections between them? What are their logical and metaphysical properties? What sorts of things have definitions and essences and what sorts of things do not? What functions do definitions and essences serve in the physical, mathematical, and human sciences? How, if at all, can we come to know them? This volume shows that answering these questions allows us to see in a new light key figures and movements in the history of Western thought. The volume’s broad historical sweep also facilitates comparisons between different figures. And it reveals important connections between different subfields of philosophy as these were developed over the centuries – logic, metaphysics, epistemology, philosophy of language, and natural philosophy among them. Definition and Essence from Aristotle to Kant will be of interest to scholars and graduate students working in the history of philosophy, history of logic, history of mathematics, epistemology, and metaphysics.
Reading Mathematics In Early Modern Europe
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Author : Philip Beeley
language : en
Publisher: Routledge
Release Date : 2020-10-20
Reading Mathematics In Early Modern Europe written by Philip Beeley and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-20 with Literary Criticism categories.
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.
Irrationality Transcendence And The Circle Squaring Problem
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Author : Eduardo Dorrego López
language : en
Publisher: Springer Nature
Release Date : 2024-05-02
Irrationality Transcendence And The Circle Squaring Problem written by Eduardo Dorrego López and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-02 with Mathematics categories.
This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.