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The present work is based on a dissertation submitted at the Fellowship Examination of Trinity College, Cambridge, in the year 1895. Section B of the third chapter is in the main a reprint, with some serious alterations, of an article in Mind (New Series, No. 17). The substance of the book has been given in the form of lectures at the Johns Hopkins University, Baltimore, and at Bryn Mawr College, Pennsylvania.
My chief obligation is to Professor Klein. Throughout the first chapter, I have found his "Lectures on non-Euclidean Geometry" an invaluable guide; I have accepted from him the division of Metageometry into three periods, and have found my historical work much lightened by his references to previous writers. In Logic, I have learnt most from Mr Bradley, and next to him, from Sigwart and Dr Bosanquet. On several important points, I have derived useful suggestions from Professor James's "Principles of Psychology."
My thanks are due to Mr G. F. Stout and Mr A. N. Whitehead for kindly reading my proofs, and helping me by many useful criticisms. To Mr Whitehead I owe, also, the inestimable assistance of constant criticism and suggestion throughout the course of construction, especially as regards the philosophical importance of projective Geometry.
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An Essay on the Foundations of Geometry Classic Reprint
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An Essay on the Foundations of Geometry (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book delves into the fascinating realm of geometry, exploring its fundamental principles and challenging long-held assumptions. The author traces the historical evolution of non-Euclidean geometries, highlighting the groundbreaking contributions of mathematicians like Gauss, Lobatchewsky, and Riemann. By examining the concept of "curvature" and its application to spaces of multiple dimensions, the book sheds light on the limitations of traditional Euclidean geometry. Through a rigorous analysis of projective and metrical geometries, the author investigates the nature of space and its relationship to our understanding of the world. The book grapples with profound philosophical questions, such as the role of axioms in shaping our knowledge and the possibility of alternative spatial realities. By questioning the very foundations of geometry, this work ultimately reveals the intricate connections between mathematics, logic, and our perception of the universe. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781330166345_0
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Paperback. Condizione: Brand New. 220 pages. 9.00x6.00x0.50 inches. This item is printed on demand. Codice articolo zk1330166345
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