Elementary Mathematics from a Higher Standpoint Volume II: Geometry
These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into Englis
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Elementary Mathematics from a Higher Standpoint Volume II: Geometry
Elementary Mathematics from a Higher Standpoint
Felix Klein
Elementary Mathematics from a Higher Standpoint Volume II: Geometry Translated by Gert Schubring
Felix Klein Translated by: Gert Schubring
ISBN 978-3-662-49443-1 DOI 10.1007/978-3-662-49445-5
ISBN 978-3-662-49445-5 (eBook)
Library of Congress Control Number: 2016943431 Translation of the 4th German edition „Elementarmathematik vom höheren Standpunkte aus“, vol. 2 by Felix Klein, Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Band 15, Verlag von Julius Springer, Berlin 1926. A previous English language edition, Felix Klein “Elementary Mathematics from an Advanced Standpoint – Geometry”, translated by E. R. Hedrick and C. A. Noble, New York 1939, was based on the 3rd German edition and published by Dover Publications. © Springer-Verlag Berlin Heidelberg 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Cover Illustration: The publisher could not determine a copyright holder and believes this picture to be in the public domain. If the copyright holder can prove ownership, the publisher will pay the customary fee. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Berlin Heidelberg
Preface to the 2016 Edition
In general, for the preface for this volume II, I can refer to the preface for volume I – especially regarding the necessary correction of „advanced“ to „higher“, regarding the notion of elementary mathematics and of elementarisation, and regarding the need for a revised translation. I should like to highlight the special features of this volume. While the first volume is dedicated to the analytic side of mathematics, this volume complements it by exposing geometry. But the second volume is complementary to the first one in two more respects. It is characteristic for the first volume that Klein – in treating arithmetic, algebra, and a
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