Foundations of geometry : Euclidean and Bolyai-Lobachevskian geometry : projective geometry [Dover edition.] 9780486835570, 048683557X

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Foundations of geometry : Euclidean and Bolyai-Lobachevskian geometry : projective geometry [Dover edition.]
 9780486835570, 048683557X

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Foundations of

GEOMETRY

Foundations of

GEOMETRY Euclidean, Bolyai-Lobachevskian, and Projective Geometry KAROL BORSUK WANDA SZMIELEW Translated by

ERWIN MARQUIT

DOVER PUBLICATIONS, INC. MINEOLA, NEW YORK

Bibliographical Note   This Dover edition, first published in 2018, is an unabridged and slightly corrected republication of the work originally published by North-Holland Publishing Co., Amsterdam, and Interscience Publishers, New York, in 1960.

Library of Congress Cataloging-in-Publication Data Names: Borsuk, Karol, author. | Szmielew, Wanda, author. Title: Foundations of geometry : Euclidean and Bolyai-Lobachevskian geometry  projective geometry / by Karol Borsuk and Wanda Szmielew ; translated by  Erwin Marquit. Other titles: Podstawy geometrii. English Description: Dover edition. | Mineola, New York : Dover Publications, Inc.,  2018. | Series: Dover Books on Mathematics | In English; translated from  Polish. | Originally published: Amsterdam : North-Holland Publishing Co. ;  New York : Interscience Publishers, 1960. Identifiers: LCCN 2018022377 | ISBN 9780486828091 | ISBN 0486828093 Subjects: LCSH: Geometry—Foundations. Classification: LCC QA681 .B633 2018 | DDC 516—dc23 LC record available at https://lccn.loc.gov/2018022377 Manufactured in the United States by LSC Communications 82809301 2018 www.doverpublications.com

Foundations of

GEOMETRY

MATHEMATICS

I

n Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry. Dover unabridged and slightly corrected republication of the edition originally published by the North-Holland Publishing Co., Amsterdam, and Interscience Publishers, New York, 1960.

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ISBN-13: 978-0-486-82809-1 ISBN-10: 0-486-82809-3 53495

9 780486 828091

www.doverpublications.com