A New Branch of Mathematics: The Ausdehnungslehre of 1844, and Ohter Works

577 Pages·1996·38.255 MB·English

by  Hermann Grassmann

A NEW BRANCH OF MATHEMATICS
Die Wissensehaft
der
extens veil Grosse
oder
die ustilelanr s7Aire,
eine neue mathematische Disciplin
dargestellt and durch Anwendungen erlautert
0011
ermann Grassmann
Lehrer an der Friedrich-Wilhelme-Sehule zu Stettin.
Erster Theil,
die lineale Ansdelniangslebre enthaltend.
Leipzig, 1844.
Verlag von Otto Wigand.
Die
Ausdeiillullgs age
ein
neuer Zweig der iiiathematik
dargestellt
and
durch Anwendungen auf die iibrigen Zweige der Mathematik,
wie auch
auf die Statik, Mechanik, die Lehre vom Magnetismus mid die
Krystallonomie erlautert
von
.i1ElerDpiann Grassmann
Lehrer an der Friedrich-Wilhelms-Sehule zu Stettin.
Mit 1 Tafel.
Leipzig, 1844.
Verlag von Otto Wigand.

• o 1:C(1)= I
A NEW BRANCH OF MATHEMATICS
The Ausdehnungslehre
of 1844
and Other Works
by
HERMANN GRASSMANN
Translated by
LLOYD C. KANNENBERG
Open Court
Chicago and La Salle, Illinois
LiekARY
MG14,-SH UNIVERSITY
OPEN COURT and the above logo are registered in the U.S.
Patent and Trademark Office.
© 1995 by Open Court Publishing Company
First printing 1995
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, recording, or
otherwise, without the prior written permission of the publisher,
Open Court Publishing Company, 315 Fifth Street, POB 599,
Peru, Illinois 61354-0599.
Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Grassmann, Hermann, 1809-1877.
[Selections. English. 1994]
A new branch of mathematics : the "Ausdehnungslehre" of
1844 and other works / by Hermann Grassmann ; translated by
Lloyd C. Kannenberg.
p. cm.
Includes bibliographical references and index.
ISBN 0-8126-9275-6.—ISBN 0-8126-9276-4 (pbk.)
1. Ausdehnungslehre. 2. Physics. I. Title.
QA205.G74213 1994
512'.4—dc20 94-24422
CIP
o (1)
CONTENTS
Foreword ix
Translator's Note xiii
I. LINEAR EXTENSION THEORY
Table of Contents 3
The Ausdehnungslehre of 1844 9
Editorial Notes 298
II. GEOMETRIC ANALYSIS
Table of Contents 315
Geometric Analysis 316
The Grassmannian Theory of Point Magnitudes,
by A. F. MObius 385
Editorial Notes 403
III. SELECTED PAPERS ON
MATHEMATICS AND PHYSICS
New Theory of Electrodynamics 417
Editorial Notes 430
On the Theory of Compound Colors 435
Editorial Notes 446
On the Various Types of Multiplication 451
Editorial Notes 469
On Electrodynamics 473
Editorial Notes 481
Mechanics According to the Principles of
Extension Theory 485
Editorial Notes 513
From Grassmann's Unpublished Papers 514
The Position of the Hamiltonian Quaternions
in Extension Theory 525
Editorial Notes 539
Bibliography of Grassmann's Principal Works 543
Index 547
vii