**History of Mathematics**

Volume: 19;
2000;
411 pp;
Softcover

MSC: Primary 01; 15;

Print ISBN: 978-0-8218-2031-5

Product Code: HMATH/19

List Price: $87.00

AMS Member Price: $69.60

MAA member Price: $78.30

**Electronic ISBN: 978-1-4704-3887-6
Product Code: HMATH/19.E**

List Price: $87.00

AMS Member Price: $69.60

MAA member Price: $78.30

# Extension Theory

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*Hermann Grassmann*

A co-publication of the AMS and the London Mathematical Society

The Ausdehnungslehre of 1862 is Grassmann's most mature
presentation of his “extension theory”. The work was unique in
capturing the full sweep of his mathematical achievements.

Compared to Grassmann's first book, Lineale
Ausdehnungslehre, this book contains an enormous amount of new
material, including a detailed development of the inner product and
its relation to the concept of angle, the “theory of
functions” from the point of view of extension theory, and
Grassmann's contribution to the Pfaff problem. In many ways, this book
is the version of Grassmann's system most accessible to contemporary
readers.

This translation is based on the material in Grassmann's
“Gesammelte Werke”, published by B. G. Teubner (Stuttgart and
Leipzig, Germany). It includes nearly all the Editorial Notes from
that edition, but the “improved” proofs are relocated, and
Grassmann's original proofs are restored to their proper places. The
original Editorial Notes are augmented by Supplementary Notes,
elucidating Grassmann's achievement in modern terms.

This volume is one of an informal sequence of works within the
History of Mathematics series. Volumes in this subset,
“Sources”, are classical mathematical works that served as
cornerstones for modern mathematical thought.

#### Readership

Graduate students and research mathematicians interested in the history of vector spaces, exterior algebra, Pfaff's problem, and the other contributions of Grassmann; historians of mathematics.

#### Reviews & Endorsements

Grassmann's classical work can be warmly recommended to mathematicians and to historians of mathematics as a source of Grassmann's mathematical ideas.

-- European Mathematical Society Newsletter

Hermann Grassmann's

-- MAA Online

#### Table of Contents

# Table of Contents

## Extension Theory

- Cover Cover11
- Title page v6
- Contents vii8
- Translator’s note ix10
- Foreword xiii14
- The elementary conjunctions of extensive magnitudes 120
- Addition, subtraction, multiples and fractions of extensive magnitudes 322
- The product structure in general 1938
- Combinatorial product 2948
- Inner product 93112
- Applications to geometry 123142
- The theory of functions 191210
- Functions in general 193212
- Differential calculus 249268
- Infinite series 263282
- Integral calculus 279298
- Index of technical terms 327346
- Editorial notes 331350
- Supplementary notes 391410
- Subject index 399418
- Back Cover Back Cover1431