About this Title
Publication: History of Mathematics
Publication Year: 2000; Volume 19
ISBNs: 978-0-8218-2031-5 (print); 978-1-4704-3887-6 (online)
MathSciNet review: MR1747519
MSC: Primary 01A75; Secondary 01A55
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.
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.
Table of Contents
The elementary conjunctions of extensive magnitudes
- Addition, subtraction, multiples and fractions of extensive magnitudes
- The product structure in general
- Combinatorial product
- Inner product
- Applications to geometry
The theory of functions