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.