The Directional Calculus - Based Upon the Methods of Hermann Grassmann #267368

The wonderful and comprehensive system of Multiple Algebra invented by Hermann Grassmann, and called by him the Ausdehnungslehre or Theory of Extension, though long neglected by the mathematicians even of Germany, is at the present time coming to be more and more appreciated and studied. In order that this system, with its intrinsic naturalness, and adaptability to all the purposes of Geometry and Mechanics, should be generally introduced to the knowledge of the coming generation of English-speaking mathematicians, it is very necessary that a text-book should be provided, suitable for use in colleges and universities, through which students may become acquainted with the principles of the subject and its applications.<br><br>The following pages present, in part, the results of eight or nine years of study and experience in lecturing to university classes upon this subject, and the Author hopes that they may aid in some measure to bring about that general study and use of directional methods, which, in his opinion, will ultimately cause the comparatively awkward and roundabout methods of Cartesian coordinates to be superseded by them, for many of the purposes of analysis.