Peano Geometric Calculus

According to the Ausdehnungslehre of H. Grassmann
Erscheinungsjahr 2013
ISBN: 978-1-4612-2132-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 150 Seiten, eBook

The geometric calculus, in general, consists in a system of operations on geometric entities, and their consequences, analogous to those that algebra has on the num bers. It permits the expression in formulas of the results of geometric constructions, the representation with equations of propositions of geometry, and the substitution of a transformation of equations for a verbal argument. The geometric calculus exhibits analogies with analytic geometry; but it differs from it in that, whereas in analytic geometry the calculations are made on the numbers that determine the geometric entities, in this new science the calculations are made on the geometric entities themselves. A first attempt at a geometric calculus was due to the great mind of Leibniz (1679);1 in the present century there were proposed and developed various methods of calculation having practical utility, among which deserving special mention are 2 the barycentric calculus of Mobius (1827), that of the equipollences of Bellavitis (1832),3 the quaternions of Hamilton (1853),4 and the applications to geometry 5 of the Ausdehnungslehre of Hermann Grassmann (1844). Of these various methods, the last cited to a great extent incorporates the others and is superior in its powers of calculation and in the simplicity of its formulas. But the excessively lofty and abstruse contents of the Ausdehnungslehre impeded the diffusion of that science; and thus even its applications to geometry are still very little appreciated by mathematicians.

Zielgruppe

Research

Autoren/Hrsg.

Peano, Giuseppe

Weitere Mitwirkende

Kannenberg, L.C.

Inhaltsverzeichnis

The Operations of Deductive Logic.- I Geometric Formations.- II Formations of the First Species.- III Formations of the Second Species.- IV Formations of the Third Species.- V Formations on a Right-Line.- VI Formations in the Plane.- VII Formations in Space.- VIII Derivatives.- IX Transformations of Linear Systems.- Editorial notes.