Geometric Calculus : According to the Ausdehnungslehre of H. Grassmann
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Bibliographic Information
Geometric Calculus : According to the Ausdehnungslehre of H. Grassmann
Birkháuser, c2000
- Other Title
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Calcolo geometrico
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Description and Table of Contents
- Volume
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ISBN 9780817641269
Description
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.
Table of Contents
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.
- Volume
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ISBN 9783764341268
Description
A translation of the 1888 text, "Calcolo Geometrico" by G. Peano, this volume provides readers with an insight into the work of a mathematician who had a significant impact on 20th century mathematics, and in particular, mathematical logic.
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