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Geometric Calculus

According to the Ausdehnungslehre of H. Grassmann

  • Book
  • © 2000

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Authors:
  1. Giuseppe Peano
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
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  2. The Operations of Deductive Logic

    • Giuseppe Peano
    Pages 1-16

  3. Geometric Formations

    • Giuseppe Peano
    Pages 17-26

  4. Formations of the First Species

    • Giuseppe Peano
    Pages 27-39

  5. Formations of the Second Species

    • Giuseppe Peano
    Pages 41-52

  6. Formations of the Third Species

    • Giuseppe Peano
    Pages 53-56

  7. Formations on a Right-Line

    • Giuseppe Peano
    Pages 57-60

  8. Formations in the Plane

    • Giuseppe Peano
    Pages 61-80

  9. Formations in Space

    • Giuseppe Peano
    Pages 81-106

  10. Derivatives

    • Giuseppe Peano
    Pages 107-117

  11. Transformations of Linear Systems

    • Giuseppe Peano
    Pages 119-144

  12. Back Matter

    Pages 145-150
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Keywords

About this book

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.

Reviews

"Giuseppe Peano (1858-1932) who distinguished himself in several branches of mathematics, was among the earliest ones to duly appreciate Grassmann's algebraic ideas."

--Zentralblatt Math.

Bibliographic Information

  • Book Title: Geometric Calculus

  • Book Subtitle: According to the Ausdehnungslehre of H. Grassmann

  • Authors: Giuseppe Peano

  • DOI: https://doi.org/10.1007/978-1-4612-2132-6

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2000

  • Hardcover ISBN: 978-0-8176-4126-9Due: 29 October 1999

  • Softcover ISBN: 978-1-4612-7427-8Published: 21 September 2011

  • eBook ISBN: 978-1-4612-2132-6Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: XV, 150

  • Topics: History of Mathematical Sciences, Mathematical Logic and Foundations

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