| Geometric Calculus: According to the Ausdehnungslehre of H. Grassmann 2000 Edition Contributor(s): Peano, Giuseppe (Author), Kannenberg, L. C. (Translator) |
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ISBN: 0817641262 ISBN-13: 9780817641269 Publisher: Birkhauser OUR PRICE: $94.05 Product Type: Hardcover - Other Formats Published: October 1999 Annotation: Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. Despite its uniqueness, Calcolo Geometrico has been strangely neglected by historians of mathematics, and even by scholars of Peano. The book has never been reprinted in its entirety, and only two chapters have ever been translated into English. In part, this neglect has been due to Peano's organization of the work. That is, the section on mathematical logic bears almost no relation to the rest of the book, and the material there was superseded only a year after its publication by Peano's second book. Since all but this first section was generally thought to be expository rather than original work, it was regarded lightly, if noticed at all, and ultimately all but forgotten. Only in very recent years have the book's unique merits begun to be recognized. Readers of this valuable translation will gain insight into the work of a distinguished mathematician and founder of mathematical logic. |
| Additional Information |
| BISAC Categories: - Mathematics | History & Philosophy - Mathematics | Calculus - Mathematics | Algebra - Linear |
| Dewey: 512.5 |
| LCCN: 99051963 |
| Physical Information: 0.58" H x 6.37" W x 9.53" (0.97 lbs) 150 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |
