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Cover: 9781461274278 | Geometric Calculus | According to the Ausdehnungslehre of H. Grassmann
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Geometric Calculus
According to the Ausdehnungslehre of H. Grassmann
Taschenbuch von Giuseppe Peano
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
[see attached for complete text]
{\it Geometric Calculus}, a translation of the1888 classic {\it
Calcolo geometrico} by G. Peano will give readers insight into the
work of a most distinguished mathematician who had a significant
impact on 20th century mathematics, and in particular, mathematical
logic.
Key features: * {\it Geometric Calculus} is an excellent model of
expository writing, * Peano's axiom system for a vector space is the
first-ever presentation of a set of such axioms, * work comes close to
being a modern introduction to linear algebra, * Peano clarifies and
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.
Details
Erscheinungsjahr: 2011
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Seiten: 172
Inhalt: xv
150 S.
ISBN-13: 9781461274278
ISBN-10: 1461274273
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Peano, Giuseppe
Übersetzung: Kannenberg, L. C.
Auflage: Softcover reprint of the original 1st ed. 2000
Hersteller: Birkh„user Boston
Birkhäuser Boston
Maße: 235 x 155 x 10 mm
Von/Mit: Giuseppe Peano
Erscheinungsdatum: 21.09.2011
Gewicht: 0,271 kg
preigu-id: 106336054
Zusammenfassung
[see attached for complete text]
{\it Geometric Calculus}, a translation of the1888 classic {\it
Calcolo geometrico} by G. Peano will give readers insight into the
work of a most distinguished mathematician who had a significant
impact on 20th century mathematics, and in particular, mathematical
logic.
Key features: * {\it Geometric Calculus} is an excellent model of
expository writing, * Peano's axiom system for a vector space is the
first-ever presentation of a set of such axioms, * work comes close to
being a modern introduction to linear algebra, * Peano clarifies and
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.
Details
Erscheinungsjahr: 2011
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Seiten: 172
Inhalt: xv
150 S.
ISBN-13: 9781461274278
ISBN-10: 1461274273
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Peano, Giuseppe
Übersetzung: Kannenberg, L. C.
Auflage: Softcover reprint of the original 1st ed. 2000
Hersteller: Birkh„user Boston
Birkhäuser Boston
Maße: 235 x 155 x 10 mm
Von/Mit: Giuseppe Peano
Erscheinungsdatum: 21.09.2011
Gewicht: 0,271 kg
preigu-id: 106336054
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