The Foundations of Geometry

Hilbert, David

ISBN 10: 1473300614 / ISBN 13: 9781473300613

Edité par Fisher Press, 2013

A propos de cet article

In. N° de réf. du vendeur ria9781473300613_new

Détails bibliographiques

Titre : The Foundations of Geometry

Éditeur : Fisher Press

Date d'édition : 2013

Reliure : Couverture souple

Etat : New

A propos de ce titre

Synopsis :

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Présentation de l'éditeur:

Dtained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University ot Gotlingen during the winter semester of 1898-1899. The results of his investigation were re-arranged and put into the form in which I hey appear here as a memorial address published in connection with the celebration at the unveiling of the Gauss-W eber monument at GB ttingen, in June, 1899, In I he Frencli edition, which appeared soon after, Professor Hilbert made some additions, particularly in the concluding remarks, where he gave an account ot the results of a recent investigation made by Dr. Dehn. These additions have been incorporated in the following translation. As a basis for the analysis of our intuition of space. Professor Hilbert commences his discussion by considering three systems of things which he calls points, straight lines, and planes, and sets up a system of axioms connecting these elements in their mutual relations. The purpose of his investigations is to discuss systematically the relations of these axioms to one another and also the bearing of each upon the logical development of euclidean geometry. A mong the important results obtained, the following are worthy of special mention; I. The mutual independence and also the compatibility of the given system of axioms is fully discussed by the aid of various new systems ot geometry which are introduced. 1. The most important propositions of euclidean geometry are demonstrated in such a manner as to show precisely what axioms underlie and make possible the demonstration. J, The axioms of congruence are introduced and made the basis of the definition of geometric displacement. 4.
(Typographical errors above are due to OCR software and don't occur in the book.)

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