Bücher von David Hilbert

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This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles: the axioms of geometry. The choice of axioms and their relations to one another is a problem which, has been discussed since the time of Euclid. This problem is tantamount to the logical analysis of our intuition of space. Hilbert attempts to choose for geometry a simple and complete set of independent axioms and to deduce from these the most important geometrical theorems so as to bring out as clearly as possible the significance of the different groups of axioms and the scope of the conclusions to be derived from the individual axioms.

Ich hatte es oft schmerzlich empfunden, daB bei der Schnelligkeit der Entwicklung unserer Wissenschaft die Zeit vOliiber ist, wo wir die gr6Bte Weisheit in den iiltesten Biichern fanden und so das Gliick genieBen konnten, das BewuBtsein der Belehrung mit dem Gefiihl der Pietat fiir das Ehrwiirdige zu verbinden. ERHARD SCHMIDT, 1919 Dieser Band des "TEUBNER-ARCHIVs zur Mathematik" enthalt die entscheiden­ den Arbeiten uber "Lineare Integralgleichungen und Gleichungen mit unendlich vielen Unbekannten", die DAVID HILBERT und sein Schuler ERHARD SCHMIDT in der Zeit von 1904 bis 1910 publiziert haben. HILBERTS Mitteilungen "Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen" sind in seinen "Gesammelten Abhandlun­ gen" nicht enthalten, weil sie 1912 bei B. G. TEUBNER in Buchform erschienen (vgl. Foto S. 278); im vorliegenden Band findet der Leser fotomechanische Nachdrucke der G6ttinger Erstver6ffentlichungen. AuBerdem wird diese Edition auch deshalb von Interesse sein, weil "Gesammelte Abhandlungen" von ERHARD SCHMIDT bisher nicht vorliegen. Fur die Erteilung der Abdruckgenehmigungen sei der Akademie der Wissenschaften zu G6ttingen und der Redaktion der Rendicondi del Circolo Matematico di Palermo gedankt.

An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.