Foundations of Geometry
Gelesen von Jim Wrenholt
David Hilbert
(1 Sterne; 1 Bewertungen)
The German mathematician David Hilbert was one of the most influential mathematicians of the 19th/early 20th century. Hilbert's 20 axioms were first proposed by him in 1899 in his book Grundlagen der Geometrie as the foundation for a modern treatment of Euclidean geometry.
Hilbert's axiom system is constructed with six primitive notions: the three primitive terms point, line, and plane, and the three primitive relations Betweenness (a ternary relation linking points), Lies on (or Containment, three binary relations between the primitive terms), and Congruence (two binary relations, one linking line segments and one linking angles).
The original monograph in German was based on Hilbert's own lectures and was organized by himself for a memorial address given in 1899. This was quickly followed by a French translation with changes made by Hilbert; an authorized English translation was made by E.J. Townsend in 1902. This translation - from which this audiobook has been read - already incorporated the changes made in the French translation and so is considered to be a translation of the 2nd edition. (5 hr 26 min)
Chapters
Desargues's theorem and its demonstration for plane geometry by aid of the axio…
6:25
Read by Jim Wrenholt
The impossibility of demonstrating Desargues's theorem for the plane with the h…
10:15
Read by Jim Wrenholt
Introduction to the algebra of segments based upon the Desargues's theorme
4:58
Read by Jim Wrenholt
The commutative and associative law of addition for our new algebra of segments
4:16
Read by Jim Wrenholt
The associative law of multiplication and the two distributive laws for the new…
12:16
Read by Jim Wrenholt
Construction of a geometry of space by aid of a desarguesian number system
9:05
Read by Jim Wrenholt
Proof of the two propositions concerning Pascal's theorem. Non-pascalian geomet…
3:33
Read by Jim Wrenholt
Analytic representation of the co-ordinates of points which can be so construct…
7:34
Read by Jim Wrenholt
Geometrical constructions by means of a straight-edge and a transferer of segme…
6:51
Read by Jim Wrenholt
The representation of algebraic numbers and of integral rational functions as s…
12:44
Read by Jim Wrenholt
Criterion for the possibility of a geometrical construction by means of a strai…
12:02
Read by Jim Wrenholt
Bewertungen
freaking author repeat the intro every new chapter !!
Dennis C
(1 Sterne)
This book poorly done.. based on this work and how little effort was given to it it's just sad. wife making repeat the intro every single new chapter to a point where you can't listen to it?