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Foundations of Geometry

Gelesen von Jim Wrenholt

(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

Preface, Contents, and Introduction

11:44

Read by Jim Wrenholt

The elements of geometry and the five groups of axioms

2:30

Read by Jim Wrenholt

Group I: Axioms of connection

3:55

Read by Jim Wrenholt

Group II: Axioms of Order

3:23

Read by Jim Wrenholt

Consequences of the axioms of connection and order

7:00

Read by Jim Wrenholt

Group III: Axioms of Parallels (Euclid's axiom)

2:33

Read by Jim Wrenholt

Group IV: Axioms of congruence

8:38

Read by Jim Wrenholt

Consequences of the axioms of congruence

20:38

Read by Jim Wrenholt

Group V: Axiom of Continuity (Archimedes's axiom)

4:20

Read by Jim Wrenholt

Compatibility of the axioms

6:36

Read by Jim Wrenholt

Independence of the axioms of parallels. Non-euclidean geometry

4:59

Read by Jim Wrenholt

Independence of the axioms of congruence

6:25

Read by Jim Wrenholt

Independence of the axiom of continuity. Non-archimedean geometry

6:24

Read by Jim Wrenholt

Complex number-systems

6:33

Read by Jim Wrenholt

Demonstrations of Pascal's theorem

14:50

Read by Jim Wrenholt

An algebra of segments, based upon Pascal's theorem

7:02

Read by Jim Wrenholt

Proportion and the theorems of similitude

5:59

Read by Jim Wrenholt

Equations of straight lines and of planes

7:49

Read by Jim Wrenholt

Equal area and equal content of polygons

5:34

Read by Jim Wrenholt

Parallelograms and triangles having equal bases and equal altitudes

5:52

Read by Jim Wrenholt

The measure of area of triangles and polygons

10:05

Read by Jim Wrenholt

Equality of content and the measure of area

8:01

Read by Jim Wrenholt

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

Equation of straight line, based upon the new algebra of segments

8:17

Read by Jim Wrenholt

The totality of segments, regarded as a complex number system

3:45

Read by Jim Wrenholt

Construction of a geometry of space by aid of a desarguesian number system

9:05

Read by Jim Wrenholt

Significance of Desargues's theorem

3:18

Read by Jim Wrenholt

Two theorems concerning the possibility of proving Pascal's theorem

3:13

Read by Jim Wrenholt

The commutative law of multiplication for an archimedean number system

5:23

Read by Jim Wrenholt

The commutative law of multiplication for a non-archimedean number system

9:46

Read by Jim Wrenholt

Proof of the two propositions concerning Pascal's theorem. Non-pascalian geomet…

3:33

Read by Jim Wrenholt

The demonstation, by means of the theorems of Pascal and Desargues

5:29

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

Conclusion

14:09

Read by Jim Wrenholt

Appendix

22:31

Read by Jim Wrenholt

Bewertungen

freaking author repeat the intro every new chapter !!

(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?