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All Episodes

Foundations of Geometry — 42 episodes

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Title
1

042 - Appendix

2

041 - Conclusion

3

040 - Criterion for the possibility of a geometrical construction by means of a straight-edge and a transf

4

039 - The representation of algebraic numbers and of integral rational functions as sums of squares

5

038 - Geometrical constructions by means of a straight-edge and a transferer of segments

6

037 - Analytic representation of the co-ordinates of points which can be so constructed

7

036 - The demonstation by means of the theorems of Pascal and Desargues

8

035 - Proof of the two propositions concerning Pascal's theorem Non-pascalian geometry

9

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

10

033 - The commutative law of multiplication for an archimedean number system

11

032 - Two theorems concerning the possibility of proving Pascal's theorem

12

031 - Significance of Desargues's theorem

13

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

14

029 - The totality of segments regarded as a complex number system

15

028 - Equation of straight line based upon the new algebra of segments

16

027 - The associative law of multiplication and the two distributive laws for the new algebra of segments

17

026 - The commutative and associative law of addition for our new algebra of segments

18

025 - Introduction to the algebra of segments based upon the Desargues's theorme

19

024 - The impossibility of demonstrating Desargues's theorem for the plane with the help of the axioms of

20

023 - Desargues's theorem and its demonstration for plane geometry by aid of the axiom of congruence

21

022 - Equality of content and the measure of area

22

021 - The measure of area of triangles and polygons

23

020 - Parallelograms and triangles having equal bases and equal altitudes

24

019 - Equal area and equal content of polygons

25

018 - Equations of straight lines and of planes

26

017 - Proportion and the theorems of similitude

27

016 - An algebra of segments based upon Pascal's theorem

28

015 - Demonstrations of Pascal's theorem

29

014 - Complex number-systems

30

013 - Independence of the axiom of continuity Non-archimedean geometry

31

012 - Independence of the axioms of congruence

32

011 - Independence of the axioms of parallels Non-euclidean geometry

33

010 - Compatibility of the axioms

34

009 - Group V Axiom of Continuity Archimedes's axiom

35

008 - Consequences of the axioms of congruence

36

007 - Group IV Axioms of congruence

37

006 - Group III Axioms of Parallels Euclid's axiom

38

005 - Consequences of the axioms of connection and order

39

004 - Group II Axioms of Order

40

003 - Group I Axioms of connection

41

002 - The elements of geometry and the five groups of axioms

42

001 - Preface Contents and Introduction