Completed chapters are marked in this color.
Assigned chapters are marked in this color.
42 of 42 (100%) sections assigned
42 of 42 (100%) sections completed
This project has a dedicated proof-listener who will listen to all sections: Rapunzelina
Section | Title | Reader | Notes | Listen Url | Status |
---|---|---|---|---|---|
0 | Preface, Contents, and Introduction | jamnitzer | PL OK | ||
1 | The elements of geometry and the five groups of axioms | jamnitzer | PL OK | ||
2 | Group I: Axioms of connection | jamnitzer | PL OK | ||
3 | Group II: Axioms of Order | jamnitzer | PL OK | ||
4 | Consequences of the axioms of connection and order | jamnitzer | PL OK | ||
5 | Group III: Axioms of Parallels (Euclid's axiom) | jamnitzer | PL OK | ||
6 | Group IV: Axioms of congruence | jamnitzer | PL OK | ||
7 | Consequences of the axioms of congruence | jamnitzer | PL OK | ||
8 | Group V: Axiom of Continuity (Archimedes's axiom) | jamnitzer | PL OK | ||
9 | Compatibility of the axioms | jamnitzer | PL OK | ||
10 | Independence of the axioms of parallels. Non-euclidean geometry | jamnitzer | PL OK | ||
11 | Independence of the axioms of congruence | jamnitzer | PL OK | ||
12 | Independence of the axiom of continuity. Non-archimedean geometry | jamnitzer | PL OK | ||
13 | Complex number-systems | jamnitzer | PL OK | ||
14 | Demonstrations of Pascal's theorem | jamnitzer | PL OK | ||
15 | An algebra of segments, based upon Pascal's theorem | jamnitzer | PL OK | ||
16 | Proportion and the theorems of similitude | jamnitzer | PL OK | ||
17 | Equations of straight lines and of planes | jamnitzer | PL OK | ||
18 | Equal area and equal content of polygons | jamnitzer | PL OK | ||
19 | Parallelograms and triangles having equal bases and equal altitudes | jamnitzer | PL OK | ||
20 | The measure of area of triangles and polygons | jamnitzer | PL OK | ||
21 | Equality of content and the measure of area | jamnitzer | PL OK | ||
22 | Desargues's theorem and its demonstration for plane geometry by aid of the axiom of congruence | jamnitzer | PL OK | ||
23 | The impossibility of demonstrating Desargues's theorem for the plane with the help of the axioms of congruence | jamnitzer | PL OK | ||
24 | Introduction to the algebra of segments based upon the Desargues's theorme | jamnitzer | PL OK | ||
25 | The commutative and associative law of addition for our new algebra of segments | jamnitzer | PL OK | ||
26 | The associative law of multiplication and the two distributive laws for the new algebra of segments | jamnitzer | PL OK | ||
27 | Equation of straight line, based upon the new algebra of segments | jamnitzer | PL OK | ||
28 | The totality of segments, regarded as a complex number system | jamnitzer | PL OK | ||
29 | Construction of a geometry of space by aid of a desarguesian number system | jamnitzer | PL OK | ||
30 | Significance of Desargues's theorem | jamnitzer | PL OK | ||
31 | Two theorems concerning the possibility of proving Pascal's theorem | jamnitzer | PL OK | ||
32 | The commutative law of multiplication for an archimedean number system | jamnitzer | PL OK | ||
33 | The commutative law of multiplication for a non-archimedean number system | jamnitzer | PL OK | ||
34 | Proof of the two propositions concerning Pascal's theorem. Non-pascalian geometry | jamnitzer | PL OK | ||
35 | The demonstation, by means of the theorems of Pascal and Desargues | jamnitzer | PL OK | ||
36 | Analytic representation of the co-ordinates of points which can be so constructed | jamnitzer | PL OK | ||
37 | Geometrical constructions by means of a straight-edge and a transferer of segments | jamnitzer | PL OK | ||
38 | The representation of algebraic numbers and of integral rational functions as sums of squares | jamnitzer | PL OK | ||
39 | Criterion for the possibility of a geometrical construction by means of a straight-edge and a transferer of segments | jamnitzer | PL OK | ||
40 | Conclusion | jamnitzer | PL OK | ||
41 | Appendix | jamnitzer | PL OK |