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

SectionTitleReaderNotesListen UrlStatus
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