CONTENTS Introduction................................................................................................................................................. 5 PART I 1. Axioms of Boolean algebra................................................................................................................. 6 2. Half-planes and their axioms.............................................................................................................. 7 3. The line.................................................................................................................................................... 8 4. Properties of the net $S_3$................................................................................................................. 10 5. Properties of the net $S_4$................................................................................................................. 12 6. Pseudopoints......................................................................................................................................... 15 7. The ordering of pseudopoints............................................................................................................. 18 8. The points............................................................................................................................................... 20 9. Continuity axiom..................................................................................................................................... 22 PART II 1. Axioms..................................................................................................................................................... 26 2. Definitions and corollaries................................................................................................................... 27 3. Convex of a set....................................................................................................................................... 28 4. Properties of relations of betweenness and of being parallel...................................................... 29 5. Hodograph.............................................................................................................................................. 33 6. Jaśkowski's theorem............................................................................................................................ 37 Inferences.................................................................................................................................................... 42