The foundations of geometry. (Q5921993)

I Philosophical preliminaries. II Projective geometry and Desargues' theorem (axioms; a finite geometry; Desargues' theorem; duality; the fourth harmonic point; a harmonic sequence and Fano's axiom). III Projective geometry and Pappus' theorem (related ranges of points; the reduction of a projectivity to two perspectivities; Pappus' theorem; the fundamental theorem on projectivities; conics). IV Affine and Euclidean geometry. V Axioms of Euclidean geometry. Ideal elements. VI Numbers (integral, rational, real and complex numbers; rings and fields; finite fields). VII Coordinate systems. VIII Order and continuity (ordered fields; order in projective, affine and Euclidean geometry; axioms of order and of continuity; von Staudt's continuity proof of the fundamental theorem; Desargues' theorem in the plane; consistency and categoricamess). IX Correspondences and imaginary elements in geometry (projectivities; involutions; collineations; correlations).