Plane Geometry. Non-defined terms, Definitions, Axioms. Basic theorems for triangles, quadrilaterals, circles, polygons. Geometric loci, geometric constructions, using the analytic-synthetic heuristics. Surface area, regular polygons, Archimedes’ Axioms, circle measuring.
Solid Geometry. Space Axioms. Parallel planes, orthogonality, Theorem of the three perpendiculars. Geometric constructions in space using the analytic-synthetic heuristics. Solids, the Platonic Solids, the sphere. Surface area and volumes of solids.

Topics of History and Didactics are discussed for every subject.