Euclidean Geometry: Operations and Constructions

This lecture explores the fundamental operations and constructions in Euclidean geometry, focusing on the interpretation of geometry through algebra. It covers the basic operations of addition, subtraction, multiplication, and division of segments, as well as the construction of figures using a ruler and compass. The lecture also delves into the concept of constructible numbers and the relationship between geometry and algebra, as pioneered by Descartes. Additionally, it discusses the comparison of triangles and the concept of proportionality. The lecture concludes with an examination of the division of segments and the construction of angles, providing a comprehensive overview of Euclidean geometry.