Elementary Operations in Geometry

This lecture covers elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles. It explores the transition from basic to advanced geometry, focusing on the bisecting of angles and segments. The lecture delves into Euclid's Elements, discussing the division of segments and angles by integers, as well as the comparison of similar triangles. It also touches on the concept of proportionality in triangles and the invariance of areas. The presentation concludes with a demonstration of the theorem on the invariance of triangle areas when the vertex moves parallel to the base.