This lecture covers the principles of elliptical geometry, focusing on the construction of elliptical arcs and conic sections. It explores the harmonious properties of tangents, diameters, and curves, as well as the universal methods for solving geometric constructions. The instructor delves into the historical context, discussing the contributions of mathematicians like Desargues and Bosse in developing geometric projective techniques. Special attention is given to the design and construction of the La Hire Pavilion, showcasing the application of geometric concepts in architectural modeling and stonemasonry.