Explore classical theorems and new results in universal hyperbolic geometry in this 42-minute video lecture. Delve into Menelaus' and Ceva's theorems, which relate to triangles and ratios of distances or quadrances. Discover the Triangle proportions theorem and the Alternate spreads theorem. Learn about the dual versions of Menelaus' and Ceva's theorems. Follow along as the instructor proves Ceva's theorem and presents its dual form. Gain insights into the connections between trigonometry and these geometric principles throughout the lecture.