Explore the fundamental laws of rational elliptic and spherical trigonometry in this 41-minute lecture. Delve into the proofs of the Spread law, Cross law, and Dual cross law for elliptic triangles using linear algebra concepts like dot products and 3x3 matrices. Discover how these formulas relate to classical theorems such as Thales', Pythagoras', and the Triple Quad Formula in an elliptic or projective setting. Compare the similarities between these results and those in Universal Hyperbolic Geometry, gaining a deeper understanding of the interconnections within geometry and mathematics as a whole.