Explore the fundamental laws of rational trigonometry in a general planar setting with a bilinear form determining quadrance and spread concepts. Delve into a purely algebraic and general approach, free from transcendental functions, real numbers, and infinite computations. Learn how to elegantly derive important mathematical formulas, including Pythagoras' theorem, the Triple Quad Formula, the Cross law, and the Triple Spread Formula. Gain insights into establishing these crucial mathematical principles without relying on traditional trigonometric methods.