Archimedes Quadrature of Parabola Prop. 1: Tangent Triangle and Area

This GeoGebra example demonstrates Proposition 1 from Archimedes' Quadrature of the Parabola, illustrating the area relationship between a tangent triangle and the parabolic segment. The core mathematical concepts include tangent properties of parabolas, Archimedes' quadrature principle, and the ratio of areas between triangles and parabolic segments. The construction uses commands such as Point, Line, Parabola, Intersect, Tangent, and Segment to create the parabola, its tangent at a point, and the resulting triangle and quadrilateral. Suitable for high school and college students studying analytic geometry, calculus foundations, or the history of mathematics, this example provides a visual proof of how ancient mathematicians approximated curved areas using geometric methods.