First-Order Axiom Systems ${\mathcal{E}}_d$ and ${\mathcal{E}}_{da}$ Extending Tarski's ${\mathcal{E}}_2$ with Distance and Angle Function Symbols for Quantitative Euclidean Geometry

Hongyu Guo

Tarski's first-order axiom system ${\mathcal{E}}_2$ for Euclidean geometry is notable for its completeness and decidability. However, the Pythagorean theorem -- either in its moder…