Franz Rothe’s books delve deeply into the mathematical framework of Pythagorean planes, geometry, algebra, trigonometry, Pythagorean, mathematical concepts, and formulas exploring their geometric, numeric, formation, and algebraic properties. It systematically addresses the congruence of segments, angles, and triangles, as well as the implications of these properties in the context of Hilbert's axioms.

It defines congruence regarding distances and provides proofs for the equivalence relations and transfer properties of segments and angles. It introduces rigid motions and their role in preserving congruence and orientation, culminating in the evidence that sufficient rigid motions exist in geometry, trigonometry, algebra, and Pythagorean planes. The equivalence of mathematical fields with lines, intersections, and properties is established, providing a bridge between algebraic, formulas, and geometric perspectives.

Then, it concludes with a derivation of different mathematical formulas for the vast area of choices of mathematical objects showcasing the practical implications of the theoretical framework. The extends of the book are ambitious, aiming to establish a solid foundation for understanding Pythagorean planes as a model of geometry that satisfies both Hilbert's axioms, renowned basic math formulas, and Euclidean properties.

However, the dense mathematical notation and technical language may pose challenges for readers who are not already familiar with the subject matter. While the book is aimed at an audience with a strong background in geometry, trigonometry, formulas, and algebra, additional explanations or examples could make the material more accessible.

In summary, the book assumes a high level of familiarity with advanced geometry, algebra, trigonometry, and mathematical techniques. While this is appropriate for a specialized audience, it limits the accessibility of the mathematical material to a broader readership.