A Course in Old and New Geometry II: Basic Euclidean Geometry provides a clear and structured explanation of the logical foundations of mathematics, starting with propositional, formulas, theories, and predicate logic. It introduces key concepts such as statements, negation, equivalence, and implication with precision, supported by truth tables and logical equivalences. It is particularly valuable for readers seeking a foundational understanding of mathematical logic.

The book is a valuable resource for understanding how these numbers and formulas impact mathematics. It successfully conveys the rigor and depth of known mathematicians highlighting its historical significance and philosophical underpinnings. The critical analysis of one's work is the limitations and the discussion of subsequent advancements demonstrates the ongoing relevance of ideas in mathematical research. It remains a commendable effort to encapsulate the essence of contributions to logic, geometry, and the formalist program.

Then, it does not merely summarize mathematical contributions but also critically examines their limitations and areas for further development. For example, it highlights the absence of axioms and theorems related to circles in Hilbert's foundations and discusses subsequent advancements by researchers like Greenberg and Hartshorne. This critical perspective adds depth to the review.

Further, it assesses models in mathematics and provides an insightful distinction between the use of models in natural sciences and mathematics. It emphasizes the dual-level thinking required in mathematical modeling and the importance of relative consistency proofs. This discussion is particularly relevant for understanding the abstract nature of modern mathematics.

Over, A Course in Old and New Geometry II: Basic Euclidean Geometry is an insightful exploration of mathematics. It is best suited for readers with a strong mathematical background who are interested in the theoretical and philosophical aspects of mathematics. The book could reach a wider audience and further enhance its impact.