This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Hermann & Cie, Paris, the onset of war delayed its release, with only proofs left as a record. The RAND Corporation's interest in 1948 revived the project, resulting in a monograph focused on the systematic development of a decision method for elementary algebra and geometry, emphasizing its practical potential in creating a decision-making machine. Under the editorial guidance of Professor J.C.C. McKinsey, this work was refined with a new draft, clarifying key theoretical aspects and introducing simplifications to the development process. The current edition reproduces RAND's publication with minor corrections, updated references, and supplementary notes that expand upon original theories, including fresh bibliographical insights. This title was originally published in 1951. This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Herma