English Title: Restricting Compass-and-Straightedge Constructions — Restricting the Degree of Freedom of Compass and Straightedge? (The Statutory Constraints of Compass-and-Straightedge Constructions and the Absence of the Plane Restriction)

This paper examines the original statutory constraints of compass-and-straightedge construction, tracing the complete historical chain from the ancient Greek tool restrictions proposed by Oenopides, through the philosophical advocacy of Plato, the establishment of postulates in Euclid's Elements, to Wantzel's 1837 field-theoretic proof of the impossibility of angle trisection. The core finding is that none of the statutory constraints of compass-and-straightedge construction — the five construction rules, the five assumptions, the physical description of tools, and Oenopides' original conditions — contains the restriction that "all constructions must be carried out in a single plane." The plane restriction is a retrospective default introduced after the establishment of the Cartesian coordinate system, not an original rule of compass-and-straightedge construction. The consequent implication is that the field-theoretic impossibility verdicts based on the fixed-plane premise (angle trisection, cube duplication, etc.) apply only to the special case of "restricted compass-and-straightedge construction," not to compass-and-straightedge construction per se.