Geometric Constructions: Classical and Projective 1

What does it mean to construct a geometric object exactly? Beginning with Euclid's tools and the logic of permitted operations, this volume develops a clear, visual account of classical construction. It follows the algebra hidden inside diagrams, explains the three ancient impossible problems, and shows how inversion, compass-only methods, projective geometry, complete quadrilaterals, and harmonic conjugates reveal the structure of exact construction.The book treats geometry as a disciplined process rather than a collection of tricks. Each construction is tied to its initial data, legal operations, invariants, and limits. Along the way, readers meet the Mohr-Mascheroni theorem, the power of inversion, and the projective obstructions that make a straightedge alone fundamentally different from a straightedge-and-compass system.Written for mathematically curious readers, students, teachers, and builders of formal or computational systems, Volume I connects synthetic geometry with algebraic reasoning while keeping the figures and construction history visible.