Classical Euclidean Geometry

This is a preliminary edition of the first of four volumes of an update to Euclid's Elements using Aristotelian set theory, entitled Classical Euclidean Geometry. This first volume includes the first three books of twelve and contains the first twenty of the twenty-two postulates of classical Euclidean geometry. The construction of the real number system through geometry is the subject of the final volume. The content of these twelve books parallel those of Euclid's first six. Euclid's work on number theory is reserved for a prequel. The purpose of this work is to provide the modern classical educator with a resource by which to introduce the quadrivium to their students.