Properties of Planes According to Euclidean Geometry. In any dimension planes are determined by the following: Presence of three non-collinear points (points that do not lie on the same line) A-line and a point that does not lie on that line. Two lines that are distinct but intersect each other at a …

The first chapter presents the five Euclid’s postulates of plane geometry. The other chapters are organized in groups of subjects: the line, angles, triangles, quadrilaterals, simili-tude, circle, and elements of space geometry. A last chapter introduces strategies in calculating surface areas and vol-umes of non-simple objects.

The most advanced part of plane Euclidean geometry is the theory of the conic sections (the ellipse, the parabola, and the hyperbola). Much as the Elements displaced all other introductions to geometry, the Conics of Apollonius of Perga (c. 240–190 bce ), known by his contemporaries as “the Great Geometer,” was for many centuries the definitive treatise on the subject.

The Axioms of Euclidean Plane Geometry. For well over two thousand years, people had believed that only one geometry was possible, and they had accepted the idea that this geometry described reality. One of the greatest Greek achievements was setting up rules for plane geometry. This system consisted of a collection of undefined terms like ...

Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce). In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools.