## Euclid Book 1

Relationships between and constructions of angles, lines, triangles, parallelograms and area

Under Development

Relationships between and constructions of angles, lines, triangles, parallelograms and area

Facts about the equality of rectangles and squares, sometimes referred to as geometric algebra

Facts about circles and their center points, segments, inscribed angles, tangents and chords

Constructing the incircle and circumcircle of triangles and regular polygons with 4, 5 and 6 sides

Facts about proportions, magnitudes and ratios and how they can be combined and constructed

Applications of proportions to plane geometry, including similarity and the construction of similar figures

Constructions of the Platonic solids inscribed in a sphere and the ratios between their edges and radii

A complete listing of constructions and theorems from Euclid’s Books 1 - 6 and 13

Geometric theorems and concepts that have corresponding entries on the Wolfram MathWorld site

Step-by-step instructions for drawing a specified geometric figure using a straight edge and compass

Propositions that are referred to as theorems as opposed to constructions

Theorems which relate to equality, proportions and ratios between geometric figures

Construction and segmentation of lines and properties related to their intersections and parallels

Relationships between angles and constructed angles such as their equality, sums and type: obtuse, acute or right

Properties of equilateral, isosceles, right and general triangles and definitions of similarity and congruence

Similarity, congruence and ratios between quadrilaterals, parallelograms, squares and their areas

Definition of similar polygons, ratios between their sides and area and properties of regular polygons

Theorems about inscribed angles, chords and tangents of circles and constructions of incircles and circumcircles