Euclid Book 1
Relationships between and constructions of angles, lines, triangles, parallelograms and area
Last updated on: 2021-08-06.
Under Development
A collection of classical geometry in computable formats along with code and diagrams.
Computable Euclid
Euclid Book 2
Facts about the equality of rectangles and squares, sometimes referred to as geometric algebra
Euclid Book 3
Facts about circles and their center points, segments, inscribed angles, tangents and chords
Euclid Book 4
Constructing the incircle and circumcircle of triangles and regular polygons with 4, 5 and 6 sides
Euclid Book 5
Facts about proportions, magnitudes and ratios and how they can be combined and constructed
Euclid Book 6
Applications of proportions to plane geometry, including similarity and the construction of similar figures
Euclid Book 13
Constructions of the Platonic solids inscribed in a sphere and the ratios between their edges and radii
Euclid's Elements
A complete listing of constructions and theorems from Euclid’s Books 1 - 6 and 13
MathWorld
Geometric theorems and concepts that have corresponding entries on the Wolfram MathWorld site
Constructions
Step-by-step instructions for drawing a specified geometric figure using a straight edge and compass
Theorems
Propositions that are referred to as theorems as opposed to constructions
Geometric Algebra
Theorems which relate to equality, proportions and ratios between geometric figures
Lines
Construction and segmentation of lines and properties related to their intersections and parallels
Angles
Relationships between angles and constructed angles such as their equality, sums and type: obtuse, acute or right
Triangles
Properties of equilateral, isosceles, right and general triangles and definitions of similarity and congruence
Quadrilaterals
Similarity, congruence and ratios between quadrilaterals, parallelograms, squares and their areas
Polygons
Definition of similar polygons, ratios between their sides and area and properties of regular polygons
Circles
Theorems about inscribed angles, chords and tangents of circles and constructions of incircles and circumcircles
