Introduction¶
Book I¶
Fundamentals of Plane Geometry Involving Straight-Lines¶
Theory of angles, triangles, parallel lines, and parallelograms.
Book 2¶
Fundamentals of Geometric Algebra¶
Theory of Rectangles
Book 3¶
Fundamentals of Plane Geometry Involving Circles¶
Theory of the Circle
Book 4¶
Construction of Rectilinear Figures In and Around Circles¶
Inscription and circumscription of triangles and of regular polygons in and about circles
Book 5¶
Proportion¶
Theory of Proportion
> The theory of proportion set out in this book is generally attributed to Eudoxus of Cnidus. The novel feature of this theory is its ability to deal with irrational magnitudes, which had hitherto been a major stumbling block for Greek mathematicians. Throughout the footnotes in this book, α, β, γ, etc., denote general (possibly irrational) magnitudes, whereas m, n, l, etc., denote positive integers > - Heiberg
Book 6¶
Similar Figures¶
Application of the theory of proportion
Book 7¶
Elementary Number Theory¶
> The propositions contained in Books 7–9 are generally attributed to the school of Pythagoras. > - Heiberg
Book 8¶
Continued Proportion¶
Book 9¶
Applications of Number Theory¶
Book 10¶
Incommensurable Magnitudes¶
> The theory of incommensurable magntidues set out in this book is generally attributed to Theaetetus of Athens. In the footnotes throughout this book, k, k ′ , etc. stand for distinct ratios of positive integers. > - Heiberg
Book 11¶
Elementary Stereometry¶
Theory of planes, coplanar lines, and solid angles
Book 12¶
Proportional Stereometry¶
> The novel feature of this book is the use of the so-called method of exhaustion (see Prop. 10.1), a precursor to integration which is generally attributed to Eudoxus of Cnidus. > - Heiberg
Book 13¶
The Platonic Solids¶
> The five regular solids—the cube, tetrahedron (i.e., pyramid), octahedron, icosahedron, and dodecahedron—were problably discovered by the school of Pythagoras. They are generally termed “Platonic” solids because they feature prominently in Plato’s famous dialogue Timaeus. Many of the theorems contained in this book—particularly those which pertain to the last two solids—are ascribed to Theaetetus of Athens. > - Heiberg