Heath¶
Books
Book I
Theory of angles, triangles, parallel lines, and parallelograms.
Book II
Theory of Rectangles
Book III
Theory of the Circle
Book IV
Inscription and circumscription of triangles and of regular polygons in and about circles
Book V
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 VI
Application of the theory of proportion
Book VII
The propositions contained in Books 7–9 are generally attributed to the school of Pythagoras. > - Heiberg
Book X
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 XI
Theory of planes, coplanar lines, and solid angles
Book XII
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 XIII
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