The First Six Books of the Elements of Euclid

Euclid, John Casey

The First Six Books of the Elements of Euclid is a foundational mathematical text that has shaped the study of geometry for over two millennia. Originally written by the ancient Greek mathematician Euclid around 300 BCE, this work presents the essential principles of plane geometry in a logical and systematic manner. The book is divided into six sections, each building upon the previous, and covers topics such as the properties of geometric figures, the nature of angles, the relationships between lines and circles, and the theory of proportion. This edition, based on the classic translation and revision by Oliver Byrne, is notable for its innovative use of color and diagrams to illustrate Euclid's propositions and proofs, making the abstract concepts more accessible and visually engaging. Byrne's approach, first published in 1847, was revolutionary for its time and remains a celebrated example of educational design. Within these six books, readers will find the definitions, postulates, and common notions that form the basis of Euclidean geometry, followed by a series of propositions—each accompanied by a logical proof. The text begins with the construction of basic geometric shapes and progresses to more complex theorems, such as the Pythagorean theorem and the properties of similar triangles. Euclid's methodical reasoning and clear structure have made The Elements a model of deductive logic and mathematical rigor. The First Six Books of the Elements of Euclid is not only a cornerstone of mathematical literature but also a testament to the enduring power of logical thought. It has influenced countless mathematicians, scientists, and philosophers throughout history and continues to be studied and admired for its clarity, precision, and beauty. This edition, available through Project Gutenberg, offers modern readers the opportunity to explore one of the greatest works of classical mathematics in a format that honors both its intellectual and visual legacy.

Table of contents

• THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID, AND PROPOSITIONS I.-XXI. OF BOOK XI., AND AN APPENDIX ON THE CYLINDER, SPHERE, CONE, Etc. WITH COPIOUS ANNOTATIONS AND NUMEROUS EXERCISES.
• Contents
• INTRODUCTION.
• 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. THEORY OF PROPORTION
• BOOK VI. APPLICATION OF THE THEORY OF PROPORTION
• BOOK XI. THEORY OF PLANES, COPLANAR LINES, AND SOLID ANGLES