Free

# Euclid's Elements Redux

By Daniel Callahan
Free
Book Description

"Euclid's 'Elements' Redux" is an open textbook on mathematical logic and geometry based on Euclid's "Elements" for use in grades 7-12 and in undergraduate college courses on proof writing. The current edition is based on John Casey's "The First Six Books of Euclid".

Many problem solvers throughout history wrestled with Euclid as part of their early education including Copernicus, Kepler, Galileo, Sir Isaac Newton, Abraham Lincoln, Bertrand Russell, and Albert Einstein. This edition is part of an effort to ensure that tomorrow's great thinkers will have that same privilege.

Online version and links to print at the book's website.

• Part 1. Introduction
• 1.1. Contributors & Acknowledgments
• 1.2. Dedication
• Chapter 2. About Euclid's ``Elements''
• 2.1. History
• 2.2. Influence
• 2.3. Outline of Elements
• 2.4. Euclid's method and style of presentation
• Chapter 3. Open Textbooks
• 3.1. Usage Rights
• 3.3. Affordability
• 3.4. Milestones
• 3.5. Instruction
• 3.6. Authorship
• 3.7. Projects
• Part 2. The ``Elements''
• Chapter 1. Angles, Parallel Lines, Parallelograms
• 1.1. Definitions
• 1.2. Postulates
• 1.3. Axioms
• 1.4. Explanation of Terms
• 1.5. Propositions from Book I: 1-26
• 1.6. Propositions from Book I: 27-48
• Chapter 2. Rectangles
• 2.1. Definitions
• 2.2. Axioms
• 2.3. Propositions from Book II
• Chapter 3. Circles
• 3.1. Definitions
• 3.2. Propositions from Book III
• Chapter 4. Inscription and Circumscription
• 4.1. Definitions
• 4.2. Propositions from Book IV
• Chapter 5. Theory of Proportions
• 5.1. Definitions
• 5.2. Propositions from Book V
• Chapter 6. Applications of Proportions
• 6.1. Definitions
• 6.2. Propositions from Book VI
• Chapter 7. Infinite Primes
• 7.1. Definitions
• 7.2. The Proposition
• Chapter 8. Planes, coplanar lines, and solid angles
• 8.1. Definitions
• 8.2. Propositions from Book XI: 1-21
• Part 3. Student Answer Key
• Chapter 1. Solutions: Angles, Parallel Lines, Parallelograms
• Chapter 2. Solutions: Rectangles
• Chapter 3. Solutions: Circles
• Chapter 4. Solutions: Inscription & Circumscription
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