Section: Book 02: Fundamentals of Geometric Algebra

This chapter proves a number of propositions which demonstrate elementary algebraic statements that are more familiar to us in the form of equations. Algebra as we know it had not been developed when Euclid wrote "The Elements". Hence, the results are more of historical importance than practical use except when they appear in subsequent proofs.

The following table lists results from this book which are also known in modern mathematics, but which were proven by Euclid purely geometrically about 2500 years ago:

Euclid's Elements Corresponding Contemporary Results
Prop 2.01 distributivity law for real numbers.
Prop 2.04, Prop 2.05, and Prop 2.07 binomial theorem and other binomial formulae
Prop 2.12 and Prop 2.13 law of cosines

Moreover, this book contains the following compass and ruler constructions:

  1. Subsection: Definitions from Book 2
  2. Subsection: Propositions from Book 2

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"